Uptake and 

Transport of 

Radionuclides by 

Stream Sediments

GEOLOGICAL SURVEY PROFESSIONAL PAPER 433-A

Prepared in cooperation with the 

U.S. Atomic Energy Commission
Uptake and 

Transport of 

Radionuclides by 

Stream Sediments

By W. W. SAYRE, H. P. GUY, and A. R. CHAMBERLAIN 

TRANSPORT OF RADIONUCLIDES BY STREAMS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 433-A

Prepared in cooperation with the 

U.S. Atomic Energy Commission

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1963
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington 25, D.C.
CONTENTS

Abstract.

Introduction ______________________________

Disposal of radioactive wastes in streams. 

Radioactivity budget in streams. ________

Characteristics of radioactive wastes which are discharged into streams______________________________

Sources of wastes.__--__--_--_-_-_______________

Nature of wastes.--__-------___-_______________

Properties and types of radionuclides________

Chemical and physical characteristics _________

Turbulent-diffusion theory for open channels___________

Classification of field, boundary, and initial conditions -___________________-___________________::

Flow system containing neither sediment nor 

biota.___________________________________

Flow system containing sediment but not biotaFlow system containing both sediment and 

biota.___________________________________

Radioactive decay._________________________

Turbulent-diffusion theories._____________________

Some theoretical solutions now available____--____

Experiments associated with theory.______________

Page 

Al

1

1

2

2

3

3

3

4

6

7

7

9

10

	Page

Sorption of radiocontaminants by stream sediments.-___ All

Sorption theories_______________________________ 11

Literature review Sorption of radionuclides _______ 13

Factors determining extent of sorption____________ 15

Sediment characteristics_____________________ 15

Characteristics of waste effluent and stream

water.---------------------------------- 15

Sediment transport as affected by drainage area and

stream characteristics _____________________________ 17

Drainage-area characteristics_____________________ 17

General considerations of sediment transport_______ 18

Geometrical characteristics of streams_______-_-_-- 19

Particle-size gradation___.______________---_--_ 21

Channel controls______________________________ 23

Criteria for identifying potentially hazardous streams. _ _ 24

Uptake by sediments__________________________ 25

Concentration and load of suspended sediment _____ 25

Conditions conducive to sediment deposition. ______ 25

Rate of buildup of radioactivity________---__-__-- 26

Classification of streams in the United States according

to hazard potential--.----------.------------------ 26

Conclusions._________________________---___--_----- 27

Glossary of terms.. __.___________________--_-------- 30

References. _ _________-_-------_-------------------- 33

Index _________-___---____------_-_-------_-------- 35

ILLUSTRATIONS

Page

FIGURE 1. Variation of specific surface of spherical sediment particles with particle diameter.________________----------- 16

2. Distribution of sediment at a vertical in the Missouri River at Kansas City, Mo _________________----_-- 18

3. Average hydraulic geometry of river channels expressed by relations of width, depth, velocity, suspended-sediment

load, roughness, and slope to discharge at a station and downstream___________---_---------------------- 20

4. Suspended-sediment and bed-material particle size gradation for three typical alluvial streams.-.-------------- 22

5. Relation of sedimentation to channel characteristics through backwater reach of Garrison Reservoir, N. Dak.,

July 7-8, 1954__________.________________....._______._____________---------------_---------------- 24

6. Concentration of suspended sediment in streams east of Mississippi River_____________-____-__-_------------ 28

7. A measure of hazard potential for stream deposition of sediment containing radioactive wastes__________-__--- 29

TABLES

Page

TABLE 1. Radionuclides in reactor-cooling water._______________________________-___---_-------------------------- 5

2. Important properties of some clay minerals._____________________________---_---_------------------------ 14

3. Comparative monthly water and sediment discharges for streams in areas with differing climate______-___--_--- 19

4. Estimated sediment-trap efficiency, in percent, of various types of structures for channel and storage control--__ 23

in

TRANSPORT OF RADIONUCLIDES BY STREAMS 

UPTAKE AND TRANSPORT OF RADIONUCLIDES BY STREAM SEDIMENTS

By W. W. SAYRE, H. P. GUY, and A. R. CHAMBERLAIN

ABSTRACT

The factors involved and the present status of research concerning disposal of radioactive wastes in natural streams are 

reviewed with respect to (1) waste characteristics, (2) dispersion 

theory, (3) sorption by sediments, and (4) sediment transport. 

Some criteria for identifying potentially hazardous streams and 

areas where knowledge is deficient are discussed.

Evidence indicates that sorption of radiocontaminants by 

stream sediments is the rule rather than the exception. The 

extent of sorption is dependent upon a large number of variables: 

the nature of the sediment and the substance being sorbed; 

the available surface area; the concentration and types of solute 

in solution; time; and, to a lesser extent, temperature.

The transport of sorbed radioactive components by fluvial 

sediments depends on factors such as the types and amounts ^of 

sediment supplied by the drainage area, channel and flow characteristics, the time distribution of streamflow, and channel 

controls.

Pool and riffle-type streams, characterized by wide variations 

in discharge and containing large amounts of fine-grained sediments, appear to be potentially the most dangerous type of 

stream with respect to the development of hazards arising from 

radiocontaminated sediments.

Present knowledge is not adequate for the purpose of predicting 

the ultimate distribution of radioactive wastes in streams, 

particularly as affected by fluvial sediments. Considerable 

research and study will by required in all the subject areas of 

this report before this situation can be improved materially.

Certain deficiencies in knowledge and theory stand out for 

example, there is a dearth of information in the literature on 

the quantities and physicochemical properties of low-level 

liquid wastes.

Current theoretical, laboratory, and field knowledge of the 

mechanics of turbulent diffusion involving instances of a confined channel, net uptake by sediment, and net uptake by biota 

is entirely inadequate.

The effect of some of the variables associated with sorption 

phenomena is not well understood. This is particularly so 

in complex sorption systems which include competing solutes, 

mixed sediments, and chemical additives such as detergents and 

electrolytes.

Despite notable advances, some of the factors involved in 

sediment-transport phenomena remain unresolved, and much 

of the associated theory is still in a stage of partial development.

INTRODUCTION

Radioactive wastes present a unique disposal problem 

(Warde and McVay, 1955) because unlike other industrial wastes they cannot be disposed of by burning, 

evaporation, or filtering, nor can they be rendered

biologically harmless by chemical treatment. Radioactivity is not detectable by any of man's five senses. 

In general, radioactive pollutants on a weight basis 

are many thousand times (Thomas, Terrill and Gilmore, 

1959) and in some cases more than a million times 

(Jensen, Eldridge, Everts and Clare, 1957) as dangerous to the health of man as are nonradioactive 

pollutants.

Since the early days of nuclear energy development, 

the U.S. Geological Survey has cooperated with the 

Atomic Energy Commission on certain technical 

problems relating to management of radioactive wastes. 

Considerations arising from the geology and hydrology 

of waste-disposal sites have been an important area of 

cooperation. This study was made cooperatively by 

the Geological Survey and the Atomic Energy Commission with staff assistance from Colorado State 

University. The purpose of the study was to determine the factors involved and the present status of 

research concerning disposal of radioactive wastes in 

natural streams.

DISPOSAL OF RADIOACTIVE WASTES IN STREAMS 

Approximately 95 percent of the short-lived low 

level liquid radioactive wastes are discharged into 

surface streams (Joseph, 1955). The radioactivity 

level of these wastes is low, but the total volume is 

large. At the Hanford installation, for example, an 

average of more than 20 million gpd of radioactive 

wastes are discharged. Since 1944, more than 2 

million curies of radioactive materials have been 

released into the environment at Hanford (U.S. Atomic 

Energy Commission, 1957).

Radioactivity surveys on the Columbia (Robeck, 

Henderson and Palange, 1954) and Tennessee (Garner 

and Kochtitzky, 1956) River systems have indicated 

that contamination of these waterways has not yet 

approached the danger level. There is real cause for 

concern in the future, however, when it is considered 

that the nation is just on the threshold of the nuclear 

age. Present estimates (U.S. Atomic Energy Commission, 1957) predict that the nuclear power plant capacity 

in the United States will increase by a factor of about

Al
A2 TRANSPORT OF RADIONUCLIDES BY STREAMS

fivefold every 5 years in the decades preceding 1980. 

Considered economically, disposal of wastes by discharge into surface streams is the most attractive 

method. It is only natural that the growing nuclear 

industry will use streams as a disposal medium to the 

maximum extent permissible.

Considering the ever-intensifying domestic, industrial 

and agricultural use of the nation's water resources 

together with the expanding nuclear industry, and the 

probable use of streams for waste disposal, it becomes 

apparent that the chances for harmful exposure to 

radiation resulting from accident or error are rapidly 

multiplied.

RADIOACTIVITY BUDGET IN STREAMS

In order that the chance for error or miscalculation 

be minimized, it is essential that the working of the dispersal mechanisms of streams with respect to radioactive wastes be thoroughly understood. In a simplified qualitative form, the problem for a particular 

radionuclide may be illustrated in terms of a radioactivity budget.

(1-D

in which

R is the radioactivity in curies of waste discharged into

the stream at time t=0, 

rn is the background radioactivity in the stream due to

natural causes and fallout at time t=0, 

rw is the radioactivity carried in solution by the water at

time t, 

r, is the radioactivity sorbed by stream sediments at

time t, 

r 0 is the xadioactivity taken up by living organisms and

entering the ecological cycle, at time t, 

rd is the radioactivity discharged from the watershed 

that is,

Jor

where r(f) is the radioactivity discharged from the 

watershed as a function of time, and 

ex * is a radioactive decay factor dependent upon time t 

and the radioactive-decay constant X which depends 

on the nuclide.

The radioactivity budget illustrates the complexity 

of the problem by suggesting the variety of physical, 

chemical, and biological laws which are operating simultaneously on the system. The problem is further 

complicated by the fact that the radioactivity in the 

stream is transported at different rates which vary 

according to both the nature of the transporting media, 

and the stream conditions. In addition, exchange of 

radioactivity occurs among the various transporting 

media. The extent of exchange depends on complex 

chemical relationships involving the characteristics of 

the radioactive waste effluent, quality of the stream

water, particle size, concentration and mineralogic content of the stream sediments, and the nature of the 

aquatic biota.

At present, the quantities of radioactivity released 

into stream waters are governed by the maximum permissible concentrations (MFC), usually with a safety 

factor of about 10, of radioisotopes in drinking water 

recommended by the National Committee on Radiation 

Protection (U.S. National Bureau of Standards 1953, 

1955, 1959). The MFC value for each radionuclide 

is based on its particular radiological and chemical 

properties with respect to their biological hazard potential to man. The MFC values do not take into 

account the various mechanisms in the stream system 

which are at work taking up and concentrating radioactivity. In some cases the concentration of radioactivity in organisms and on sediment particles exceeds 

the concentration of radioactivity in the water by 

several orders of magnitude (Robeck, Henderson and 

Palange, 1954).

Present data and knowledge are entirely inadequate 

for evaluating the radioactivity budget in any given 

stream system. The deficiency is even greater with 

respect to use of the budget concept as a means of predicting the behavior of radioactive wastes in streams. 

Knowledge is particularly lacking with respect to the 

uptake processes and the initial dispersion of radioactivity in streams by turbulent diffusion.

CHARACTERISTICS OF RADIOACTIVE WASTES WHICH 

ARE DISCHARGED INTO STREAMS

Perhaps the outstanding general characteristic of 

low-level liquid wastes is the extremely wide variation 

in their chemical and physical properties (Blomeke, 

1958). It is safe to say that as the size and complexity 

of the nuclear industries increase, the wastes will increase both in quantity and diversity.

Low-level wastes are arbitrarily defined as having a 

radiation intensity at the emitting surface of less than 

50 milliroentgens per hour as opposed to high-level 

wastes which have an intensity of more than 2 roentgens per hour (Joseph, 1955). The activity of low-level 

wastes may be as much as 104 times the long-term exposure limit considered permissible for humans (Gorman, 1955).

Although the specific activity of the low-level wastes 

is relatively low in contrast to high-level wastes, considerable total amounts of radioactivity are involved 

owing to the large volumes of waste effluents. At the 

Hanford plant, which is the largest producer of lowlevel wastes, approximately 640 million gallons of waste 

effluent containing about 50,000 curies of radioactive 

materials is discharged into the environment each 

month (U.S. Atomic Energy Commission, 1957). On
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A3

this basis the average specific activity of this waste is 

on the order of 0.02 microcuries per ml (/xc/ml).

SOURCES OF WASTES

Low-level, liquid wastes of the types which are released into streams originate from many kinds of 

sources. By far the greatest source of radioactive 

wastes are the chemical-processing plants where irradiated reactor fuels are processed to reclaim the unburned 

nuclear fuel (Blomeke, 1958). The low-level wastes 

resulting from these operations arise from second- and 

third-cycle operations, fuel dejacketing, chemical and 

analytical laboratories, evaporator condensates, and 

cell- and equipment-decontamination wastes. Another 

large source is the water used in reactor cooling systems. 

Other sources result from the medical and industrial 

use of radioisotopes, various laboratory, laundry and 

decontamination operations, and the processing of 

natural radioactive ores.

Some of the low-level wastes are derived from intermediate and high-level wastes which have undergone 

chemical treatment for removal of some of the more 

dangerous radionuclides. Others have been retained 

in storage for varying periods of time to permit reduction of activity by natural radioactive decay.

With respect to the more hazardous radionuclides, 

it is probable that in the future more problems will 

arise from the combined operations of many small 

enterprises, than from the larger enterprises which are 

able to afford elaborate treatment facilities. Accidental 

releases of the hazardous radionuclides are always a 

possibility.

NATURE OF WASTES

It is impossible to formulate an adequate description 

of the nature of low-level liquid wastes in a few general 

statements because of the wide variety in the composition of the different wastes. As with other industrial 

wastes, the characteristics of atomic wastes may vary 

not only from one installation to another but also to 

some extent with respect to time at any given site. 

The nature of radioactive wastes may be classified, 

however, with respect to criteria such as the properties 

and types of radionuclides, chemical characteristics, 

and significant physical characteristics.

Obviously the factor which sets atomic wastes apart 

from other wastes is radioactivity. A stream has no 

self-purification capacity for radioactive wastes in the 

sense that it does for ordinary organic pollutants 

(Tsivoglou, Harward and Ingram, 1957). Organic 

pollutants undergo biochemical oxidation resulting 

from bacterial attack in a stream, by which process the 

stream rids itself of the pollutant in a short time. No 

comparable process occurs for radioactive pollutants.

There is no known chemical treatment by which

radioactive wastes can be rendered biologically harmless. 

Even though the physical and chemical form of the 

waste may undergo change the radioactivity remains 

unaffected and is reduced only by natural radioactive 

decay which occurs at a definite rate, different for each 

radionuclide.

The apparent concentration of radionuclides in the 

water may be reduced owing to uptake by stream 

sediments and biota. However, this does not represent a reduction in the total amount of radioactivity 

in the stream environment, but rather a transfer from 

one phase of the stream environment to another.

PROPERTIES AND TYPES OF RADIONUdjIDES

The significant properties of radionuclides with 

respect to waste-disposal problems are (1) nuclear, (2) 

biochemical, and (3) chemical.

The important nuclear properties are the rate of 

radioactive decay, the type of radiation, and the energy 

of radiation. Wastes containing radionuclides characterized by a slow rate of decay a long half life if 

continuously discharged into the environment in significant amounts would build up the concentration of 

radioactivity in the environment over a long period of 

time before reaching a condition of equilibrium with 

respect to activity level. The concentration of radioactivity of radionuclides having a rapid decay rate, 

however, would reach a level of steady equilibrium 

rather quickly. Curves illustrating this phenomenon 

are shown by Rodger (1954). Furthermore, radioactivity emanating from long-lived nuclides would 

contaminate the environment lor a long period if a 

large quantity were released accidentally, whereas, the 

radioactivity would decay rapidly where short-lived 

nuclides were involved. After a time interval of 10 

half lives, radioactivity decays to about 0.1 percent of 

the activity level at the beginning of the time interval. 

The half life of radionuclides ranges from fractions of a 

second to more than a million years.

The relative hazards resulting from ingestion of 

radionuclides aside from the quantity and energy level 

of radioactivity depend primarily on biochemical 

considerations. Some of these biochemical considerations are initial body retention, fraction going from 

blood to critical body tissue, radiosensitivity of tissue, 

size and essentiality of critical organ, biological half life, 

and specific ionization and attenuation of energy in 

body tissue (U.S. National Bureau of Standards, 1953).

From a biologist's standpoint, other factors being 

equal, radionuclides with an intermediate decay rate, 

say a half life of 5 to 50 years, are the most hazardous 

when ingested on a weight basis (U.S. National Bureau 

of Standards, 1953). Long lived nuclides must be 

present in relatively larger quantities in order to give
A4 TRANSPORT OF RADIONUCLIDES BY STREAMS

off as much radiation as shorter lived radionuclides 

during a given time interval, say a person's normal 

remaining life span. At the other extreme, radionuclides with very short half lives normally are less 

hazardous unless exposure is maintained by continued 

uptake, since the activity of such radionuclides when 

deposited in the body soon decays to an insignificant 

level.

When taken internally, alpha emitters, owing to their 

high, specific ionization are considered to be about 20 

times as damaging as either beta or gamma emitters 

(U.S. National Bureau of Standards, 1953). However, 

gamma rays, owing to their great penetrating power, 

are considered to be the most hazardous for external 

radiation of the body, excepting the artificially induced 

neutron emitters.

The maximum permissible concentrations for various 

radionuclides as recommended by the U.S. National 

Bureau of Standards (1953, 1955, 1959) have been computed on the basis of relative hazard from nuclear and 

biochemical considerations. It is significant to note 

that as more information on the adverse biological 

effects of radiation has become available, the tendency 

has been to revise downward, in many cases rather 

sharply, the MFC's for most radionuclides. The 

MFC for many of the radionuclides found in radioactive waste solutions are listed in table 1. It is 

recommended (U.S. National Bureau of Standards, 

1959) that the MFC of unidentified radionuclides in 

water not exceed 10 ~7 fj.c/ml.

The chemical properties of radioactive isotopes are 

essentially identical to those of the corresponding 

nonradioactive isotopes having the same atomic 

number. With respect to waste disposal in streams, 

the chemical properties are important in so far as they 

influence sorption by sediments, and uptake by aquatic 

biota. For example, studies on the Columbia River 

(Robeck, Henderson and Palange, 1954) revealed 

concentrations of P32 in the river plankton which were 

as much as 10,000 times the concentration in the water.

Fortunately most of the radionuclides which have 

been identified in the low-level liquid wastes are of the 

less hazardous variety. In table 1 are listed the 

nuclides and some of their properties that have been 

identified in the Columbia River (Robeck and others, 

1954), (Conley, 1954), (Foster and Rostenbach, 1954), 

and in the cooling water of the Low Intensity Test 

Reactor (LITR) at the Oak Ridge National Laboratory 

(Moeller, 1957). These should be fairly typical of 

the radionuclides found in reactor-cooling water.

CHEMICAL, AND PHYSICAL, CHARACTERISTICS

The importance of the chemical and physical characteristics of waste effluents is in their effect on the 

reactions occurring between the radioactive materials

and the stream environment. One example is how the 

chemical constituents of the waste effluent might affect 

the uptake of radioactivity by stream sediments and 

biota. Physical characteristics of the waste effluent 

such as specific gravity, viscosity, surface tension and 

temperature are important in so far as they affect 

dispersion by turbulent diffusion of the wastes throughout the flow cross section. These are areas which 

apparently have received very little systematic study; 

however, some of the known characteristics of low-level 

liquid wastes can be listed, and possible areas of importance suggested.

In general, reactor-cooling waters contain significant 

quantities of corrosion products; used solvents contain 

kerosenes, tributyl phosphates, I2 , and Ru; and solvent 

washes contain NaOH and Na2CO3 (Joseph, 1958). 

Condensates usually consist of very nearly pure water. 

The pH range of low-level liquid wastes is usually 

between 4 and 9.

At Hanford the reactor-cooling water discharged 

into the river consists of treated Columbia River water 

with an approximate dissolved-solids content of 100 

ppm before treatment (Barker, 1959, personal 

communication).

At Knolls Atomic Power Laboratory, Schenectady, 

N.Y., radioactive laboratory wastes and "hot" laundry 

wastes are combined and discharged into the Mohawk 

River. The properties of these wastes vary considerably, and may be acidic at one time and basic at 

another. It has been observed at KAPL, however, 

that differences in temperature between the waste and 

the river water control the mixing far more than do 

the differences in composition (Barker, 1959, personal 

communication).

At the Dresden Nuclear Power Station near Chicago, 

it is proposed that several types of low-level wastes be 

discharged into the river. These include high-purity 

water (1 ppm), medium-purity water (100 ppm), 

laboratory-drain wastes and other corrosive waters, 

and laundry wastes, all of which will be mixed together 

in varying proportions before discharge (Falk, 1958).

Laundry and laboratory wastes are apt to contain 

significant quantities of detergents and water-softening 

agents which may be important with regard to uptake 

characteristics.

Where radionuclides in the waste effluent are accompanied by isotopic carriers, their behavior in the 

stream environment may vary considerably from that 

of the corresponding carrier-free nuclides.

Such information on the chemical and physical 

characteristics of low-level liquid wastes as is available 

should be systematically assembled and analyzed. 

Supplemental information as required to fill in the
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A5

TABLE 1. Radionuclides in reactor-cooling water

Half life: s, seconds; m, minutes; h, hours; d, days; y, years

Mode of decay: K, /if-eleetron capture; IT, isomeric transition

MFC: Maximum permissible concentration, based on hazard resulting from exposure continued over a long period of time. (From U.S. National Bureau of Standards, 1959)

Mode of formation: FF. fission product

[Data from Kinsman, 1957; Moeller, 1957; Oak Ridge Nat. Lab., 1960]

Location

Columbia River _ ______

Oak Ridge LITR.__ _

Radionuclide

As76

Ba140

C06»

Cr"

Cu<«

Mn56

Na24

P32

Si"

Sr»9

Sroo

Ba1*0

Br80

Br«ta

Brs2

Get"

Ce143

Co«°

Cr«

Cu<«

JP18

Fe58

J131

J132

J133

J135

La"0

Mn56

Mo"

Na24

Np238

Pa233

Sbi22

Sr«

Sr82

TC9«m

Te132

Xe131ml

Xei33 + Cs133m

Xei35 +Cs]35m

Y«im

Zn65

Half life

26. 8h

12. 8d

5. 3y

27. 8d

12. 8h

2. 6h

15. Oh

14. 3d

2. 6h

53. Od

28. .Oy

12. 8d

18. Om

4. 6h

35. 9h

32. 5d

33. Oh

5. 3v

27. 8d

12. 8h

1. 9h

45. Id

8. Id

2. 3h

21. Oh

6. 7h

40. Oh

2. 6h

2. 8d

15. Oh

2.3d

27. 4d

2. 8d

9. 7h

2. 7h

6. Oh

3. 2d

4. 8X10-10s

5.3d

9. 2h

50. Om

245. Od

Mode of decay

ft~,y

ft~, y

ft~, y

K, y

K, ft~, ft+, 7

ft~, y

ft , y ft~

ft~,y ft~

ft~

ft~, y

K, ft~, 0+, y

IT 7

ft- y

ft- y

ft- y

ft- y

K,y,

K, ft~, ft+, y

ft+

ft-, y

ft~, y

ft~,y

ft-, y

ft~, y

ft~, y

ft~, y

ft~,y

ft~, y

ft~,y

ft~, y

ft-, K, ft+, 7

ft~, y

ft~, y

IT, 7

ft~, y

IT

ft~,y ft~, y

IT

K, ft+, y

MFC in water G-c/ml)

2X10-4

2X10~4

5X10-4

2X10-2

2X10~3

10~3

3X10~4

2X10-4

2X10~3 10-* io-«

2X10~4

4X10-*

9X10-4

4X10-4

5X10~4

2X10~2

2X10~3

5X10-3

6X10-*

2X10-5

6X10~4

7X10-5

2X10-4

2X10-4

ID"3

4X10-4

3X10~4

10~3 l 10~3

3X10-*

5X10-*

6X10-*

6X10~2

2X10-*

3X10~2

10~3

Primary mode of formation

Induced

FP

Induced

Induced

Induced

Induced

Induced

Induced

Induced

FP

FP

FP

Induced

Induced

Induced

FP

FP

Induced

Induced

Induced

Induced

Induced

FP

FP

FP

FP

FP

Induced

Induced

Induced

Induced

Induced

Induced

FP

FP

Induced

FP

FP

FP

FP

FP

Induced

gaps should be added, and the combined results 

published.

TURBULENT-DIFFUSION THEORY FOR OPEN CHANNELS

Waste, contaminants, or tagged materials when 

introduced into an ambient flow field a natural 

stream, for example may be (1) fixed in place, (2) 

dispersed by molecular diffusion, (3) dispersed by 

diffusion of a submerged jet, (4) dispersed by the process of turbulent diffusion, or (5) subjected to two or 

more of these processes simultaneously for example, 

the simultaneous occurrence of molecular and turbulent 

diffusion is common. In nearly every field situation, 

however, turbulence is by far the most important 

mechanism causing dispersion in streams.

Considering the whole problem of waste dispersal, 

however, dispersion of waste solutions is not the only 

effect produced by turbulent exchange. In sediment644015 O 62 2

carrying streams, for example, sediment particles are 

distributed by turbulence. This is a very important 

consideration when the nature of the contaminant is 

such that it can be sorbed and subsequently released 

from stream sediments.

In view of the roles of turbulent diffusion with respect 

to both waste dispersion and the distribution of contaminated sediments, turbulent diffusion assumes great 

importance in studies concerned with use of natural 

streams as a disposal medium for radioactive materials.

Application of turbulent-diffusion theory to problems 

of waste disposal in alluvial streams, canals, and rivers 

appears to be slight. While hundreds of papers on 

the turbulent diffusion of material into a fluid of 

homogeneous properties are in the literature, the 

number referring to the roles of diffusion and fluvial 

sediments in waste disposal is small. It is gratifying
A6 TRANSPORT OF RADIONUCLIDES BY STREAMS

to note, however, that considerable work is being 

initiated in this field of study.

In this section the field conditions which must be represented by the boundary conditions in an analytical 

treatment will be discussed and classified. Next, a 

summary of diffusion theory will be given, in which 

specific reference will be made whenever the work 

reviewed was in regard to open-channel or closedconduit flow-diffusion problems. The effect of fluvial 

sediments on the concentration of radionuclides in the 

stream will also be introduced. And lastly, some 

experiments reported in the literature will be 

summarized.

Molecular diffusion is neglected herein, though hi 

many field problems it is not correct to neglect it. 

The relative roles of molecular and turbulent diffusion 

is discussed in an excellent review of turbulent diffusion 

by Batchelor and Townsend (1956). An incompressible fluid is assumed.

CLASSIFICATION OF FIELD, BOUNDARY, AND INITIAL 

CONDITIONS

There are very few major field problems such as 

radioactive-waste disposal in alluvial streams where 

large sums of money cannot be saved by considering 

the problem on paper before going into the field. 

Before doing this paper work, however, it is necessary 

to classify the problems to be resolved. This section 

will present a typical classification of field conditions 

which could be directed toward aiding theoretical 

analysis of turbulent diffusion in alluvial channels.

For theoretical purposes the field environment 

which controls the boundary conditions assuming an 

alluvial channel, could be classified in order of increasing 

complexity as follows adding radioactive decay only 

at the end.

FLOW SYSTEM CONTAINING NEITHER SEDIMENT NOR 

BIOTA

This environment may be subdivided, as follows:

1. Channel of infinite width and constant slope with 

steady flow.

2. Channel of fixed finite width and constant slope 

with steady flow.

3. Channel of infinite width and constant slope with 

unsteady flow.

4. Channel of infinite width and variable slope with 

unsteady flow.

5. Finite width of uniform channel with unsteady flow.

6. Finite width of nonuniform channel with unsteady 

flow.

7. Finite width of uniform channel containing curves 

with steady flow.

8. Finite width of uniform channel containing curves 

with unsteady flow.

9. Finite width of nonuniform channel containing 

curves with steady flow.

10. Finite width of nonuniform channel containing 

curves with unsteady flow.

FLOW SYSTEM CONTAINING SEDIMENT BUT NOT BIOTA

The environment for this situation becomes even 

more complex than that described in the previous 

paragraph. Considering the theoretical approach that 

will probably first be applied to this condition the 

continuity equation for mass it seems that the presence of sediment can best be handled by assigning to 

the sediment field a spatially distributed sink strength 

for radioactivity. This will undoubtedly have to take 

into account the effect of sediment size and associated 

chemical activity. This sink must be added into the 

continuity equation; the description of the channel and 

flow environment remains the same as in the section 

above. Since the sediment will not always permanently 

retain the sorbed radioactivity, perhaps the artifice of a 

secondary source, effective sink strength or multicomponent continuity equations will have to be employed.

Apparently practically none of the existing diffusion 

theories have been applied to the above field condition. 

However, the basic continuity equation for conservation 

of mass for "k" phases has been formulated (de Groot, 

1952). The interaction case such as exists with the 

condition of sediment being present is not clearly formulated in the diffusion theories.

FLOW SYSTEM CONTAINING BOTH SEDIMENT AND BIOTA

The problem of the first and second situation discussed is again compounded. To date, apparently 

neither the basic multiphase kinematic or dynamical 

equations involved have been published; nor have really 

appropriate boundary conditions been developed to 

include sediment and biota. However, the situation of 

a channel containing both sediment and biota is the 

most common one in nature.

Parker (1958) is one of the few to attempt an analytical expression for concentration including sediment and 

biota. He multiplied the expression for the concentration distribution derived from so-called Fickian theory 

for a simple geometry by e~Nt where e is the base of 

Naperian logarithms, N is a "river-uptake coefficient" 

and t is the time. This procedure leaves much to be 

desired.

It seems reasonable to consider both the sediment 

and biota in the flow system as sinks for the radioactivity, to be added to the basic continuity equation. 

These sinks would have to be spatially distributed and, 

of course, have appropriate nuclear-decay multipliers 

incorporated. The biological sinks, and secondary 

sources such as dying zooplankton, would have to be 

idealized. Also, in using sinks and sources to represent
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A7

the influence of biota, account would have to be taken, 

at least if short time periods are being considered, of 

the cyclic behavior both in time and location of such 

sources and sinks due to diurnal feeding and rhythmic 

vertical migration of the biotic life.

RADIOACTIVE DECAY

Decay of the radioactive constituents in the waste 

can be accounted for in the theory for any of the above 

conditions by introducing the appropriate timedependent exponential decay expressions.

Initial conditions for analytical purposes are mostly 

associated with the character of the source of contaminant. However, the relative mass density of the 

contaminant and the ambient flow field is also important density currents may completely change the 

origin of the source in the analytical coordinate system 

employed as far as applying turbulent diffusion theory 

is concerned.

Common sources of radioactivity to be associated 

in the theory with the above environmental factors 

may be classified, in general, as follows: 

1. Zero relative mass 2. Finite nonzero reladensity of contami- tive mass density, 

nant compared to 

ambient fluid.

a. Plane source normal 

to the direction of 

the mean flow; instantaneous or of 

finite time.

b. Source at or above 

the stream bed:

1. Instantaneous 

point or volume 

source.

2. Line source across 

or along the direction of flow; 

finite or infinite

The above situations are involved in setting initial 

conditions in an analytical study. Perhaps the most 

common is the continuous (or infinite) line source 

from a point, such as a pipeline outlet, in the direction 

of flow. A constant source strength, in time, is usually 

assumed. Also, in general, any relative mass density 

is usually due only to temperature differences of the 

two fluids. It seems that researchers have assumed, 

based on some evidence, that the viscosities and other 

physical properties of the waste effluents are nearly 

identical to those of pure water.

In considering the turbulent-diffusion problem with 

respect to the type of source, it becomes evident that

in many situations consideration must be given to the 

turbulent diffusion of submerged jets. In this report, 

however, this problem has been considered as secondary 

since the scale of diffusion in the vicinity of the source 

is small compared to turbulent diffusion from the 

turbulence generated by channel-boundary shear and 

wind shear. Where density currents of waste products 

are suspected, the use of submerged-jet theory (Rouse, 

1950) must be given attention if study of turbulent 

diffusion immediately adjacent to the source is desired. 

Jet theory also becomes important if the waste is 

discharged into the stream at velocities much different 

from the stream velocity. However, under other circumstances it may be desirable to use density-current 

flows to keep the waste concentrated in a small portion 

of the open' channel.

TURBULENT-DIFFUSION THEORIES

Nearly all diffusion theories with which the hydraulics 

engineer is acquainted fall into two classes: the Fickian 

and the statistical. The Fickian theories are sometimes considered the "old" theories while the statistical 

are the "new" theories. A few theories, which have 

heretofore had only limited application in hydraulics, 

will also be mentioned.

The equation commonly used as a basis for analysis 

of diffusion is the Fickian equation extended to turbulent diffusion

(3-1)

where C is "concentration", t is time, v is the velocity 

vector, K is the diffusion "constant" and V2 is the 

Laplacian operator. The v-vC term accounts for convection transfer. Seldom are the limitations of this 

equation mentioned, or the character of K, in applying 

it to hydraulic problems. A derivation adopted from 

Pai (1957) points out some of the background of this 

equation.

If C=C(x,y,z,t) is the concentration at a point in

space then \ vCdr=total mass of subject material in v. 

By conservation of mass

^+V(Ct>)=0. (3-2)

Substituting in v=v'-\-v and C C'+C with the customary definitions and applying Reynold's averaging 

rules,

f
A8 TRANSPORT OF RADIONUCLIDES BY STREAMS

Applying Boussinesq's exchange coefficients,

ac . ac

. a c

w' = vzic-c- » . . . - 

ac c-cdx (3-4)

It is now evident that the nine v</s define the diffusion 

tensor which in general is a function of the spatial 

coordinates.

It is frequently assumed that the x,y,z axes are the 

principal axes of the diffusion tensor. Here v^=0 

fori^j. Now dropping the averaging bars, letting 

Kt=Vv, where i=j, and assuming v-#=0,

Assuming further that Kt is a constant such that 

Ki=K2=K3 (homogeneity) then

(3-1)

Some of the available solutions of this equation for 

special cases, largely drawn from atmospheric diffusion, 

will be presented later.

Statistical turbulent-diffusion theories in Lagrangian 

form and their applications are well summarized 

(Frenkiel 1953). In general, only an infinite or semiinfinite domain has been considered. One of the most 

important points made by Frenkiel is that the Fickian 

theories are applicable only for large dispersion times 

such that

t»Lh

where Lh is the Lagrangian time scale of turbulence 

such that

Lh= f Rh (a)da

in which Rh is the Lagrangian velocity auto-correlation 

coefficient defined by

= u'A (t)u'A(t+h)

(3-6)

The fundamental equation of statistical turbulent 

diffusion in the Lagrangian system in an isotropic and 

homogeneous turbulence field is

tf = 2vr* f *(<-a)JB*(a)da = 2ll73 Pda, f "

jo Jo Jo (3-7)

where y2 is the variance of y or a measure of the diffusion 

in the y direction as a function of time. When 

it follows that

and when

where

** I 1 -r (3-8)

2 dh*

The X/, is called the Lagrangian microscale of turbulence. 

Also, if £«XA,

ytttjfip. (3-9)

Statistical turbulent-diffusion theories in Eulerian 

form have been worked on by several authors (Batchelor, 1951), (Taylor, 1921), (Goldstein, 1951), (Michelson, 1954). However, no application has been made to 

open-channel flow problems of waste disposal. These 

researchers have used or extended continuous stochastic 

processes or random-walk (discontinuous-movement) 

theories.

The continuous stochastic process approaches consist 

of finding the equation for the probability P(r,t] that 

the point defined by the vector r lies in the volume of 

fluid containing the contaminant. Assuming only 

that the turbulent flow field is homogeneous and the 

mean flow zero,

> ><> D/2T J\

(3-10)

from which it can be shown that % is a tensor of second 

order. It can be shown that for very small (t £0 )

(3-H)

and for very large (t tQ) that % >constant. Thus 

Vn is initially zero, then increases linearly with time 

and finally tends to a constant value thus, demonstrating that for large times v{j can be replaced by 

K= constant.

The random-walk or discontinuous-movement method 

of treating turbulent diffusion, an application of the 

theory of random functions, was first extended by 

Taylor (1921) in considering diffusion by continuous 

movements. This resulted in the same equation as 

that given immediately above. Goldstein (1951) 

extended Taylor's analysis upon quite rational grounds. 

Goldstein's equation has the form of the telegraph 

equation of theoretical physics. Several diffusion cases 

can be derived from his basic-difference equation. For 

isotropic diffusion in one dimension the motions are 

continuous and the displacements take place at finite 

velocities the basic diffusion equation is

(3-12)
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A9

where v satisfies y=vt and A is a constant. For aniso 

tropic diffusion, the equation becomes

ac

dy

The first form above of the telegraph equation 

corresponds to the case of no leakage from the cable. 

The second case includes leakage. These equations are 

derived on the assumption of partial correlations 

between the directions of motions in any two consecutive time increments dt. Also, these equations are of 

the hyperbolic type the solutions are somewhat 

different from the parabolic equations of the Fickian 

theory.

The above two equations, which appear on theoretical 

grounds to more truly represent the diffusion phenomena, at least in their derivation, have been only incompletely applied to the diffusion problem. Michelson 

(1954) has investigated some points in the mathematics. 

It is significant to note that the parabolic form of the 

turbulent-diffusion equation can be derived from the 

same difference equation by assuming zero correlation 

between consecutive motions and that the particles 

move with infinite velocity. Harleman (1959) has 

pointed out that, close to the source, the solution of 

these equations differs materially from the Fickian 

theory solutions.

In the category of miscellaneous theories, there is 

Richardson's (1926) distance-neighbor theory, which 

has some similarity to Kolmogoroff's subsequent work. 

In Richardson's theory the basic equation for each 

range of separation L, for the distribution of a quantity 

Pis

(3-14)

where

in which a is a diffusion parameter. Comparison to the 

Fickian theory quickly shows the dependency of the 

diffusion on the scale of the phenomena being investigated. In a confined channel the scale must, of course, 

reach a maximum.

In the development of a theory to explain the increase 

of the diffusion coefficient K in the Fickian theory with 

distance from the source in a semi-infinite domain, 

Lettau (1951) introduced a term for the advection 

due to boundary shear. He replaces the usual K by 

^(apparent) where

V

K (apparent) =

where (x #o) is the distance from the source.

SOME THEORETICAL SOLUTIONS NOW AVAILABLE

One of the best ways to evaluate the present level of 

theoretical knowledge of turbulent diffusion in alluvial 

open channels is to summarize some of the theoretical 

solutions now available. The subsequent tabulation 

will make clear that not even the simplest of conditions 

involving sources and sinks, such as used to represent 

sediment and biota, has been resolved for open channels. 

Also, only very simple conditions in confined channels 

have been treated most works discuss semi-infinite 

domains with a unidirectional flow. However, consideration has been given by various authors to vertical 

velocity profiles, elevated sources and thermal stability 

(in the atmosphere). Crank (1956) includes some 

solutions for conditions where the diffusion coefficient 

is dependent on concentration.

For Fickian theories: 

1. Instantaneous point source at the origin in an

infinite isotropic homogeneous turbulence field. 

If a quantity Q of material is released at a point

source at t=Q from an origin moving with the

mean flow, the concentration given by Roberts

(1923) is

-(««). ( 3_i5)

2. Instantaneous point source at the origin in an infinite 

anisotropic homogeneous turbulence field. 

Releasing the isotropy condition above, Roberts 

(1923) gives

(3-16)

3. Continuous infinite line source along the bed, normal

to the stream velocity.

Roberts (1923), under the conditions of a velocity 

profile such that

gives the concentration as

or * T -f "I2(m""+a 1

VI "i ' f L(n» n+2)*Kal (3-17)

where S=, }n^n=l m, and T is the gamma (m Ti+2)

function.

4. Same as case 3 immediately preceding, but with 

approximate logarithmic velocity profile. See 

Calder (1949).

5. Continuous point source, infinite isotropic domain. 

Roberts (1923), when Q is the emission rate, 

r2=a;2+2/2+;z2 and U is the mean velocity in the 

z-direction, gives
A10 TRANSPORT OF RADIONUCLIDES BY STREAMS

Q ^r (3-18)

6. Continuous point source, infinite anisotropic domain. 

Roberts (1923), when Q is the emission rate, 

r2=x2 -\-y2 -\-z2 and U is the mean velocity in the 

jr-direction, gives

C(x,y,z)=- tr (3-19)

7. Continuous infinite cross-stream line source in bed

of isotropic homogeneous flow field. 

Roberts (1923), where Q is again the emission rate, 

states

Ui*

(3-20)

Solutions lor continuous infinite elevated cross-stream 

sources in isotropic and anisotropic conditions may be 

found in Sutton (1953). Kellogg (1952) has considered 

spherical volume sources. Yih (1952) solved for 

several cases with m and n independent the twodimensional equation

(3-21)

Many other special conditions are considered in the 

literature. See, for example, the references in Meteorological Abstracts (1953).

For the statistical theories, Frenkiel (1953) gives: 

1. Instantaneous point source at the origin in an

infinite isotropic homogeneous region, where Q is

the quantity of material released,

C(x,y,z,t)= Q _N3/2 e2»^2 . (3-22)

Gifford (1955) has considered relatively arbitrary

volume sources related to this.

2. Instantaneous point source at the origin in an infinite 

anisotropic homogeneous region, where Q is the 

total quantity of material introduced,

Q

(3-23)

3. Continuous point source in an infinite isotropic 

homogeneous domain with origin at the source

Relative T> i + meanl i

concentration J (3-24)

(Solutions are also given for short and long distances from the source.)

4. Infinite-line sources normal to mean velocity. 

Frenkiel also gives solutions for this situation. 

They are too lengthy to present here.

EXPERIMENTS ASSOCIATED WITH THEORY

Very few experiments directly applicable to turbulent 

diffusion of material from sources in alluvial open 

channels are available. Those of Taylor (1954), Orlob 

(1958), Parker (1958), and Harleman and others (1959) 

seem the most applicable. There are, however, some 

excellent papers in the literature on the use of radioisotopes for beach- and harbor-drift studies. Also, 

many papers are available on experiments in atmospheric and oceanographic diffusion, normally including 

only a plane horizontal boundary and no confining 

walls or hills. Few of the papers consider, analytically 

or experimentally, the effect of sediment or biology on 

waste dispersion.

Taylor (1954) solved analytically for the diffusion 

coefficient K for flow in a uniform straight circular 

pipe in the turbulent-flow regime. His result is

K=lQ.lr0UVTQ/P U '

His analysis is based on the "universal velocity-distribution" equation of mixing-length theory, where r0 is 

the pipe radius, U the mean velocity, VWp the shear 

velocity. He then compared this to experiments in 

straight and curved pipelines. It was demonstrated 

that the theory compared well with experiments for a 

straight pipeline, but not for a curved pipeline.

The expression for K may be transformed so as to 

apply to the open-channel situation. The result is

K= 7.15R UT/J= 20.2/2 V (3-25)

where R is the hydraulic radius, U the mean stream 

\velocity and / the Darcy-Weisbach coefficient of 

channel friction. Taylor does not give the required 

magnitude of the dispersion time before the equation 

has reasonable validity.

Orlob (1958) conducted an excellent piece of hydraulic research on turbulent diffusion. He investigated 

the turbulent diffusion of floating polyethylene particles 

in the homogeneous turbulence field at the surface of a 

uniform steady open-channel jflow in a flume. He 

demonstrated that the Fickian diffusion coefficient increased rapidly close to the source and gradually approached a constant value as distance from the source 

increased. Some indications of a preliminary nature 

are given for turbulence intensity and scale as a function of Reynolds number, channel slope, and other 

parameters. These are pioneering experiments in 

obtaining turbulence measurements in open channels.
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS All

Parker (1958) reported on several field experiments 

on pipelines, reservoirs and open channels. These 

experiments do not adequately elucidate turbulent 

diffusion in open channels. Field experiments by 

other scientists have also done little to date to explain 

diffusion in open channels. Theory and experiment 

frequently give concentrations differing by 100 percent 

even when no sediment or biota is present.

Glover (1956, 1957, unpublished data) reported on 

two laboratory experiments and one field experiment. 

These data will be of value in future work. Glover also 

reported some theoretical work; largely similar to the 

work of earlier investigators. He did, however, 

attempt to consider the effect of vertical boundaries, 

confining a stream, perhaps the only author other than 

Taylor (1954) to do so. Unlike Taylor, however, 

Glover did not consider in an explicit manner the influence of velocity gradients. Glover considered the 

diffusion coefficient K to be a constant.

Harleman and others (1959), have conducted both 

an extensive review of the literature and some very 

fundamental laboratory research. Primary emphasis 

was on the problem of waste disposal in estuaries and 

other large bodies of water. They concluded from onedimensional tests in a turbulence flume and from review 

of the literature, that for waste disposal problems 

having large dispersion times, the Fickian theory is as 

satisfactory as the statistical theories. They also made 

a suggestion for translation of coordinates in order to 

account for the effect of near-source deviations of the 

diffusion coefficient K from a constant value.

SORPTION OF RADIOCONTAMINANTS BY STREAM 

SEDIMENTS

One aspect of the problem of radiocontaminants in 

streams which has received relatively little systematic 

attention is concerned with the role of fluvial sediment 

in dispersing, transporting, and concentrating radioactive substances. Indications are that sorption reactions are the rule rather than the exception when 

extremely dilute solutions, such as low-level liquid 

wastes, come into contact with solid surfaces (Carritt 

and Goodgal, 1953). The concentration of radioactive 

substances on the surface ol sediment particles may be 

many thousands of times greater than the concentration 

in the surrounding solution.

When significant amounts of radioactivity are sorbed 

by sediment particles, knowledge of the sediment 

supply and the sediment-transport characteristics of 

the stream clearly becomes an important factor in assessing the rate of dispersal and the ultimate distribution 

of radioactivity in the stream environment.

Sorption of radionuclides can be either an asset or a 

liability. Under controlled conditions, sorption of radionuclides by sediment can effectively reduce the concentration of dissolved radionuclides in the waste water. In a 

natural stream environment, however, uncontrolled 

sorption of radioactive substances by sediments must 

be considered as a potential hazard. Radioactivity 

could build up over long periods of time in sections of 

a stream where the rate of accumulation of radioactivity induced by sediment deposition exceeds the 

rate of natural radioactive decay. Such deposits 

might occur along the convex banks of meandering 

rivers, or in reaches of a stream where flow velocities 

are reduced. Some of these contaminated deposits 

would be periodically flushed out at high water, and 

then be redeposited farther downstream as the floodflow 

receded.

The key to the sediment aspect of the problem of 

low-level liquid-waste disposal is sorption. To what 

extent does sorption occur? What forms of sorption 

are involved? What factors control the extent of 

sorption, and what are the relationships among these 

factors? For the most part only qualitative answers 

can be given to these questions at the present time. 

Many of these are at best tentative and incomplete. 

Following is a brief summary of: (1) current sorption 

theories, (2) some of the relevant literature, and (3) 

factors determining the extent of sorption.

SORPTION THEORIES

Sorption may be described as the process of taking up 

and holding either by adsorption or absorption. In solutions, adsorption refers to the uptake and concentration of 

a solute at the surface of a sorbent, whereas absorption 

implies a generally uniform penetration of the solute 

into the sorbent. Sorption reactions involving stream 

sediments and radioactive solutes generally belong in 

the adsorption category. However, in practice it is 

often impossible to separate the effects of adsorption 

from those of absorption. Consequently, the nonspecific term "sorption" will be used in the remainder 

of this section.

According to McBain (1950), sorption comprises a 

number of phenomena, the most commonly recognized 

of which is the accumulation of one or more substances 

at an interface. Combination of the sorbed substance 

with a solid at an interface may involve strong chemicalvalence bonds chemisorption or weaker physical 

interaction through van der Waals forces physical 

sorption or both. The uptake of radioactivity by 

stream sediments may involve either chemisorption or 

physical sorption; frequently it involves both types, 

whence analysis of the problem becomes considerably 

more complicated.
A12 TRANSPORT OF RADIONUCLIDES BY STREAMS

Sorption may occur wherever there is a surface or an 

interface. Sorption may occur at any surface; the 

most important, and most complex surfaces, however, 

are the interfaces between solutions and solids, such as 

the surfaces of colloidal particles in a liquid medium. 

The substances sorbed at an interface may be products 

of reaction or hydrolysis, unaltered molecules, or 

particular ions. Sorption may be complicated by the 

orientation of molecules at the interface, by diffusion 

into a solid, and by the surface mobility of sorbed 

molecules.

According to Daniels (1948), there must be a layer 

of atoms and molecules at the extreme surface of a 

solid which have some valence forces or other attractive 

forces that are not so fully utilized as those associated 

with the atoms and molecules in the interior which are 

completely surrounded by other molecules. The residual forces on the surface of sediment particles in solution 

are used up, and the free energy reduced, by means of 

sorption reactions. The extent of sorption may vary 

widely. It is dependent on the specific nature of the 

sorbent solid and the substance being sorbed, the 

available surface area, the concentration and types of 

solute in solution, the time, and the temperature.

Surface-tension phenomena are known to be intimately related to sorption reactions, but the mechanics 

of tensions at solid-liquid interfaces are not very well understood. It is known though that when the surface tension 

of a solvent remains constant as the concentration of 

solute increases, no sorption occurs (McBain, 1950). 

This behavior is typical over a certain range of solute 

concentration in solutions containing soap or a detergent. Neither the critical range of solute concentration nor the requisite concentration of soap or detergent 

is defined.

Sorption isotherm. The Freundlich equation, which 

is derived from the empirical classical isotherm, states 

that

-=jfcc» (4-1)

when

x is the weight of material sorbed by m grams of

sorbent, 

c is the concentration of solution in equilibrium with

the solid,

k is an empirical constant, and 

n is an empirical constant having a value between

about 0.5 and 0.1.

The values of the empirical constants k and n are 

determined by experiment for each solute, adsorbent 

and temperature. Temperature, however, according 

to McBain (1950), does not greatly affect sorption from 

solutions.

The classical isotherm applies with fair accuracy 

to the various types of sorption from solution over a 

very wide range of concentrations. The form of the

isotherm indicates correctly that appreciable sorption 

occurs even at extremely low concentrations, especially 

at low values of n. It has been shown that c is a true 

equilibrium concentration which is reached by both 

sorption and desorption for a particular value of x/m. 

The classical isotherm holds true only for definite 

total times of exposure. Owing to the inaccessibility 

of fine pores of solids, the competition between solvent 

and solute, anr1 the diffusion into the solid, sorption 

reactions may }iiire long periods of time, even up 

to years, to reach completion. McBain (1950) gives 

Burt's empirical formula

-

m

(4-2)

where t is now time and k and n again are empirical 

constants, for the time effect. For very prolonged 

sorption this expression is modified to the form

log -? = (4-3)

where a is the saturation value and s is the value of 

x/m at any given time.

Competition between solute and solvent for the surface of a solid is an important factor when solution 

concentrations are high. However, in extremely dilute 

solutions, such as most low-level radioactive waste 

liquids, sorption of the solvent has only a negligible 

effect upon sorption of the solute.

In mixed solutions which contain more than one 

solute the competition is more complicated, and the 

attainment of equilibrium is slower. Each solute 

lessens the sorption of others; however, it has been 

demonstrated that in time the solutes which sorb 

strongly largely displace the more weakly sorbed 

solutes.

Physical sorption, Physical sorption is characterized 

by small heats of adsorption, by reversibility, and by 

rapid attainment of equilibrium (Glasstone, 1940). 

Physical sorption is nonspecific in character and occurs 

on chemically inactive surfaces (Taylor and Taylor, 

1942). This type of sorption is attributed to the effect 

of van der Waals forces which are thought to result 

from molecular attraction due to dispersion forces. 

The classical isotherm is applicable to systems in which 

physical sorption predominates.

Sorption of solutes on the surface of sand and silt 

particles in streams is primarily physical. Although 

physical sorption also occurs with colloidal clay particles, it is secondary to other types of sorption, particularly ion exchange.

Owing to the reversibility and rapid attainment of 

equilibrium which are typical of physical sorption, 

the concentration of solutes on the surface of sand and
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A13

silt particles would tend to be quite sensitive to the 

concentration of solutes in the water. The sensitivity 

would be less when diffusion of the solute into the solid 

is a significant factor.

Ion exchange. Ion exchange, which is a type of 

chemisorption, may be described as the process by 

which ions sorbed at the surface of a solid are replaced 

by other ions of like sign. In a disperse system, such 

as that represented by a suspension of sediment particles in water, ion exchange occurs when ions in solution 

first displace and then replace ions which are sorbed on 

the surface of the particles.

In soil chemistry, ion-exchange phenomena are generally associated with the fine-grained soils and in. 

particular with the expanding-lattice montmorillonite 

clays. Ion exchange occurs to some extent with larger 

grained sediments; however, exchange capacity diminishes rapidly as particle size increases. Ion-exchange 

capacity depends both on the specific surface and the 

chemical and mineralogical characteristics of the sediments involved.

Particles in a colloidal suspension carry an electric 

charge. Most clay particles carry a negative charge 

and in a colloidal system behave essentially as anions 

(Baver, 1956). Consequently the negatively-charged 

clay particles sorb available positively-charged cations 

from solution. This phenomenon is known as ionic 

adsorption. The magnitude of the electric charge on 

the clay particles is known as the zeta potential. High 

zeta potentials are associated with high ionic-adsorption 

capacities and stable suspensions. Conversely potentials of small magnitude are associated with flocculation 

and subsequent settling of clay particles.

In the cation-exchange process, those ions which are 

sorbed strongly tend to displace those which are not 

as strongly sorbed. The energy with which an adsorbed 

cation is held to a particular type of clay particle, in an 

aqueous environment, is determined by considerations 

relating to hydration and valence (Baver, 1956). For 

isovalent cations the bonding energy varies inversely 

with the effective radius of the hydrated ion, and hence 

directly with the atomic weight. The relative bonding 

energies of some common exchangeable cations may be 

expressed in terms of the Hofmeister or lyotropic ion 

series

Cs+>Rb+>K+>Na+>Li+

for monovalent cations, and

Ba++>Sr++ >Ca++>Mg++

for divalent cations.

Bonding energy tends to increase with valence, 

although there is a slight amount of overlap at the

644015 O 62 3

beginning of the monovalent series and the end of the 

divalent series.

Considering the facts that: (1) Sr90 and Cs137 are the 

most abundant of the long-lived fission products, and 

(2) Ca, Mg, K, Na are among the most abundant 

exchangeable cations in clay-mineral soils, the relative 

positions of the ions in the Hofmeister series is of 

especially great practical significance where waste solutions contain fission products.

An exception to the rule is the banding energy 

associated with the hydrogen ion, which exceeds that 

of the divalent cations. This apparent contradiction 

is generally attributed to the explanation that the 

adsorbed hydrogen is actually in the form of a hydromuni ion (H3O) + .

Jenny and Reitemeier (1935), who contributed a 

great deal toward establishing the foregoing relationships, also demonstrated that ionic exchange increases 

approximately as the sixth power of the zeta potential.

Thus the close relationship among the various 

phenomena of cation exchange, energy of adsorption, 

zeta potential and flocculation seem to be fairly well 

established.

The chemical and mineralogical nature of clays as 

well as the sorbed cations are instrumental in determining the surface behavior of clay particles. Important 

properties of some clay minerals are listed in table 2.

LITERATURE REVIEW SORPTION OF 

RADIONUCLIDES

Radioactive materials are essentially identical with 

their stable counterparts in ordinary chemical and 

physical behavior. Although sorption is influenced 

to a slight extent by the difference between isotopic 

weights of radioisotopes and corresponding stable 

isotopes, this effect is negligible when the atomic 

number of the sorbed ion is greater than 10. In fact 

the influence is so small that radioactive tracers are 

commonly used in quantitative investigations of 

sorption reactions. Few studies have been undertaken, 

however, with a definite view toward obtaining a 

better understanding of the role of fluvial sediments 

in concentrating radioactivity by sorption. Studies by 

Carritt and Goodgal (1953) and Barker (1958) are 

among the few which are directly applicable to the 

problem.

Carritt and Goodgal studied the uptake of various 

radioactive components from solution by suspensions 

of Roanoke River and Chesapeake Bay sediments, 

bentonite, fuller's earth, and powdered Pyrex glass. 

Each of the solutions studied contained one of the 

following dissolved radioactive substances: Phosphate, 

iodide, sulfate, strontium, copper, and iron. Phosphate, 

iodide, and sulfate occur as anions in waste solutions.
A14 TRANSPORT OF RADIONUCLIDES BY STREAMS

TABLE 2. Important properties of some clay minerals 

[After R. £. Danielson, 1956, written communication]

Group and lattice type

Montmorillonite group (2:1

Illite or hydrated mica group

(2: 1 nonexpan ding lattice) .

Name

Halloysite _ __ _____

Montmorillonite. _ _

Beidellite. _________

Illite-______-_______

Py rophy llite _______

Typical empirical formula

Al2Si2O5 (OH) 4 ------ ___ _______ __.___ ______

Al2 Si2O5 (OH) 4 nH2O_ _____________________________

(Al2 . 67Mg. 33)Si4O10 (OH) 2Na.33 nH2O-____ _ _________

Al2 . 16 (Al.88Si3.i4)Oio(OH) 2Na.33nH2O_ _______________

Fe2 (A1.33Si3.67)Oio(OH) 2Na. 33 nH2O-_-____-_____--___

Mg8(A1.3iSi|.0) O10 (OH) 2Na. 33 nH2O___ _ _____________

(Alj.reMg.se) (A1.6oSi3 .4o) O10 (OH) 2K.6o ________________

A_4Si8O_o(OH)4-..-- - - 

Cationexchange 

capacity 

(meg/lOOq)

3-15

40-50

80-125

60-90

60-70

20-30

20-40

Approximate 

size 

range 

(M)

0. 5-2

.04- 2

.01- 1

.05- 5

.01- 1

.01- 1

Strontium, iron, and copper usually occur as cations in 

solutions. Additional variables which were either 

controlled or measured in the experiments were pH 

(hydrogen-ion concentration), temperature, contact 

time, concentration of suspended solids and reacting 

dissolved solids, and ionic strength.

The methods employed in these experiments were 

simple. Basically they consisted of assembling measured amounts of the various ingredients, placing them 

in a stoppered flask, keeping the contents in suspension 

by means of a shaking machine, and withdrawing 

samples for analysis at periodic time intervals. The 

solids in the samples were centrifuged from suspension 

and analyzed for radioactivity. Analysis of the supernatant solution for radioactivity provided an independent check.

The results of the experiments by Carritt and Goodgal indicate that, depending upon the specific conditions involved, any of or all the variables they 

investigated may have an important influence on the 

rate and extent of sorption. Most of their data plotted 

according to the classical empirical isotherm, and the 

extent of sorption was definitely shown to increase 

with contact time. Not much can be added to the 

above in the way of general conclusions. The data 

are too few and the variables too many to permit an 

adequate evaluation of the effects of pH, temperature, 

ionic strength, and concentration of suspended solids 

which would cover all the combinations of sediment 

types and radioactive components.

Some of the more specific conclusions reached by 

Carritt and Goodgal (1953) are as follows:

1. The uptake of phosphorus by Roanoke River 

solids bentonite and fuller's earth was shown 

to be maximum in the pH range (4-7) in which 

the H2PO4~ ion predominates;

2. It was demonstrated that the mechanism by which 

phosphorus was taken up involved both a rapid adsorption process and a slow diffusion process;

3. Strontium, copper, and ferric iron were found to 

precipitate from solution as basic salts under 

appropriate conditions. Added solids acted as 

a "sweeper" aiding the settling of finely divided 

precipitate;

4. Very little iodide was sorbed by any of the suspended 

solids.

5. The sorption of sulfate sulfur by Roanoke River 

sediment was found to be maximum in the pH 

range below 4, which favors formation of the 

HSOr ion.

In general, the percentage of radionuclides sorbed 

by sediments with respect to the initial quantity of 

radionuclides in solution ranged between 10 percent 

and 90 percent in Carritt and Goodgal's experiments. 

The initial concentrations of radioactivity in these 

experiments were several orders of magnitude in 

excess of the recommended maximum permissible 

concentrations. In natural streams where radioactivity concentrations might be on the same order of 

magnitude as the MFC, a greater percent of sorption 

would normally be expected under otherwise comparable conditions.

Calculations based on one of the isotherm tests 

in which the sediment concentration was 629 ppm of 

Roanoke River solids, and the initial solution concentration was 11.5 microgram-atoms of phosphorus per 

liter, showed that approximately 10 percent of the 

phosphorus was sorbed in 1 minute at which time the 

concentration of phosphorus on the surface of the 

sediment particles was estimated to be more than 

10,000 times that in the surrounding solution.

Barker (1958) conducted sets of experiments similar 

to those of Carritt and Goodgal in which sorption due 

to ion exchange of cesium and strontium by kaolinite, 

illite, halloysite and two types of montmorillonite was 

investigated. Cation-exchange capacity determinations of these clays through the use of trace amounts of 

Sr90 and Cs137 compared well with exchange-capacity
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A15

determinations by other methods. The effect of various 

concentrations of sodium chloride and calcium chloride, 

which are common electrolytes in natural waters, on 

the sorption of carrier-free strontium and cesium by 

illite, halloysite and montmorillonite 21 (bentonite) 

also was investigated. Sorption of cesium and strontium by these three clay minerals from solutions 

containing added amounts of strontium nitrate and 

cesium chloride carriers was studied in addition. 

Sediment concentrations and contact times were 

maintained constant at 4,000 ppm and 17 hr in these 

experiments.

Barker found that the percentage of carrier-free 

cesium sorbed by clay is decreased as the concentration 

of calcium or sodium in solution is increased. Results 

for the calcium and sodium solutions were very nearly 

the same. The concentration of calcium was found to 

have a much greater effect on the sorption of strontium 

than the concentration of sodium. The fact the 

strontium sorption from the calcium solution was 

considerably less is attributed to the marked chemical 

resemblance between strontium and calcium, the ions 

of which compete for exchange positions on a nearly 

equal basis. Barker concluded that as a first approximation the sorption of small quantities of cesium by 

clays from most natural waters would depend only 

upon the total concentration of cations in the water, 

but that predictions concerning the sorption of strontium would necessitate the additional consideration of 

the sodium-calcium ratio in the water.

Comparison between the results of the carrier-free 

and the carrier-added experiments indicated that both 

the concentration of radioactive substance and the 

concentration of sodium and calcium affect the amount 

of radioactivity sorbed. In general, however, changes 

in the total ionic concentration of the solution were 

found to have a greater effect than changes in the 

cesium or strontium concentration within the range to 

be expected in most natural waters.

In summary it might be said that Carritt and Goodgal's more comprehensive work, involving a relatively 

large number of variables, points the way toward many 

areas which require further attention. However, 

Barker's more intensive work, though smaller in scope, 

has resulted in more definitive answers. Both 

approaches are needed at this time.

FACTORS DETERMINING EXTENT OF SORPTION

From the foregoing discussion it is clearly evident 

that characteristics of the sediment and the waste 

effluent, and the quality of stream water are all intimately related to sorption phenomena involving radioactive waste components and stream sediments. 

Considering the relatively meager amount of available

knowledge and data on the subject it would be presumptuous to draw conclusions pertaining to the 

relative importance of the many factors involved. 

Factors which are known to be significant and their 

estimated qualitative effects are listed in the following 

paragraphs.

SEDIMENT CHARACTERISTICS

Probably the most important single sediment 

characteristic affecting the extent of sorption is particle 

size. Particle size is important in determining both 

the extent and type of sorption. Sorption capacity of 

stream sediments is roughly proportional to the 

available surface area. From figure 1 it is seen that 

for a given weight or concentration of spherical sediment particles, the total surface area of 1-micron clay 

would be 1,000 times as great as that for 1-millimeter 

sand. The fact that the chemical activity of soil 

particles tends to decrease as the particle size increases 

is instrumental in making ion exchange the normally 

dominant mechanism in sorption by clays, and physical 

sorption the principal mechanism in sorption by sands 

and silts.

The chemical and mineralogic nature of sediments, 

particularly of clays, is also important in determining 

the extent of sorption. The cation-exchange capacity 

of the clay and the position of the adsorbed cations in 

the Hofmeister ion series with respect to that of the 

radioactive cations in solution are significant factors in 

this regard.

Apparently very little information which relates 

various types of sediments to their capacities for absorption by diffusion of a solute is available.

Concentration of sediment in a stream is important 

insofar as it is related to the total surface area available 

for sorption reactions.

CHARACTERISTICS OF WASTE EFFLUENT AND STREAM

WATER

Waste effluent and stream water are considered 

together because it is the mixture of the two which 

determines the characteristics of the solution in the 

sorption system.

Concentration of radioactive waste effluent in stream 

water is of course an important factor in determining 

the amount of radioactivity which is sorbed by stream 

sediments. The classical or Freundlich isotherm equation indicates that for a particular solution-sediment 

system, the amount sorbed depends largely on the 

concentration in the solution of the material being 

sorbed. Any one of a number of chemical characteristics of the waste effluent-stream solution may, however, radically alter the complexion of the entire 

sediment-solution sorption system.
A16 TRANSPORT OF RADIONUCLIDES BY STREAMS

105

10*

103

102 

1

< Clay ,

\

G=2.65

\

\

< Silt j

\

\

\

x Sand

\

\

X

\

< Gravel >

103 

102 

10

>" 10-3 10-2 o.l 1.0 10

PARTICLE DIAMETER, IN MILLIMETERS 

FIGUBE 1. Variation of specific surface of spherical sediment particles (sp gr 2.65) with particle diameter.

The composition of the radionuclide-bearing substance is important in this regard. For example, systems containing appreciable quantities of sediments 

with exchangeable cations would show a marked preference for sorbing cations over anions, regardless of 

whether the cations and anions are radioactive or stable.

In systems involving ion exchange the position in the 

Hofmeister ion series of the radioactive cation is also a 

significant factor. As indicated on p. 13, exchange 

occurs according to the order of the cations in the 

series; cations toward the beginning of the series tend 

to displace those which follow. Also, polyvalent 

cations tend to displace divalent cations, which in turn 

tend to displace monovalent cations.

The presence in the solution of competing nonradioactive substances may greatly reduce the uptake of 

radioactivity by sediments. In streams, competing 

nonradioactive substances might originate from other 

types of industrial wastes or froni natural sources.

It has been demonstrated that the extent of sorption 

may be greatly influenced by the effect of the pH of the 

solution on the ionic forms in solution. Changes in 

the pH of the solution lead to the formation of different 

ions which may be either more or less readily sorbed 

than before. The critical pH range depends on the 

various components of the system. Considerable 

further investigation is required in this area.

Another area requiring investigation is the effect of 

detergents in solution on sorption. It is well known 

that detergents reduce the surface tension of water, 

and it is thought that sorption is reduced by the presence of detergents in solution. However, the relationship between the concentration of detergent and the 

effect on sorption is largely unknown.

Under appropriate conditions it is known that certain 

radioactive ions will combine as salts with other materials and precipitate from solution. Although uptake 

of radioactivity by sediments will be reduced by the 

extent to which the concentration of radioactivity in 

solution is decreased by precipitation reactions, the 

radioactive precipitates may themselves become a 

source of hazard. Detergents in solution tend to 

inhibit precipitation.

Concentrations of flocculating agents in solution 

sufficient to induce flocculation and subsequent deposition of clay particles constitute another source of 

potential hazard. The addition of neutral salts will in 

general reduce the zeta potential or negative charge of 

clay particles, thereby inducing flocculation. The flocculating power of a salt increases with the sorbability 

of its cation component. Flocculating agents in natural streams may arise from such sources as industrial 

wastes and the intrusion of brackish tidal waters.
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A17

The physical characteristics of the waste effluent 

such as density and viscosity affect uptake by sediments 

insofar as they affect the distribution of the radioactive 

components over the stream cross section by turbulent 

diffusion. Sorption from solution is to some extent 

affected by the temperature of the solution, but temperature effects over the normal range of stream temperatures generally seem to be secondary to other 

considerations.

It is apparent from the preceding discussion that the 

factors influencing the uptake of radioactivity by sediments are many, varied, and often not very well understood. In natural streams the sorption systems are 

further complicated by the fact that several factors 

will normally be operating simultaneously, thereby 

obscuring cause and effect relationships. A great deal 

of additional research and information is a prerequisite 

to adequate criteria for predicting the extent to which 

sorption of radiocontaminants by sediments may occur 

in natural streams.

SEDIMENT TRANSPORT AS AFFECTED BY DRAINAGE 

AREA AND STREAM CHARACTERISTICS

Einstein (1950) has classified the total sediment load 

or sediment transport of a stream into fine-material 

load and bed-material load. The fine-material load 

consists of particles finer than most of the material 

found in the stream bed, whereas particles composing 

the bed-material load are found abundantly in the bed.

The particles of fine-material load are moved by small 

fluid forces and, therefore, are in nearly continuous 

suspension by natural streams. The quantity of such 

material in transport by a stream then depends on the 

rate at which these fine particles become available as 

affected by the environment or characteristics of the 

drainage area, and not on the ability of the flow to 

transport them. On the other hand, sediment of the 

coarser sizes found in large quantities in the stream 

bed of alluvial channels will be transported at a rate 

depending on the relative capacity of the stream for 

moving these sizes.

Experience of the Geological Survey in measuring 

sediment transport during the past 2 decades substantiates these general theories. Most streams readily 

transport silt and clay fractions (as much as 0.062 mm 

in diameter) as wash load. The quantity of these fines 

moved by the stream at a given time is very nearly 

equal to that released by the environmental factors 

within the drainage basin. The quantity of the various 

coarser sizes (sand and gravel) in transport is closely 

related to water discharge if the supply is not proportional to the water discharge, then the stream will 

aggrade or degrade its bed, thus maintaining its loadcapacity relationship.

The sediment load, or transport, of a stream then 

involves variables from two categories, as follows:

1. Environmental factors associated with the supply of 

sediment from the drainage area and included 

within the broad terms of climate, physical character of the watershed, and land use.

2. Stream channel and flow factors associated with the 

quantity of flow, channel geometry, particle size 

of sediment in transport, and channel control.

As expected, the difficult and broad subject of the 

environmental factors has been investigated in only 

small and usually unrelated segments unrelated because studied in different geographical areas and with 

different objectives. Examples would include the data 

from small reservoir surveys collected by various 

agencies of the Department of Agriculture and the 

Department of the Interior and by some State agencies. 

Limited interpretation of these data is underway. 

(See Glymph, 1954; Maner, 1958; Langbein and 

Schumm, 1958; and Stall and Bartelli, 1959.) The 

area of investigation is so large that progress seems 

negligible.

Stream channel and flow characteristics of streams, 

on the other hand, have been or are in a more advanced 

state of investigation. The magnitude and pattern of 

streamflow have been intensively studied on a routine 

basis. In the process of obtaining these data, much 

information about channel geometry is being obtained. 

Channel roughness and certain hydraulic characteristics as may affect sediment transport are being actively 

investigated with recirculating flumes. Progress in this 

area has been sufficient for design and initiation of a 

sound course of study that should yield substantial 

progress in the near future.

DRAINAGE-AREA CHARACTERISTICS

It has been noted that the transport of fine sediment 

in a stream is largely controlled by factors of supply 

in its drainage basin. Some of these factors include:

1. Nature, amount, and intensity of precipitation.

2. Condition and density of the channel system.

3. Orientation, degree, and length of slope of the watershed area.

4. Soil type.

5. Land use.

These factors can be allied logically to either or both 

of two forces: those that resist or those that advance 

the rate of erosion and transport. For example, precipitation of low intensity occurring at ideal intervals 

may advance the growth of vegetation and thereby 

advance the resisting force. If precipitation is very 

intense after a drought, or occurs over an area without 

cover, it is likely to cause a large amount of erosion. 

Because of the interrelationship of these factors, and
A18 TRANSPORT OF RADIONUCLIDES BY STREAMS

the large variance associated with each, it is difficult 

to define erosion and transport from a small area.

Many workers in the field of erosion and soil loss 

have correlated considerable data, but they find large 

areas within the factors that cannot be defined by 

present data. In one recent investigation, Wischmeier 

and others (1958) showed that an index consisting of 

the product of rainfall energy and maximum 30-minute 

intensity of the storm is the outstanding variable for 

correlation with soil-loss data from 5 locations in the 

Midwest each having 131 to 207 observations.

One of the most perplexing problems in handling 

soil-loss data is that of accounting for deposition within 

the drainage basin. The sediment yield of a large basin 

is usually less than the sum of its subbasins because of 

deposition and channel aggradation during transport 

from the small areas. The factor "condition and density 

of the channel system" is probably the most important 

index of this phenomenon. Data assembled by Glymph 

(1951) shows the relation of net sediment yield to size 

of drainage area. For a drainage area of 5 square miles, 

the yield ranges from 400 to 4,000 tons per square 

mile, for 500 square miles, 100 to 2,000 tons, and for 

50,000 square miles, 60 to 1,200 tons.

Because of the complicated interrelations among the 

environmental factors affecting sediment yield, and 

because they have not been studied sufficiently, a 

detailed discussion of each factor will not be attempted 

in this treatise. Some of these factors have been considered indirectly in an analysis of the trend of sediment yield of the Brandywine Creek at Wilmington, 

Del. (Guy, 1957). In this study the parameters of total 

runoff, rainfall intensity, and season of the year evaluate 

to some degree the factors considered in this section.

GENERAL CONSIDERATIONS OF SEDIMENT 

TRANSPORT

Streamflow turbulence results in the continuous motion 

of fluid vertically across a horizontal plane within the 

stream and transports not only fluid and momentum 

but also suspended sediment. This condition alone 

would tend to produce a uniform distribution of sediment in a given vertical section of streamflow; however, 

the constant settling of the particles due to gravitational force counteracts this process. Under equilibrium 

conditions, the upward components of turbulence travel 

toward a region of lower concentration, and the downward components toward a region of higher concentration. Thus, the rate of increase in suspended-sediment 

concentration toward the bottom depends on the degree 

of turbulence in the stream and the settling velocity of 

the particles.

Sediment of extremely small size (colloidal) may be 

suspended by Brownian movement or electrolytic 

charges. Particles of this kind are, therefore, suspended 

independently of turbulence and theoretically are transported by a velocity equivalent to the suspending fluid.

It is logical that all particles in a colloidal suspension 

will maintain uniform vertical as well as horizontal 

dispersion through a reach of stream, if they are dispersed uniformly at the entrance of the reach. Observations show further that natural turbulence in 

most streams is sufficient to suspend clay and silt 

(diameters less than 0.062 mm) uniformly for all 

practical purposes. Sand, however, is suspended less 

easily and therefore its concentration in a vertical section of a stream must increase from top to bottom in 

accordance with the operation of the turbulencesuspension theory. Figure 2 (U.S. Inter-Agency com-

"- 10

 z. -

o _

CD

8

CO

I 

"S

o

CONCENTRATION: 1 SPACE=100 PPM BY WEIGHT

FIGURE 2. Distribution of sediment at a vertical in the Missouri River at Kansas City, Mo. From U.S. Inter-Agency Committee (1948).
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A19

mittee, 1948) illustrates the vertical concentration of 

several size classes from clay to very coarse sand, thus 

contrasting the nearly uniform concentration from top 

to bottom of the clay and silt with the increasing concentration of sand from top to bottom.

The concentration distribution of sand in suspension 

by a stream then is a function of the size available for 

transport, the roughness of the stream bed, and the 

velocity characteristics of the stream. Hubbell and 

others (1956) show that the suspended-sediment concentration at different verticals in the cross section of a 

sand-carrying stream may vary widely and that sand 

transport is associated with hydraulic characteristics 

of the stream that fluctuate widely in both time and 

space for a given stream.

Streams having a relatively uniform rate of water 

discharge are expected to transport sediment at a relatively uniform rate, particularly the coarser fractions 

that depend on the transport capacity of the stream. 

Streams having a widely varying rate of water discharge 

are expected to exhibit very large variations in sediment 

discharge because in addition to the increased transport 

capacity with increased water discharge, rainfall causes a 

change in supply of fine sediment. This contrast is largely 

a function of climate and its related factors such as vegetation. Table 3 contrasts the monthly water and sediTABLE 3. Comparative monthly water and sediment discharges 

for streams in areas with differing climate

1954 water year

May ________________

July.............................

September .......................

Total. .....................

Discharge of Scantic 

River at Broad Brook, 

Conn, (area 98 square 

miles)

Water 

(cfs-days)

1,860 

2,560 

5,400 

3,490 

3,800 

5,850 

5,850 

6,540 

2,830 

1,610 

1,780 

5,120

46, 700

477

Sediment 

(tons)

56 

60 

331 

91 

136 

222 

540 

322 

88 

33 

69 

512

2,460

25.1

Discharge of Pecos 

River near Artesia, N. 

Mex. (area 15,300 

square miles)

Water 

(cfs-days)

701 

1,710 

1,810 

1,610 

1,200 

1,220 

7,900 

9,660 

500 

24 

10,000 

1,040

37,400

2.44

Sediment 

(tons)

321 

550 

642 

330 

244 

168 

70,100 

130, 400 

216 

6 

198, 700 

927

402,500

26.3

ment discharge of the Scantic River at Broad Brook, 

Conn., with the Pecos River near Artesia, N. Mex., 

for the 1954 water year.

GEOMETRICAL CHARACTERISTICS OF STREAMS

Relation of channel geometry to sediment transport. A 

natural stream in equilibrium condition has a geometrical pattern of slope and cross section to fit the water 

discharge and the size distribution and rate of transport

of sediment. Leopold and Maddock (1953, p. 51) 

state that

. . . even in the youthful topography of the headlands where 

streams are gradually downcutting and are, therefore, not graded, 

the stream-channel characteristics and slope tend to be adjusted 

to the discharge and sediment load. Even the ungraded parts 

of a channel system exhibit a neat pattern characterized by a 

tendency toward a regular increase of width and depth downstream with increasing discharge and with a concomitant decrease in slope.

and

Load and discharge are characteristics of the hydrology, 

geology, and physiognomy of the drainage basin. They are 

furnished to the trunk stream channels and are essentially 

independent of the trunk channel system.

In somewhat more specific terms, figure 3, a reproduction of figure 19 from Leopold and Maddock (1953, 

p. 27) shows how slope, roughness, sediment load, 

velocity, depth, and width vary with discharge at a 

station and downstream. Sections A and C represent 

headwater conditions of low and high flow, respectively. 

In considering the differences at the headwater section 

with increase of flow, note the small increase in slope, 

the small decrease in roughness, the large increase of 

sediment load, the moderate increase of velocity, 

depth, and width. With respect to differences in 

sections A and B, where B is downstream and at the same 

flow frequency as A, river slope decreases moderately, 

roughness decreases slightly, sediment load increases 

moderately probably because the water discharge 

increases ,velocity increases slightly, and depth and 

width increase moderately. The sediment load has 

the greatest contrast when considering both the increase in flow and a downstream section.

Leopold and Maddock (1953) also state that stream 

channel geometry varies in response to sediment 

transport as follows:

At constant discharge, an increased velocity at constant width 

is associated with an increase of both suspended load and bed 

load in transport. At constant velocity and discharge, an 

increase in width is associated with a decrease of suspended 

load and an increase in bed load in transport.

Boundary roughness. Resistance to streamflow in a 

given reach of a stream is the sum of the roughness 

created by the size of particles on the stream bed, the 

size of ripples and (or) dunes made up of these particles 

on the bed, and the bank roughness. The relative 

importance of any one of thetee may depend on the 

particle size of sediment in transport, the stream 

velocity, the shape of the cross section and the sediment 

load in transport. For example, the important roughness factor in a wide shallow stream having a bed of 

medium sized sand and with a mean velocity of 4 feet 

per second is the dune-and-ripple roughness.

In addition to the particle roughness, a given stream 

may flow successively and (or) simultaneously in several
A20 TRANSPORT OF RADIONUCLIDES BY STREAMS

EXPLANATION

DISCHARGENote: All scales are logarithmic

Change downstream for discharge 

of given frequency

Change at gaging station for 

discharges of different frequencies

FIGURE 3. Average hydraulic geometry of river channels expressed by relations of width, depth, velocity, suspended-sediment load, roughness, and 

slope to discharge at a station and downstream. From Leopold and Mad dock (1953).
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A21

"regimes" of flow. This is most clearly demonstrated 

by gradually increasing the velocity in a laboratory 

flume having a deep bed of sand which has been planed 

smooth. The flow regimes, with increasing velocity, 

are ripple, dune, plane, and antidune. The sediment 

in transport increases in this order. With regard to 

roughness, the plane-bed regime has less resistance to 

flow than does the dune regime.

In a natural stream the shift from a dune to a plane 

regime results in an increase in velocity and, consequently, a decrease in gage height even though the 

quantity of flow has increased. The regime of stream 

flow affects the depth as well as the rate of bed movement. For the ripple regime, the depth of disturbance 

is not as severe as the dune and antidune regimes. 

Simons and Richardson (1959) found lenses of fines in 

the bed during the ripple regime which are not present 

for the other regimes when these fines are carried as 

suspended load. They also found that under the dune 

regime the fine material does not settle and coat the 

bed, but there is a constant exchange between the fine 

material in suspension and that in the bed. Thus, 

when "clear" water returned, and if the stream remained in the dune regime, the fine material would be 

removed from the bed.

The banks of a stream may have little effect on the 

total resistance to flow if the stream is wide and shallow. 

A deep narrow section, on the other hand, may receive 

a large part of the total resistance from the bank. The 

bank roughness may result from the shape and size of 

the particles of sediment in the deposits or residual 

material, from vegetation, or from man-made devices. 

The roughness condition of the bank affects the 

nature and quantity of deposition along the bank during 

the recession of any storm runoff. Sand-bed streams 

have been observed that had mud deposits too deep and 

soft to wade across after the recession of storm runoff 

(less than bankfull stage) containing a large concentration of fine suspended sediment. These deposits were 

at a straight reach of the channel where one would not 

expect bank "building" and, therefore, it is assumed 

that this deposit would be eroded away during the 

rising stage of the next runoff. This kind of deposit 

is, then, only of a semipermanent nature. The roughness of a braided stream would have an increase in 

bank roughness proportional to the percentage increase 

of banks encountered for a representative number of 

cross sections in a reach.

Alinement of channels. Streams flowing in alluvium 

generally exhibit rather poor alinement ranging from 

an occasional bend for some streams to a high degree 

of meandering for others. Such bends affect the 

secondary circulation and hence the location and depth 

of scour and deposition in the stream bed. The cross

section of a river with a straight channel and a relatively 

flat bed is approximately trapezoidal in shape; whereas, 

a section at a bend is roughly triangular in shape with 

the deep part near the outside bank. Carey and Keller 

(1957) in a study of bends found that the deposit of 

sand on the inside bank of a bend was mostly that 

scoured from the outside bank immediately upstream. 

Thus the sand tends to travel across the thalweg in the 

reach of reversing curvature. The coarser sands are 

obviously deposited at the lower elevations and toward 

the head of the bar during such deposition. This phenomenon of cut and fill is most active at bankfull stage. 

At less than bankfull stage, velocities will be lower and 

incapable of depositing the sand at a reasonable height 

on the inside bend; and at more, the flow down the valley 

will tend to create currents not parallel to the bend of 

the stream channel and probably reduce the cut-and-fill 

velocity. Fine sediment from many sources may be 

deposited on the upper part of the inside bank during 

bankfull or higher stages. Occasional lenses of fines 

(silt and clay) in the fill bank (inside of bend) have been 

observed which logically are deposited by receding 

flood waters, then bound in place by rank vegetation 

before burial by sand during the next flood.

Experiments with hydraulic models at the Waterways 

Experiment Station (Lipscomb, 1952) show that the 

size of bends becomes smaller with either a decrease in 

flood discharges, the slope, or the angle of entrance to the 

bend; and, that the more erodible the banks, the wider 

and shallower will be the crossings to transport the 

greater load.

Both the straight or meandering types of stream on a 

sand bed have a relatively uniform gradient. However, 

if the stream channel contains considerable quantities 

of gravel and possibly rocks, the gradient is likely to be 

irregular and the channel will consist of alternate pools 

and riffles. This pool-and-riffle type of stream is 

logically susceptible to the collection of deposits of fine 

sediment during relatively long periods of low flow followed by rather sudden removal with increasing velocity 

during the early part of increased flow in the channel. 

The deposition of these fine sediments during low flow 

would be relatively high in concentration of radioactivity 

because of the small sediment transport of the stream 

under these conditions.

PARTICLE-SIZE GRADATION

Effect of chemical quality of water. Concise theory on 

the nature of flocculation for suspended sediment in 

natural streamflow is lacking. General experience has 

been obtained by noting the difference between apparent 

and ultimate size gradations when a given sediment is 

analyzed in settling mediums of both native stream 

water and distilled water with a dispersant. As men-
A22 TRANSPORT OF RADIONUCLIDES BY STREAMS

tioned previously, streamflow at a given reach has various degrees of turbulence ranging from little at the bank 

and other "dead water" areas to compound secondary 

circulation at midchannel. The turbulent motion 

inhibits flocculation because it, in effect, tends to prevent the drifting of particles toward each other that 

would ordinarily occur in still water. Turbulence is 

also a factor in disrupting floccules, if formed in quiet 

water.

It may be stated, then, that flocculation of sediment 

probably varies as the chemical nature of the stream, 

the kind of clay, the concentration of clay, and inversely, 

with the turbulence of streamflow. Since clay particles 

are very irregular in shape, it is assumed that mechanical as well as chemical binding is involved. This 

would be most likely for the clay-to-clay floccule and 

less likely for the clay-to-silt or clay-to-sand floccule.

Effect on surface area. Average-size gradation curves 

for both simultaneous suspended-sediment and bedmaterial samples are illustrated in figure 4 for three 

streams. These curves are considered indicative of 

the typical range of sizes of the particles of sediment 

transported by alluvial streams. Some streams may 

be encountered that are more unusual than those 

illustrated; for example, streams from the Sand Hills 

of Nebraska may contain suspended sediment of 

nearly the same particle size as that of the bed, and 

streams tending toward the pool-and-riffle condition

will have a much larger range of bed-material sizes, 

particularly the coarser sizes.

As indicated in the section of this report "Factors 

determining extent of sorption", the capacity of sediment for sorption of radioactive waste is related to the 

surface area of the sediment. On this basis, the 

particle-size curves of three streams indicate increasing 

capacity to carry such waste in the order, Middle Loup 

River at Arcadia, Nebr., Loup River at Fullerton, 

Nebr., and Mississippi River at St. Louis, Mo. On the 

basis of these average size-distribution curves, the 

surface area (computed as loosely packed spheres) of 

the bed-material sediment is 60, 140, and 100 squarecentimeters per cubic centimeter, respectively; and 

the suspended sediment is 350, 4,530, and 27,400 square 

centimeters per cubic centimeter, respectively. The 

sorptive capacity of the suspended sediment is, therefore, many times that of the bed material; and since 

most of the sediment is moved in the sampled or 

suspended zone, it is assumed that suspended-sediment 

transport is the more important consideration. It is 

further evident that the fines or sediments brought 

into the stream from sheet erosion are the most important as far as sorptive capacity is concerned. Hence, 

environmental factors contributing to erosion in the 

upland areas of the drainage basin may be more critical 

with respect to radioactive waste disposal than the 

transport characteristics of the stream channel.

100

z 40

20

0.001 0.002 0.005 0.01 0.02 0.5 0.1 0.2 0.5

PARTICLE SIZE, IN MILLIMETERS

FIGURE 4. Particle-size gradation of suspended sediment and bed material for three typical alluvial streams.

2.0 5.0
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A23

CHANNEL CONTROLS

Channel controls affect the suspension and deposition of sediment because of their control of the flow of 

water. A large deep reservoir holding water for weeks 

or months may trap 100 percent of the inflowing sediment and cause separate deposits of sands and fines, 

whereas a bank lining would change only the flow 

characteristics and thereby change the mode of sediment transport. The effectiveness of a given control 

in altering normal suspension and deposition depends 

not only on the control itself, but also on the character 

and concentration of the sediment in transport and on 

the chemical character of the water.

Trap efficiency. Table 4 shows the estimated efficiency of several kinds of structures for trapping the 

clay, silt, and sand fractions of sediment. The capacityinflow ratio for reservoirs, or the acre-feet of capacity 

per acre-feet of annual flow has been related to trap 

efficiency of normally ponded reservoirs by Brune 

(1953). The curve defined by data from more than 

40 measurements indicates the following:

Percent sediment 

Capacity-inflow ratio trapped

0.005-_--___-___-__--__ 30

0.02. __________________ 60

0.1-______-_-___.______ 85

Percent sediment 

Capacity-inflow ratio trapped 

0.3____________________ 95

1.0_________________.__ 98

TABLE 4. Estimated sediment-trap efficiency, in percent, of 

various types of structures for channel and storage control

Description and purpose

Large drainage areas 10,000 square miles or more: 

Reservoirs for power and storage (high capacity-inflow

Reservoirs for irrigation and water supply: 

High capacity-inflow ratio ..

Bank or channel control

Soil Conservation Service structures on drainage of 10 

square miles or less: 

Detention reservoir with draw-down tubes and sediment storage:

Low capacity-inflow ratio

Drop spillways, chutes, and other channel-control 

structures- -....

Clay

80-100

70-100 

10-100 

0-50 

0-60 

0 

0

10-70 0-30

0

Silt

100

100 

50-100 

0-80 

0-80 

0 

0

50-100 

10-50

0

Sand

100

100 

100 

20-100 

20-100 

0-50 

0

100 

80-100

0

Brune also notes that the Tennessee Valley Authority 

has used the ratio of the period of retention to the 

mean velocity as an index to trap efficiency. This is 

similar to the capacity-inflow ratio because both imply 

a rate of water movement through the reservoir.

Reservoir deposition. The ideal concept of reservoir 

deposition assumes that deposition begins at the upstream limit of backwater effect with the deposition 

of the largest particles in transport. Increasingly 

finer particles are deposited with progressive decrease 

in transport capacity of the flow until all material of 

the size of fine sand or larger is deposited. The silt

and clay sizes are transported, in an undefined manner, 

beyond the sand deposit. Deposition of these fine 

particles may occur in an unknown sequence along 

the floor of the reservoir. Density flows may result 

in the transport of clay throughout the length of the 

reservoir. This idealistic pattern is complicated by 

the forward growth of the sand deposits over previously 

deposited silts, encroachment of one kind of deposit 

over another owing to fluctuations in pool level, 

reworking of deposits by waves and erosion, and threedimensional flow phenomena, such as seasonal turnover 

of deep waters, owing to temperature gradient 

(thermocline).

The headwater deposit may be relatively simple as 

in a long narrow reservoir, or it may be extremely 

complicated owing to the presence of many side 

channels, as for the Mississippi Kiver at the Gulf of 

Mexico.

Figure 5 (Witzigman, 1955) illustrates the relation 

of suspended-sediment concentration and particle size 

to cross-sectional area, depth, and mean velocity for 

the backwater reach of Garrison Keservoir the narrow 

or confined type July 7 to 8, 1954. The concentration decreases with increasing cross-sectional area and 

depth and decreasing velocity downstream.

Density currents, which are capable of moving fine 

sediment throughout a reservoir, are caused by differences in temperature, salinity, and more usually, 

sediment content. The relatively muddy stream entering a clear reservoir collides and partly mixes with the 

"still" water and then moves along the bottom propelled by the slope of the bed of the impounding 

reservoir and the pressure of additional muddy water 

on the delta deposits. Deposits from "dead" density 

currents will consist of fine clays and may occur in 

the deepest water near the dam.

Degradation downstream from control. The Corps of 

Engineers (1959) in a study of sediment problems in 

the Arkansas Kiver, notes the following factors for 

the occurrence of degradation downstream from a 

control:

1. The stream must have carried a relatively large 

bed-material load prior to completion of the control, as this is a measure of its ability to transport 

the existing bed material.

2. The control must provide sufficient detention time 

of water in the reservoir to trap most of the bedload.

3. If most of the load was transported by large discharges prior to construction, then these large 

discharges must prevail to some degree after construction.

4. Material in the bed must be of a size ordinarily 

carried as bedload with the new flow regime.
A24 TRANSPORT OF RADIONUCLIDES BY STREAMS

CM

CM

CO 

CM

AGGRADATION 

< Q 

CO CO CM CM

RANGES

CO 

CM m

CM CM 

I 20 3.5

£ 1560

CC 

O

1550 1540 1530 1520 1510 

RIVER MILEAGE (1941 ADJUSTED)

1500 149C

o

8

FIGURE 5. Relation of sedimentation to channel characteristics through backwater reach of Garrison Reservoir, N. Dak., July 7-8,1954, from Witzigman (1955).

CRITERIA FOR IDENTIFYING POTENTIALLY 

HAZARDOUS STREAMS

In general the criteria for identifying streams which 

are potentially hazardous with respect to the deposition 

of radioactive sediments are not simple and clearcut. 

More often than not, a hazardous situation will involve 

the combined action of several factors. Taken individually, none of the factors might cause objectionable conditions; taken collectively, however, the

addition or subtraction of a single factor might radically 

alter the entire picture.

The development of a hazardous situation obviously 

implies the requirements that there be U) uptake 

and concentration of significant quantities of radioactivity by stream sediments, (2) stream geometry 

and sediment conditions conducive to extensive local 

deposits of contaminated sediments, and (3) a rate 

of buildup of radioactivity in deposits which exceeds
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A25

the rate of natural radioactive decay. In this section 

the hazard criteria are identified and briefly discussed 

in terms of these three requirements.

UPTAKE BY SEDIMENTS

With respect to the sediment itself, the total available 

surface area of the suspended-sediment particles is the 

most obvious index of hazard potential. Concentration and size distribution are fairly reliable indicators 

of surface area.

Fortunately the greater sorption capacity of the 

fine sediments is to some extent offset by the tendency 

of colloidal materials to remain in suspension except 

when flocculation occurs. Heavy concentrations of 

contaminated fine sediments might occur in density 

currents at the bottom of reservoirs and pools, but 

there the chances for dangerous exposure to humans 

would be small.

The chemical and mineralogical nature of the sediments, particularly the fines, are also a factor to be 

considered in assessing hazard potential. Sediments 

characterized by high ion-change capacities and high 

zeta potentials would bear watching. The nature 

and amount of sorbed nonradioactive components 

should be considered as an indication of residual 

sorption capacity for radioactive components.

Concentration of radioactivity in the waste-stream 

water solution is obviously related to hazard potential. 

The chemical composition of radioactive components 

would be important in estimating the extent to which 

sorption might occur.

The total ionic concentration in solution is likewise 

an important factor. Normally a low-ionic concentration of nonradioactive substances would mean correspondingly increased sorption of radioactive 

substances.

The reversibility of sorption reactions should also 

be considered. Irreversible sorption reactions would 

in most cases be considered as potentially more hazardous than reversible reactions.

The presence of significant quantities of a flocculating 

agent in streams containing radiocontaminated clays 

could be a source of danger.

The degree of dispersion of radioactivity in the stream 

cross section should be evaluated. For example, 

concentration of the radioactive wastes in a density 

current flowing along the bottom of a stream would 

probably lead to an increased degree of uptake by the 

more stable bed sediments. Generally this would be 

considered undesirable.

CONCENTRATION AND LOAD OF SUSPENDED 

SEDIMENT

The concentration and load of suspended sediment 

in streams can be considered one of the important

criteria for identifying potentially hazardous streams 

because of the effect on amount of available surface 

area for sorption. Further, it is important as a factor 

in the nature and extent of deposition and erosion 

within the stream system.

The nature of the concentration and (or) load variation with respect to time may be important because it 

is expected to indicate the capacity or lack of capacity 

of the stream to transport a given input of waste. For 

example, a stream with a relatively uniform water 

discharge and high concentration of fine sediment 

would probably maintain the waste in suspension on, 

or with, the fine sediment. On the other hand, a 

stream with a large range of water discharge and sediment load recieving the same concentration of waste 

would be expected to carry the waste in "slugs", because 

the waste not having an abundance of fine suspended 

sediment for sorption during low flow periods, would 

probably be sorbed on the particles in the stream bed. 

Then, during the relatively short periods of storm runoff 

with high concentrations of sediment, the waste held 

on the bed may be exchanged to "free" suspended 

particles and (or) moved downstream considerable 

distances as bedload.

Discharge-weighted mean concentration of sediment 

is being mapped for the United States by Rainwater 

(1959 personal communication) as a part of a Geological Survey project on composition of rivers, and can 

be used as one means of classifying potentially hazardous streams. The variation of sediment concentration 

and load with respect to time, however, has not been 

defined, nor have criteria been established or sufficient 

data made available for this kind of definition. This 

can be approximated, however, on the basis of climate, 

size of drainage basin, and control of the stream flow. 

The magnitude of time variation in concentration and 

load would be expected to be greater, for example, on 

most Kansas streams than on South Carolina streams, 

and on the uncontrolled upper Colorado than on the 

controlled lower Missouri River.

CONDITIONS CONDUCIVE TO SEDIMENT DEPOSITION

Conditions conducive to the formation of sediment 

deposits containing large amounts of radioactive waste 

are more likely to be found on the inside of a bend on 

a stream near the source of waste disposal rather than 

on the banks of a straight stream channel, on a stream 

exhibiting a considerable range of sediment concentration and water discharge rather than a stream of nearly 

uniform water discharge and sediment concentration, 

and on a stream with man-made channel controls 

rather than on an uncontrolled stream.

Sediment of the coarser fractions, usually deposited 

on the point bar on the inside of a stream bend, is
A26 TRANSPORT OF RADIONUCLIDES BY STREAMS

derived mostly from that being cut from the outside 

bank of the opposite bend immediately upstream. The 

finer fractions, usually deposited only at the upper 

elevations of the bar, or during the recession of the 

storm runoff event, may be derived from many sources 

including bank cutting in the immediate channel, or 

gully and sheet erosion in the upper part of the drainage basin. The point bar at the first bend immediately 

downstream from a source of waste may then be built 

of a large mass of contaminated sand. In this discussion it is assumed that the waste is sufficiently mixed 

with stream flow so that contact with the sediment in 

transport is relatively uniform.

Streams of widely varying discharge are conducive 

to bank and flood plain deposits. The most rapid 

deposition on the inside bank of the meandering 

channel occurs during the high rates of flow; especially 

so, for the fines at the top of this deposition bank. 

Flood plain deposits obviously cannot occur without 

the generally unusual high rates of flow. Deposits of 

fines along stream banks other than point bars usually 

occur during the recession of a storm event for which 

relatively large concentrations of fines are carried. 

These may be of only minor significance because they 

are transported and deposited when stream flow and 

concentration are considerably greater than average 

and, therefore, the concentration of waste in the deposit 

is likely to be low. This again assumes a uniform 

rate of waste disposal.

Deposits of contaminated sediment may accumulate 

within the controlled channel when flow and sediment 

concentration are low for long periods of time; and 

thus, with a constant rate of waste disposal, the concentration of radioactivity in the water and on the 

sediment would be high. Similar to channel control, 

the most critical deposits on the pool-and-riffle type 

of stream are likely to occur during the long periods of 

low flow when the fines are deposited in the slack 

water resulting in an intensive concentration of radionuclides in the pool. With this type of stream, the 

deposit is usually removed during the rising stage of 

the next period of storm runoff.

In summary then, the sedimentation criteria for 

identifying potentially hazardous streams may include:

1. The sediment concentration and water discharge 

or load. High concentrations of sediment may 

cause many kinds of deposits but may result in 

relatively low concentration of radionuclides. 

Low concentration of sediment may result in 

some small accumulations of sediment deposits of 

high waste content.

2. The time variation in sediment concentration and 

load. The waste, under uniform release, is likely 

to build up during low flow and then move as a

slug for possible deposit on high banks or flood 

plains during high flow.

3. The nature of channel geometry. A meandering 

channel is characterized by building of point bars 

on the inside bends. The pool-and-riffle type of 

stream accumulates the waste in pool reaches 

during long periods of low flow. A channel maintaining flow almost continuously in the dune 

regime moves fine sediment in and out of the 

bed almost uniformly in time, whereas a channel 

flowing in the ripple regime most of the time may 

accumulate fines in the bed as lenses and upon 

occasional shifting to the dune regime will move 

these fines from the bed.

4. The nature and extent of water and channel controls. 

Reservoirs, for example, may trap up to 100 

percent of the sediment, whereas other controls 

may serve only to concentrate the waste only 

during the low flow.

BATE OF BUILDUP OF BADIOACTIVITY

In order to assess the hazard potential arising from 

the buildup of radioactivity in sediment deposits, both 

the decay rates of the radioactive components and the 

rate of sediment deposit at locations like those discussed 

in the preceding section would have to be investigated. 

Also, the frequency a;t which sediment deposits are 

flushed out and their subsequent movement and 

deposition would need to be considered. A combination of conditions involving an intermediate or slow 

radioactive decay rate, a high deposition rate of contaminated sediments, and infrequent flushing of deposits 

would usually be the most hazardous.

CLASSIFICATION OF STREAMS IN THE UNITED STATES 

ACCORDING TO HAZARD POTENTIAL

The hazard potential of radioactive waste in streams 

may be considered in view of differences in stream flow, 

in channel geometry, and in the concentration and character of sediment as they may affect deposition of sediment and consequent waste. However, streams are 

very complex with respect to the magnitude and variation of these features; and, therefore, classification according to hazard potential is difficult and indeed 

almost remote in view of limitations concerning basic 

knowledge of the relation of these features.

A review of the sedimentation criteria for identifying 

potentially hazardous streams for radioactive-waste 

disposal discussed in the previous section indicates 

many conflicting aspects for consideration. For example, a stream with relatively large water and sediment discharges may be conducive to extensive deposition and erosion within the channel; but, because of 

the high rates of water and sediment movement, the
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A27

concentration of radioactive waste may be very low. 

Further, a meandering channel results in a nearly continuous building of a deposit as a point bar, but most 

of this building occurs during high rates of water 

discharge when the concentration of waste in the water 

is low.

The sand-bed stream of good alinement and carrying 

a relatively uniform water discharge and concentration 

of fine sediment would be the least hazardous kind of 

stream to transport a given uniform amount of radioactive waste without accumulating extensive and (or) 

concentrated deposits. This would assume the flow in 

the channel to be in the dune, plane-bed, or antidune 

regimes so deposits of the fine sediment would not accumulate in the bed; and, if minor bank deposition 

occurred, it would be when the flow in the channel 

and concentration of sediment are relatively high. 

Such a stream would have relatively minor and uniformly concentrated accumulations of waste in relation 

to both time and space in the bed and along the banks.

One of the most hazardous conditions may occur 

either on the pool-and-riffle type of stream or a large 

river controlled with low dams for navigation purposes. 

For these situations, the pool or pools immediately 

downstream from the disposal outlet may accumulate 

extensive and highly contaminated deposits in the bottom of the pools. This results from the relatively low 

water discharge and very low concentration of sediment, 

and, consequently, a very high concentration of waste, 

accumulating for long periods of low water flows. When 

a relatively large increase in flow occurs after weeks or 

months of accumulation, most of the contaminated deposit will move downstream and thus become available 

for bed, bank, or flood-plain deposition.

The range of conditions encountered with regard to

(1) the quantity of sediment and water discharge,

(2) the variation of sediment and water discharge with 

respect to time, (3) the mineralogic composition of the 

sediment, (4) the channel geometry, and (5) the nature 

and extent of the water and channel controls makes it 

apparent that each site of radioactive-waste disposal is 

unique with respect to the effect of sediment in causing 

hazardous deposits of waste. Most of these criteria 

vary considerably in a given stream. With regard to 

channel geometry, for example, Leopold and Wolman 

(1957) state that straight channels cannot be readily 

differentiated from meandering and braided patterns 

by definitive combinations of hydraulic variables, yet 

the regular spacing and alternation of shallows and 

deeps is characteristic of all patterns.

Figure 6 illustrates the general magnitude of waterdischarge-weighted suspended-sediment concentration 

for streams east of the Mississippi River as one of the

factors in the criteria that may be useful for classification. This map is being extended to include the remainder of the United States, at the time of this 

writing (1959).

Another factor for which some data are available concerns the particle size or the relative sorptive capacity 

of the sediment in transport for the different streams. 

This factor is illustrated in figure 7 where the ordinate 

is a measure of the difference in bed and suspendedsediment sizes and plotted as a ratio of the median (50 

percent) bed size to the median suspended-sediment 

size; where the abscissa is a measure of sediment fineness and is plotted as the product of the sizes for which 

both the suspended-sediment and bed sizes contain 

15 percen.t by weight finer. The graph indicates an 

increasing potential for hazardous deposits in the direction of increasing difference of bed and suspendedsediment size and in the direction of decreasing measure 

of coarseness.

Many dimensional and dimensionless diagrams may 

be prepared by different measures resulting from the 

data on the particle size of suspended and bed sediments. These may include surface area of the particles, 

the standard deviation of the size gradation a measure 

of the range in sizes and combinations of these with 

the concentration and load in transport. A logical, but 

untried, plot would relate the surface area for a unit 

concentration in suspension to the median size of suspended sediment with the standard deviation of size 

as the third variable.

CONCLUSIONS

Many of the mechanisms involved in the dispersion, 

transportation, and concentration ol radioactive wastes 

in natural streams by sediments are complex and not 

well understood. In this section, the various subject 

areas of this report are evaluated according to present 

knowledge. Areas where knowledge is particularly 

deficient are indicated.

Characteristics of waste materials. The properties of 

low-level liquid wastes, which are of interest with regard 

to potential hazards arising from the contamination 

of stream sediments, may be classed as (1) nuclear, 

(2) chemical, and (3) physical characteristics.

Nuclear characteristics of the radionuclides contained in the wastes such as type and energy level 

of radiation, and radioactive decay rate coupled with 

the biochemical characteristics determine the potential 

health hazard resulting from a given amount ol radioactivity.

The chemical composition of the radioactive waste 

solution is an instrumental factor in determining the 

extent to which sorption of radioactive components
A28 TRANSPORT OF RADIONUCLIDES BY STREAMS

Concentration class 

in parts per million

FIGURE 6. Concentration of suspended sediment in streams east of Mississippi River. From written communication, F. H. Rainwater, 1959.
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A2

8 1000

cf ^8

cSh-~

Z

LU

5

O

LU 

V)

O

LU

O

Z

& 100

D 

</)

O

Z

<

Q

LU

CD

LL.

0

LUtsi

V)

Z

LU 10

O

Z

LU 

CC

UJ

LL.

LL.

Q

U0

LU

QC

D

(/)

LU

5

1 

A

£>

o

»

0 «

X

X

X

ffl

A

 =*= 

0

n

1

EXPLANATION

 Bijou Creek near Wiggins, Colo.

O Mississippi River at St. Louis, Mo.

X Mississippi River at Mayersville, Miss.

<T Yadkin River at Yadkin College, N. C.

A Loup River at Fullerton, Nebr.

BB Fivemile Creek at Shoshoni, Wyo.

0 South Fork White River at White River, S. Dak.

Hh Medicine Creek at Cambridge, Nebr.

 Middle Loup River at Arcadia, Nebr. 

 Snake River at Burdge, Nebr.

D Colorado River (4 sections) Needles, Calif.

to Taylor's Ferry

*

D

lO'5 lO'4 ID'3 10-2 10' 1

MEASURE OF RELATIVE COARSENESS OF BED AND SUSPENDED SEDIMENT, D15Bx015S MILLIMETERS 2 

FIGUKE 7. A measure of hazard potential for stream deposition of sediment containing radioactive wastes.

by sediments occurs. Total ionic concentrations, pH 

values, the presence of organic compounds such as 

detergents, and reacting dissolved substances are all 

important in this respect.

Physical characteristics of the waste solution such 

as viscosity, density, and temperature are important 

in determining how effectively the radioactivity will 

be dispersed through the stream section by the process 

of turbulent diffusion.

There is considerable information in the literature 

on the nuclear characteristics of low-level radioactive 

waste solutions, but considerably less information on 

the chemical composition and physical characteristics. 

Data on the last two aspects should be systematically 

assembled and analyzed, and the results should be 

published.

TurbvJ.ent diffusion. The literature on turbulent 

diffusion of submerged jets and diffusion by boundarygenerated turbulence is very extensive. Nearly all 

this literature, however, considers an infinite or semiinfinite domain rather than a confined channel. The 

applicability of the solution for these domains to 

confined channel problems, whether by statistical or 

Fickian theory is very much restricted. Literature 

applying the concept of sediment and aquatic biota as

sources and sinks for radioactivity discharged in an 

alluvial channel is sparse, even when the relatively 

well-advanced status of the Fickian approach to analysis of turbulent diffusion is considered. Well-planned 

theoretical investigations and field and laboratory 

experiments are needed.

Sorption. Available evidence indicates that sorption 

of waste materials from solution by stream sediments 

is the rule rather than the exception. Experiments 

have demonstrated that sorption of radioactive components from dilute solutions may exceed 90 percent, 

and that the concentration of radioactivity on the 

surface of sediment particles may become many thousands of times as great as the concentration in the 

surrounding liquid.

Ion exchange is apparently the predominant mechanism involved in the sorption of radiocontaminants 

by stream sediments, although physical sorption may 

also play an important role particularly where the 

coarser sediments are concerned. However, owing 

to the inverse relationship of both specific surface and 

surface chemical activity to particle size, sorption 

capacity per unit weight of sediment tends to increase 

as particle size decreases.
A30 TRANSPORT OF RADIONUCLIDES BY STREAMS

M*uch literature on sorption phenomena has originated 

from physical chemistry and allied fields. Ion exchange, in particular, has been subjected to considerable 

study. Other types of sorption such as physical 

sorption and, in particular, sorption by diffusion into a 

solid are less well understood. Experimental techniques 

are reasonably straightforward and quite well established. In any case a fairly adequate frame of reference 

for the continued study of sorption phenomena has 

been developed, at least for the relatively simple 

systems which involve only a single solvent, solute, 

and sorbent.

There is, however, a considerable deficiency of 

knowledge concerning the mechanics of sorption in 

more complex systems. The effects of pH, total ionic 

concentration and detergents on sorption reactions 

require considerable further investigation as does 

sorption from mixed solutions. The sorption capacities 

of different types of sediments under various sets of 

conditions should be studied. The reversibility of 

sorption reactions is another area requiring attention.

Bed sediments probably sorb less waste than do 

suspended sediments where the solutes are for the most 

part uniformly distributed throughout the flow cross 

section. It appears, however, that little work has 

been done on this aspect of the sorption problem. It 

would be advisable to investigate sorption by bed 

sediments.

The study of sorption phenomena in natural streams 

will require the collection and compilation of a great 

deal of additional basic data from streams throughout 

the nation on the physical and mineralogical properties 

of sediments, and the presence of competing solutes 

in the water.

Sediment transport. Identification of potentially 

hazardous streams on the basis of fluvial sediment 

transport is a new field of endeavor. The broad 

subject of evaluating the drainage area or environmental 

factors, as they affect the quantity and character of 

sediment supplied to the streams, has been investigated 

in only small and usually unrelated segments. The 

subject of channel and flow characteristics of streams, 

as they affect the rate of transport and the nature and 

extent of deposition, is more advanced but still contains 

many undetermined elements.

The environmental and channel problems cannot be 

considered separately becuase the accumulation of 

sorbed radionuclides in the stream bed and in other 

kinds of deposits will depend on the movement of 

individual sediment particles, whether they be in 

suspension or moved intermittently. The nature of 

particle movement will depend on the flow characteristics of the channel as they affect suspension or other 

movement. In consideration of gross transport and

deposition, the depth to which ripple or dune movement 

takes place, the interchange and circulation of fine 

sediment with coarse, and the nature of semipermanent 

deposits with respect to the frequency and magnitude of 

runoff events are primary.

GLOSSARY OF TERMS

Absorption the process of taking up within, implying 

nearly uniform penetration.

Adsorption the process of taking up on the surface.

Aggradation the general raising of the bed of a stream 

in a given reach.

Anti-dunes symmetrical sand and water waves which 

are in phase and moving slowly upstream in groups of two or more, 

becoming gradually steeper on their 

downstream face until they break.

Bed load that part of the solids load of the stream 

which is moving in almost continuous 

contact with the streambed, being 

rolled or pushed along by the force of 

the moving water.

Clay crystalline fragments of minerals, essentially hydrous aluminum or magnesium 

silicates less than about 0.004 millimeters in size.

Concentration dry weight of material per unit volume 

or unit weight of solution. Concentration of sediment is often expressed 

in parts per million (ppm) by weight; 

of solutes, in parts or equivalents per 

million; of radioactivity in microcuries 

per milliliter (/jc/ml).

Curie the quantity of a radioactive substance 

which undergoes 3.70 x 1010 disintegrations per second.

Degradation the general lowering of the bed of a 

stream in a given reach.

Density current a relatively dense mass of water moving 

slowly through a body of standing 

water by virtue of a difference in temperature, concentration of solutes, or 

concentration of fine sediment.

Desorption the release of sorbed matter to solution.

Dune a sand wave of approximately triangular 

cross section (in a vertical plane in the 

direction of flow) with a gentle upstream slope and steep downstream 

slope which travels downstream by 

movements of the sand up the upstream slope and the deposition of it 

on the downstream slope, 

the amount of ions which are chemically 

sorbed on solids in such a fashion that 

they can be replaced by other ions. 

An indication of chemisorption capacity. Exchange capacity is usually 

expressed in milliequivalents (meq) 

per 100 g of material at neutrality 

(pH 7).

Flood plain the portion of a river valley covered by 

water in time of flood and built of 

sediments carried by the stream.

Exchange capacity
UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A31

Gravel 

Half life

Ion exchange 

Sorption isotherm 

Isotope

Isotropic diffusion

MFC 

Nuclide

pH

Radioactive decay

Radioisotope 

Radionuclide 

Riffle

Ripple

Roentgen

inorganic granular material in the size 

range of 2.00 to 64.0 millimeters.

one of the fundamental characteristics 

used to identify a particular radioactive species, the half life of a radioisotope is the time required for onehalf the atoms to decay.

the process by which exchangeable 

sorbed ions are displaced and subsequently replaced by other ions of like 

sign.

a curve representing the relationship 

between sorption from and concentration of solute in solution, for conditions 

of constant temperature.

any of two or more nuclear species having 

the same atomic number, therefore 

representing the same element, but 

having different mass numbers, hence 

different atomic weights.

the diffusion process is isotropic in character. Isotropic implies that the character of the diffusion is independent 

of coordinate direction at any given 

specified point.

maximum permissible concentration of 

radioactivity often expressed as microcuries per milliliter (juc/ml) or micromicrocuries per liter (ju^c/1).

any nuclear species characterized by the 

number of neutrons and protons of 

which it is composed, and therefore 

characterized by its atomic number 

(the number of protons), and its mass 

number (the number of protons and 

neutrons).

the negative logarithm of the hydrogen 

ion concentration in gram atoms per 

liter. A pH value of 7 indicates 

neutrality, numbers less than 7 increasing acidity, and numbers greater 

than 7, increasing alkalinity.

a probability process; the rate of decay is 

proportional to the number of radioactive atoms present at any time.

a radioactive isotope.

a radioactive nuclide.

a short and shallow reach of stream 

channel with a slope considerably 

greater than the stream valley, the 

section containing rock or a deposit of 

the more coarse material moved by 

the stream.

small ridges and/or crests, and troughs 

similar to dunes in shape, but smaller in 

magnitude, which have rather small 

width normal to the direction of flow.

a unit of radiation defined as the quantity 

of X- or gamma-radiation such that 

the associated corpuscular emission 

per 0.001293 gm. of air (=1 cc STP) 

produces, in air, ions carrying 1 

electrostatic unit of quantity of electricity of either sign. A roentgen is

equivalent to 1.61 x 1012 ion pairs per 

gram of air or the absorption of 83.8 

ergs of energy per gram of air. The 

abbreviation for milliroentgen (10~3 

roentgen) is mr.

inorganic granular material in the size 

range of 0.062 to 2.00 millimeters.

fragmental material that originates from 

weathering of rocks and is transported 

by, suspended in, or deposited by 

water.

the ratio of dry weight of sediment to 

total weight of the water-sediment 

mixture, usually expressed in parts per 

million (ppm).

inorganic granular material in the size 

range of 0.004 to 0.062 millimeters.

a dissolved substance.

a substance capable of, or used in, 

dissolving something.

a substance that sorbs.

the process of taking up either by 

absorption (within) or adsorption (surface.)

an index of the extent of surface of a 

disperse system which is expressed as 

the surface area per unit weight or 

per unit volume of the dispersed phase.

sediment moving in suspension in water 

as a result of turbulent currents or by 

colloidal suspension.

percentage of sediment trapped by a 

channel or water control structure.

a term used herein which is also sometimes called turbulent exchange, eddy 

diffusion or dispersion. The transfer 

of matter by means of the eddy motion 

of the fluid in a turbulent flow field.

that part of the sediment load of a 

stream, usually silt and clay, which is 

composed of particle sizes smaller 

than those found in appreciable quantities in the shifting portions of the 

stream bed.

the magnitude of the electric charge of 

soil particles in a colloidal suspension, 

usually expressed in millivolts (mv). 

More explicitly, the zeta potential is 

defined as the work required to bring 

a positive charge from the potential of 

a free solution to the point where the 

charge will migrate with the colloid 

when subjected to an electropotential 

gradient.

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Batchelor, G. K. and Townsend, A. A., 1956, Turbulent diffusion: 

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Sand 

Sediment

Sediment concentration

Silt

Solute 

Solvent

Sorbent 

Sorption

Specific surface

Suspended sediment 

or suspended load

Trap efficiency 

Turbulent diffusion

Wash load

Zeta potential
A32 TRANSPORT OF RADIONUCLIDES BY STREAMS

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UPTAKE AND TRANSPORT BY STREAM SEDIMENTS A 33

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INDEX

Abstract.

Page

Al

Barker, F. B., studies onsorption________________________ 14-15 

Biochemical properties of radionucleides ___________________ 3-4 

Biota in flow systems, relation to turbulent diffusion in alluvial channels__ 6-7 

Boussinesq's exchange coefficients in Fickian equation_____________ 8

Capacity-inflow ratio, relation to trap efficiency in reservoirs_________ 23 

Carritt and Qoodgal, studies on sorption .-__________________ 13-14 

Cation-exchange process.. __ ______._____________ 13 

Cesium, carrier-free, percentage sorbed by clay...______________ 15 

Channel alinement, relation to sediment transport_______________ 21 

Channel factors associated with sediment transport_____________ 17,19,20 

Channel roughness, relation to sediment transport_______________ 19-21 

Channel system, relation to sediment yield..__________________ 18 

Channels in flow systems, classification..____________________ 6 

Chemical nature of sediments, affecting sorption________________ 15 

Chemical properties of radionuclides... _.__._______._____ 4 

Chemical quality of water, effect on flocculation________________ 21-22 

Chemisorption, defined. ___________________________ 11 

Continuous infinite cross-stream line source, in bed of isotropic homogeneous

flow field______________________....___...... 10

Continuous line source along stream bed____________________ 9 

Continuous point source, infinite anisotropic domain..____________ 10 

infinite isotropic domain ___... ___________________ 9,10 

Continuous stochastic process applied to turbulent diffusion._________ 8 

Copper, precipitated as a basic salt. ........ __ .._.__ 14

Darcy-Weisbach coefficient, used in determination of diffusion coefficient K.. 10 

Degradation downstream from control, factors for_______________ 23 

Diffusion coefficient K, analytical determination________________ 10,11 

Discontinuous-movement method applied to turbulent diffusion. . 8-9

Environmental factors associated with sediment supply...__.-._____ 17

Eulerian form for statistical turbulent-diffusion theories__._ ......_ 8

Exchangeable cations in clay-mineral soils__._ ____._______ 13

Fickian theories for turbulent diffusion ..___.....____..____ 7-8,9-10

Field conditions, relation to turbulent diffusion in alluvial channels...___ 6-7

Flocculation of sediment, affected by chemical quality of water. ____ 22

relation to turbulence_ _________________________ 22

relation to type of clay..__________________________ 22

Freundlich isotherm equation____._____________________ 15

Glossary of terms_._ ..___.______.______________ 30-31

Hazard potential, stream deposition of radioactive sediment__._.____ 28,29 

Hazardous streams, sedimentation criteria for identifying____._____ 26 

Hofmeister ion series._ . . . 13,15

Infinite line sources normal to mean velocity.___._______._____ 10 

Instantaneous point source, infinite anisotropic homogeneous turbulence field. 9,10 

infinite isotropic homogeneous turbulence field_______ _____ 9,10 

Ion-exchange process__. _______. _____________..______ 13 

Ionic adsorption____-_-____..._____-_-___-_-____ 13,25 

Iron, ferric, precipitated as a basic salt 14

Lagrangian system, statistical turbulent diffusion theories. 

Lyotropic ion series_.. _ __ 

Page

Microscale of turbulence, Lagrangian system.. A8 

Mineralogic nature of sediments, affecting sorption.-. 15 

Molecular diffusion, referred to_____._._. __ . 6 

MFC of unidentified radionuclides, recommended 4

Nuclear properties of radionucleides 3 

Orlob, research on turbulent diffusion . 10

Particle-size gradation of suspended sediment 21-23 

Particle size of sediments, affecting sorption....... 15,28,29

Phosphorus, uptake by bentonite and fuller's earth__ 14 

Precipitation, relation to sediment transport 17-18

Radioactive wastes in streams, disposal_ 1-2

properties and types__ .. 3-4

sources__ ..____....___ 3

Radionuclides, properties with respect to waste disposal- 3-4

Reactor-cooling water, radionuclides in 4,5

Relative mass density of radioactive contaminant..__.. .. . 7

Reservoir deposition, ideal concept of. 23,24

Reynold's number, used in research on turbulent diffusion. 10

Sediment characteristics. 16-17 

Sediment deposition, conditions conducive to... . 26-26 

Sediment in flow systems, relation to turbulent diffusion in alluvial channels. 6-7 

Sediment transport .___ . 30 

Sinks for radioactivity in a flow system_ ....... 6

Sorption, defined . 11

factors influencing extent ... . 15,29-30

Sorption isotherm______ ...___ ......__ 12

Source, along stream bed, continuous line. ..__ 9 

in bed of isotropic homogeneous flow field, continuous infinite cross-stream

line 10

in infinite anisotropic domain, continuous point__.... . 10

in infinite anisotropic homogeneous turbulence field, Instantaneous point. 9,10

in infinite isotropic homogeneous turbulence field_ 9,10

normal to mean velocity, infinite line________..._____ 10

Statistical theories of turbulent diffusion. ___..__ - 8-9,10

Stochastic processes in turbulent-diffusion theory...... 8

Strontium, precipitated as a basic salt._ .. 14 

Submerged-jet theory applied to turbulent diffusion.. 7 

Surface area, relation to particle size of sediment .. . 22 

Surface-tension phenomena.. ____ .- - 12 

Suspended sediment, concentration in hazardous streams 25,27,28

Time scale of turbulence, Lagrangian system. .. 8

Turbulence, relation to sediment transport... .. 18-22

Turbulent diffusion, fundamental equation in Lagrangian system. 8

in dispersion of waste solutions___ .. 5-6,29

theories in Eulerian form_......__ .. 8

Uptake of radioactivity by suspended sediment..... 25 

Velocity auto-correlation coefficient, Lagrangian system. 8

Waals, van der, sorption forces .. 11 

Waste effluent, characteristics . .. 16-17,27-28 

Watershed area, relation to sediment transport 17

Zeta potential, in ionic exchange .. 13,25

A35