Mass Transfer Studies in Sorbing Porous Media: III. Experimental Evaluation with 2,4,5-T
M. TH. VAN GENUCHTEN,2 P. J. WlERENGA, 3 AND G. A. O'CONNOR3
ABSTRACT
„
.
j u.
*.
., _, . . . ., «.
Comparisons are made between observed and calculated effluent
concentration distributions for the movement of 2,4,5-T (2,4,5trichlorophenoxyacetic acid) through 30-cm long unsaturated soil columns. The comparisons are made using both analytical and numericalsolutions of a previously published model, which included the effects of
intra-aggregate diffusion and adsorption. The results in this study indicate that intra-aggregate diffusion and adsorption/desorption are themain mechanisms responsible for effluent tailing. An estimated 60% of
the adsorption was found to occur in the stagnant region of the soil.
When intra-aggregate diffusion was included in the model, the observed adsorption/desorption
hysteresis phenomenon found to be sigF.„..i n several. earlier. . . .studies,.
ui less- important.
mficant
w a sushown. t oub e muchin describing the observed concentration distributions.
Additional Index Words: intra-aggregate diffusion, adsorptiondesorption, hysteresis, miscible displacement, 2,4,5-T.
_____________________N PART
THIS• STUDY(van uenucmen
Genurhrpn ana
and Wierenaa
7™ , I OF,UDYJ V
Wierenga,Liy/oa), a theoretical model was developed to describe themovement of chemicals through unsaturated, aggregatedI

sorting porous media. Analytical solutions were derived forboth the mobile and immobile liquid regions of the medium,

assuming the presence of a linear equilibrium isotherm.
These solutions were subsequently
used in vpart II (van,-,,, ....
.„!_ ,J. .
.
,., . .
Genuchten and Wierenga, 1977; this issue) to describe tntlum
movement through unsaturated, aggregated Glendalec a^ y loam. In this paper, part III of the study, the theoreticalmodel will be used to describe experimental data on the
movement of the herbicide 2,4,5-T (2,4,5-trichlorophenoxyacetic acid) through the same Glendale soil. As was mentioned in Part I, no analytical solutions exist when either theadsorption isotherm is nonlinear, or when the adsorptiondesorption process is not single-valued (hysteretic). For.1.
j-.• i » u •
L.
j TU
mese
conditions
be used. The .
. . . numerical.
, techniques. , . , must.
numerical solutions used in this analysis were programmed
in IBM S/360 CSMP as described by van Genuchten and
Wierenga (1974; 1976b).
'Journal article no. 568, Agric. Exp. Stn., New Mexico State Univ., Las
Cruces, NM 88003. The work upon which this report was based was supported in part by funds obtained from the U.S. Dep. of the Interior, Officeof Water, , Resources Research, as authorized under the. Water Resources
Ac of%4 Received 8 March 1976 Approved 9 Nov 1976

"Formerly Graduate Student, Dep. of Agronomy, New Mexico State
Univ.; presently Research Associate, Dep. of Civil Engineering, Princeton^g£%£^. of Agronomy, New Mexico state Univ., Las
Cruces, NM 88003.

279

VAN GENUCHTEN ET AL.: MASS TRANSFER STUDIES IN SORBING POROUS MEDIA: III

Table 1—Soil-physical data for data for various displacements
through Glendale clay loam.
Exp.
no.

TracerPulse period

Bulkdensity, p

Water
content, 6Flux, qg/cm3

cm 3 /cm 3

cm/day

TI

h
days

6 r-

Largestaggregate
size
mmExperiment 1
3

1-1
1-2
1-4
1-5

H
H
2,4,5-T
3
H

1.360
1.360
1.360
1.360

2-1
2-2
2-4
2-5

3

H
3
H
2,4,5-T
3
H

1.361
1.361
1.361
1.361

3-2
3-3
3-4
3-6

3

1.222
1.222
1.222
1.222

3

0.460
0.460
0.473
0.460

5.09
5.09
5.11
2.55

2.334 6.331
1.389
0.512
7.672
2.761
1.990 10.76

2.0
2.0
2.0
2.0

2.361
7.215
0.452 1.389
2.460 7.708
1.762 10.77

2.0
2.0
2.0
2.0

2.475
3.212
6.076
9.653

6.3
6.3
6.3
6.3

Experiment 2
0.464
0.468
0.479
0.467

4.55
4.57
4.59
2.29

Q
UJ

m

t£

2.4,5-T§< *Experiment 3H
2,4,5-T
3
H
3
H

0.454
0.475
0.445
0.434

17.0
17.0
4.20
1.32

3.102
3.994
1.909
1.788

2,4,5-T
3
H

1.309
1.309

0.456
0.433

16.8
4.04

J / ,/ ,*£'/ /° /°°''J
If//

Experiment 4
4-1
4-2

z

4.948
1.871

4.028
6.021

6.3
6.3

MATERIALS AND METHODS
The same experimental setup as discussed in part II (van Genuchten and Wierenga, 1977) was used to study the movement of
2,4,5-T through 30-cm long soil columns uniformly packed withthe same aggregated (Glendale clay loam soil as was used for thetritium experiments. Concentrations of 10 ppm of 2,4,5-T wereused for the leaching studies. Radioactive 2,4,5-T with a specificactivity of 4.93 /iCi/mg, and labeled at the carboxyl position wasadded to unlabeled herbicide solution. Activities of the 2,4,5-T14C
were determined on a Packard TriCarb Model 3310 liquid scintillation counter, using Aquasol (New England Nuclear, Boston,
Mass.) as the counting medium. Relative effluent concentrations(cm) were obtained by dividing the herbicide concentrations in theeffluent (Cm) by the concentration of the herbicide pulse (C0)applied to the columns.
A total of five runs were made with four columns, using Glendale clay loam of two different aggregate sizes and employing soil
water fluxes (q), ranging from 4.0 to 17.0 cm/day. The experimental data for the various 2,4,5-T displacements are given in
Table 1. Included in this table are the soil physical data of several
tritium displacements at similar water contents and flow velocities
through the same columns. The experiments in Table 1 are numbered by column and flux (q).
The equilibrium adsorption isotherm for 2,4,5-T and the Glendale clay loam was determined using duplicate 1:1 mixtures of 25
g of soil and 25 ml of various herbicide concentrations in 0.01/V
CaCl2. Each sample was shaken for 24 hours and then centrifugedat 1,500 rpm for 15 min. The 24-hour shaking period was experimentally determined to be more than sufficient time to obtain equilibrium between sorbed and solution concentrations (G. A.
O'Connor, 1972)4. Ten milliliters of the supernatant was removed
and analyzed for 14C activity and the count rates were converted toherbicide concentrations. The difference between the original herbicide concentration and that in the supernatant was assumed to be
the result of adsorption.
Equilibrium desorption isotherms were obtained using the same
duplicate 1:1 soil-to-herbicide solution mixtures used for the adsorption study. The 10-ml supernatant sample removed from thecentrifuged samples to determine the initial adsorption was replaced by 10 ml of 2,4,5-T-free 0.01/V CaCl2. The soil was
loosened from the tubes by vigorous hand shaking. The samples
were then shaken mechanically for 24 hours to establish a new
4
G. A. O'Connor. 1972. Soil adsorption and desorption of 2,4,5,-T.
Agron. Abstr. p. 92.

'•'!*'r//* ADSORPTION EXPERIMENTAL» DESORPTION EXPERIMENTAL—————

S = 0.6I6 C°-792

/

0.344

5

10

IS

EQUILIBRIUM CONCENTRATION

Fig. 1—Equilibrium adsorption and desorption data for 2,4,5-T sorption on Glendale clay loam.
equilibrium, centrifuged, and another 10-ml extraction and analysis of the supernatant was made. This procedure was followed foreach successive desorption step. In total, seven data points were
determined for each of four desorption curves.
The adsorption studies for 2,4,5-T were repeated using two different soil solution ratios: 20 g of soil mixed with 30 ml of herbicide solution, and 30 g of soil with 20 ml of herbicide solution.
No differences in adsorption were found. The adsorption points
obtained with these two additional adsorption studies were used,
together with the earlier results to construct the equilibrium adsorption isotherm.
RESULTS AND DISCUSSION
The equilibrium adsorption and desorption data for 2,4,5T and Glendale clay loam are given in Fig. 1. The data
show that adsorption and desorption cannot be described by
the same relation, and hence, are nonsingle valued (hysteretic). Both the adsorption and desorption isotherms could be
described by Freundlich-type equations of the form:

S = KCN.

[1]

The coefficients K and N in Eq. [1] are different for adsorption and desorption. Values for K and N are listed in Table
2; they were obtained following the procedures outlined by
Hornsby and Davidson (1973) and van Genuchten et al.
(1974). In this study a value of 2.3 for the ratio NaAs/NAes
was obtained, as shown by the data in Table 2. This value
was found to be independent of the maximum concentration(Cmax) before desorption is initiated. Similar values werereported in several earlier studies on the adsorption anddesorption of several pesticides from different soils (Swan-

280

SOIL SCI. SOC. AM. J . , VOL. 41, 1977

Table 2—Parameters used in Eq. [1] to describe the adsorption anddesorption of 2,4,5-T on Glendale clay loam. Cmax is the solution concentration before desorption is initiated. The subscripts "ads" and"des" indicate adsorption and desorption, respectively.
Process

Chemical

fads

^ads

Adsorption
Desorption
Cmax = 5.87 Mg/cm'
Cmax" 7.41/L<g/cm^
Cmax = 10.30 jug/cm'
Cmax - 14.35 f*g/cm3

2,4,5-T
2,4,5-T

0.616

0.792

*des

Wdes

1.36
1.51
1.75
2.03

0.344
0.344
0.344
0.344

son and Dutt, 1973; Hornsby and Davidson, 1973; van
Genuchten et al..., 1974). Somewhat smaller values (closer
to one) however, were obtained by Farmer and Aochi(1974) and Wood and Davidson (1975).
Observed and calculated 2,4,5-T effluent curves for column experiment number 2-4 are shown in Fig. 2. The solidline represents the analytical solution for the concentrationin the mobile liquid (cm). Since this solution requires alinear adsorption isotherm (see van Genuchten and
Wierenga, 1976a), it was necessary to approximate thenonlinear adsorption isotherm in Fig. 1 by a straight line.
The following procedure was used to linearize the equilibrium isotherm. We denote the linearized isotherm by
S=KlaAsC and require that the areas under the isotherms
over the range 0-10 ppm (all columns were leached with 10ppm solutions) for both the linearized and the nonlinear
Freundlich equations be the same (Fig. 1). Thus

r 10
Jo

KladsCdC=

r 10
Jo

0.

[2]

where KlaA& (=0.426) is referred to as the linearized adsorption constant. From the value of 0.426 a retardation factor/?
(for notation see the appendix) of 2.210 was calculated. A
three-parameter curve fitting was then carried out with thepreviously described GAUSHAUS nonlinear curve fitting
program (van Genuchten and Wierenga, 1977) to obtain estimates for the dimensionless parameters /3, P, and a whichappear in the analytical solution. Results obtained for four

2,4,5-T displacements are given in Table 3. Included in thetable are data obtained from several tritium displacements
through the same columns. The fraction of the adsorption
sites located in the dynamic region of the soil (f), wassubsequently calculated for each 2,4,5-T displacement
using Eq. [17] of van Genuchten and Wierenga (1977) i.e.

= </>+/(/?- i)f• — !

R- 1/=(0.596)(2.21.) -(0.862)—————(T21J————— = °'376'

Rm = 1 +fpKNCmfl-1/e,[6]

Since N<\, Rm will decrease with increasing concentration
Cm. Retardation of the chemical will be more extensive at
the lower and less extensive at the higher concentrations ascompared to the linear case. The net result will be a steeper

K

Nods = 0.792 (NON-SINGLE VALUED)
426

N•— Kads =0 - 616

N

ods ' °-

ods " '-O00 (SINGLE VALUED).8
od3 = 0-792 (SINGLE VALUED)

u, .4

.2

3

[5]

The solid line in Fig. 2 was calculated with the analyticalsolution and shows a fairly good agreement with the experimental data. The dashed-dotted line was obtained with thenumerical solution of van Genuchten and Wierenga(1976b), using the value off as calculated above and including the nonlinearity of the adsorption isotherm. The differences between the nonlinear (numerical) model and thelinear (analytical) model are rather small. The breakthrough part of the curve becomes somewhat steeper and thepeak concentration decreases when the nonlinearity is taken
into account. These two effects of the nonlinear isotherm on
the calculated curves are easily explained by considering theretardation factor Rm of the dynamic region (van Genuchten
and Wierenga, 1976a)•- K ods = 0.616

2[4]

For the data of experiment no. 2-4, one obtains

i.o

I

[3]

or

4

5

PORE VOLUME-T

Fig. 2—Observed and calculated 2,4,5-T effluent curves for experiment 2-4. The open circles represent observed data points.

281

VAN GENUCHTEN ET AL.l MASS TRANSFER STUDIES IN SORBING POROUS MEDIA: III

Table 3—Summary of various 2,4,5-T and tritium displacements through Glendale clay loam. The tritium data were obtained from van Genuchten
and Wierenga (1977). The superscripts 1 and f indicate linearization and fitted, respectively.
Exp.
no.

Tracer
3

R

(3

P

a

/

*

D

a

2

cm /day

I/day

«f

4ds

^ads/^ads

1.06

1.06

1-1
1-2
1-4
1-5

H
H
2,4,5-T
3
H

1.027
1.027
2.225
1.027

0.926
0.926
0.661
0.928

95
95
41
95

1.47
1.47
0.55
0.56

0.400t0.400t0.433
0.400f

0.940
0.940
0.940
0.942

3.7
3.7
8.4
1.9

0.25
0.25
0.09
0.048

2.301

0.009
0.009
0.453
0.009

2-1
2-2
2-4
2-5

3

H
H
2,4,5-T
3
H

1.026
1.026
2.210
1.026

0.850
0.887
0.596
0.830

45
45
37
45

1.50
1.31
0.88
1.05

0.400t0.400-j0.376
0.400t

0.862
0.900
0.862
0.841

7.6
7.2
9.1
3.9

0.23
0.20
0.13
0.080

2.279

0.009
0.009
0.450
0.009

3-2
3-3
3-4
3-6

3
H
2,4,5-T
3
H
3
H

1.024
2.139
1.025
1.025

0.841
0.616
0.872
0.717

56
19
56
56

0.39
0.21
0.72
1.96

0.852
0.852
0.884
0.725

24.0
68.0
5.7
2.2

0.22
0.12
0.10
0.086

4-1
4-2

2,4,5-T
%

2.223
1.027

0.602
0.788

20
57

0.39
0.93

0.400t0.409
0.400t0.400f0.399
0.400f

0.850
0.798

64.0
6.2

0.22
0.12

3

3

1.855

2.476

0.009
0.338
0.009
0.009
0.489
0.009

0.79

1.15

t Assumed to be 0.400.

front and a higher peak concentration for the curve based on
the nonlinear model.
Figure 2 also shows the effect of the observed hysteresison the numerical results. The break-through side of theeffluent curve is not affected by the hysteresis, but the relative concentration during elution decreases much faster andmore prolonged tailing occurs at the higher pore volumes ifhysteresis is taken into account. From Fig. 2 one may
conclude that both the nonlinearity of the adsorption isotherm, as well as the observed hysteresis do not affect theshape and position of the effluent curve to any great extent.
All three calculated curves describe the experimental datareasonably well. Note that an/-value of 0.376 was obtained
from the data presented in Fig. 2. This indicates that morethan 60% of the adsorption occurs in the stagnant region of
the soil.
The dispersion coefficient D used to construct the three
curves in Fig. 2 is higher than the dispersion coefficientused to describe tritium displacement through the same column at the same velocity. Table 3 shows that the Peclet
numbers based on the 2,4,5-T displacements are smaller
than those determined from the tritium data. Theoretically,
only one value of the Peclet number should hold for all displacements through the same column, independent of the
tracer used, provided the flow velocities are sufficiently
high that longitudinal diffusion is negligible compared tomechanical dispersion (Perkins and Johnson, 1963). The
discrepancies between the Peclet numbers for 2,4,5-T andtritium are in our opinion due to the existence of kinetic
phenomena during adsorption of the herbicide. This study
assumes equilibrium adsorption, a condition which may nothave been met during the leaching experiments. In a studyof the equilibrium times for 2,4,5-T and Glendale clay
loam, G. A. O'Connor (1972)4 showed that although theinitial adsorption rate was very fast, complete adsorption
could be obtained only after herbicide and soil were shaken
for several hours. When a kinetic adsorption mechanism ispresent, the front portion of the effluent curve will be lesssteep, as shown in previous studies (van Genuchten et al.,
1974; van Genuchten and Wierenga, 1974). By neglecting
the kinetic effects and using an equilibrium instead of a kinetic model, a higher dispersion coefficient will hence benecessary in order to obtain the same description of the front

portion of the curve. It should be mentioned that in addition
to the occurrence of kinetic phenomena, the curve-fitted
value of the Peclet number will be influenced also by thefact that a linearized adsorption relation is used in themodel, instead of the nonlinear one observed. However,this effect is small as shown by the differences between thesolid and dashed lines in Fig. 2. It should be further notedthat a slightly different value of D will somewhat affect thevalue of the mass transfer coefficient a that is obtained;
however, it will not influence the value of/obtained withthe curve-fitting procedure.
The solid line in Fig. 2 was obtained with the linear adsorption model, using a value of 0.426 for the (linearized)
adsorption constant, obtained from the batch equilibrium
studies. This coefficient may also be estimated directly fromthe effluent curve, using a four-parameter rather than athree-parameter curve fit. Results for experiment No. 1-4
are shown in Fig. 3, where the solid line was calculatedwith a fitted adsorption constant of 0.453, while the dashedline was obtained with the linearized adsorption constant of
0.426. Both calculated curves are essentially the same.
Note that the values of the parameters D, a, and/obtainedwith the four-parameter curve fitting are also very close to
those determined with the three-parameter fitting. Values ofthe fitted adsorption constant (ATfads)for the four 2,4,5-T displacements are listed in Table 3. The values of /Sffads agree
reasonably well with the linearized adsorption constant^'ads, the average A"fads being nearly identical to AT'ads. Thissuggests that, when assuming a linear adsorption isotherm,
the adsorption constant can be estimated with reasonable accuracy from the effluent data. However, Green et al. (1972)
in a study on the movement of picloram through two aggregated soils obtained much higher values for KfaAs than
could be accounted for by means of equilibrium measurements. It appears that additional experimental verificiation,using different pesticides and soils is necessary before definite conclusions can be reached.
Figure 4 compares observed and calculated 2,4,5-T effluent curves for experiment no. 4-1. The largest aggregate
size used for this experiment was 6.3 mm, compared to 2.0mm for the data shown in Fig. 2 and 3. The solid line in Fig.
4 again represents the analytical solution using the linearized adsorption constant. A reasonable description of the282

SOIL SCI. SOC. AM. J., VOL. 41,

1977

1.0

Exp.

Kflds * 0.453
0-8.8 cm2/doy
a = 0.084 '/day

1-4

2,4,5-T.8

f • 0.421

o6

i
1*
g

K

ods ' °-426
D = 8.4 cm2/day
o = 0.093 '/dayf • O.433

I

.4
1

.2

-

3

4
PORE VOLUME-T

Fig. 3~Observed and calculated 2,4,5-T effluent curves for experiment 1-4. Calculations were based on the linear adsorption model, with andwithout fitting the adsorption constant Ka,ls to the effluent data. The open circles represent observed data points.
1.0
Exp.

4-1

Nad,-I.OOO

d s * 0.426

2.4,5-T.8i

q = 16.8 cm/day$ .6

8 = 0.456
0 « 64 cm^/dao = 0.22 '/day$ = O.850
f = 0.399

SINGLE VALUED.2
NON-SINGLE VALUED___i____i___A
PORE VOLUME-T

Fig. 4—Observed and calculated 2,4,5-T effluent curves for experiment 4-1. The adsorption constant A"1 was obtained by linearization of the equilibrium adsorption isotherm. The open circles represent observed data points.

experimental data is obtained, even though in this case thefitted adsorption constant was found to be 15% higher thanthe linearized value (Table 3). Note that an/-value of approximately 0.40 was obtained from the data in Fig. 4.
Hence 40% of the adsorption occurred in the dynamic and
60% in the stagnant region of the soil. Similar values for/were obtained for the other displacements (Table 3),
suggesting that the relative location of the sorptlon sites is
not influenced significantly by either aggregate size or bulk
density.
Table 3 further shows that the values of the mass transfer
coefficient, a, obtained from the 2,4,5-T displacements arelower than those obtained from the tritium displacements at
similar flow velocities. This may be expected since the masstransfer coefficient is proportional to the diffusion coefficient (Coats and Smith, 1964), and the diffusion coefficientof tritium is very large compared to those of most organic
chemicals (Wang et al., 1953; International Critical Tables,
1929). The data in Table 3, except for the displacements incolumn 4, show that the ratio of the mass transfer coefficients of 2,4,5-T and tritium is approximately 0.5 (±0.15)
at similar flow rates. A comparison of experiments 4-1 and
4-2 is meaningless, since the displacements of 2,4,5-T andtritium in this column were carried out at different velocities(a is a function of the average pore-water velocity).
The inclusion of hysteresis in the model does not appreciably affect the calculated curves (Fig. 2 and 4). Thus, forthe conditions of this study, intra-aggregate exchange ofVAN GENUCHTEN ET AL.: MASS TRANSFER STUDIES IN SORBING POROUS MEDIA: III

283

i.o - WITH

INTRA-AGGREGATE

—————

.8

WITHOUTSINGLEDIFFUSIONVALUEDINTRA-AGGREGATE—————SINGLE— ————NON-SINGLEDIFFUSIONVALUEDVALUED

Nods=I.OOO
q = 5.ll

cm/day0.473
f=0.433
a = 0.093

I/day

0=8.4
$=0.940

^ 4
PORE

5

6

7

VOLUME -T

Fig. 5—Observed and calculated 2,4,5-T effluent curves for experiment 1•4, with and without including intra-aggregate diffusion. The open circles
represent observed data points.

2,4,5-T between mobile and immobile regions was far more
important than the hysteresis in the adsorption-desorption
process. The effects of hysteresis, however, become more
pronounced when intra-aggregate diffusion is neglected, as
was suggested in several earlier studies (e.g., Swanson andDutt, 1973; van Genuchten et al., 1974). This is clearly
demonstrated in Fig. 5, where the experimental data of experiment no. 1-4 are compared with calculated curves,which include (solid line) or neglect intra-aggregate diffusion (dashed and dashed-dotted lines). The dashed line
includes the effect of hysteresis and was obtained with thenumerical program of van Genuchten and Wierenga (1974,
example 1). The dashed-dotted line assumes no hysteresis.
The linear adsorption model without intra-aggregate diffusion (a=0, j6=l) reduces then to the solution of Lindstrom et al. (1967). The more or less symmetrical curve obtained with this solution fails to describe the data in Fig. 5.
When hysteresis is included in the calculations, the observed tailing during elution of the chemical is fairly welldescribed. However, hysteresis has no effect on the breakthrough side of the curve, and hence, cannot explain theearly appearance of the chemical in the effluent nor thetailing at the higher concentrations. Tailing during breakthrough will remain largely unnoticed when relatively shortpulses are used. This may have influenced earlier conclusions about the importance of hysteresis on solute movement in soils (Swanson and Dutt, 1973; van Genuchten etal., 1974).
The break in the effluent concentration distributions during break-through of the chemical, and its subsequent tailing off, has been observed also by Kay and Elrick (1967)
for the movement of lindane through Honey wood silt loam,
and by J. M. Davidson (unpublished data, 1973) for the
movement of picloram through Norge loam. Kay and Elrick(1967) attributed the tailing to intra-aggregate diffusion andadsorption, a phenomena which is substantiated by both experimental and theoretical descriptions of 2,4,5-T effluent
curves in this study.

In Fig. 4 a comparison was made between the linear adsorption model and the observed data from experiment No.
4-1. An accurate description of the data was obtained,
especially during break-through of the chemical. The parameter values presented in Fig. 4 were also used to calculate concentration profiles inside the column for both themobile (c^ and the immobile liquids (cim). The results are
given in Fig. 6. The differences in concentration between
the two liquid regions are significant. For example, the relative concentration in the mobile region at a depth of 20 cm
reaches a value of 0.5 after only 0.8 days, while it takes
about 2.3 days for the concentration in the immobile region
to reach this same value. Previously, (van Genuchten and
Wierenga, 1977) similar distributions for tritium wereshown. Although still considerable, the differences between
cm and cim for tritium were less than those shown in Fig. 6.
This may be expected, since tritium adsorption is very small(K = 0.009), and material which diffuses into the stagnant
region of the soil can be stored only in the (immobile) liquid.
The fraction of the chemical diffusing into the stagnant
region which will remain in solution may be calculated byconsidering the transport equation which describes the diffusional exchange between dynamic and stagnant regions.
Assuming linear adsorption, this equation is given by (vanGenuchten and Wierenga, 1976a, Eq. [16][0™ + (1 ~f)pK](dCim/dt) = a(Cm - C,m).

[7]

The first term on the left represents the material stored in theimmobile liquid, while the second term gives the material
adsorbed by the stagnant region. The fraction remaining insolution hence is given by

Using the data from experiment no. 4-1, one may calculatethat only 17% of 2,4,5-T will remain in solution, while theremaining 83% will be adsorbed (for tritium nearly 100%

284

SOIL sci. soc. AM. J., VOL. 41, 1977
1.0 |————————————————————————————————————————————————————————————————Ir.
—_____ 5 0 __________2,4,5- T
IMMOBILE LIOUD-C|m

£

°

5

10

°0

5

10
DISTANCE

15

15
ALONG

2O

25

30

20

25

30

COLUMN - Z (cm)Fig. 6—Concentration profiles inside column 4, at different times during leaching with 2,4,5-T. Values of the parameters used to construct the
curves are given in Fig. 4. Numbers on the curves indicate time (days) after leaching was initiated.
will remain in solution). Thus, when sorption increases, relatively more material can diffuse into the stagnant region of
the soil. Since this diffusion is very slow compared to the• . , i , „ r i
1-1
»u
i- »u
"im
rate at which the bulk of
the chemical moves through thesoil, the differences between the concentrations cm and cim
are expected to increase progressively as sorption increases.
APPENDIX-NOTATION
C0= influent concentration (jttg/cm3)
Cl= concentration break-through side effluent curve
Cm,Cim = concentration in mobile and immobile liquid, respectively (;u,g/cm3)
c m ,cim = relative concentrations (Cm/C0;Cim/C0, respectively).
D= dispersion coefficient (cm2/day)/= fraction adsorption sites in dynamic region
I 0 ,Ii= modified Bessel functions
K, N= constants in Freundlich sorption isotherm: S = KCN
L= length of column (cm)P
= peclet number of column: P = vmL/Dq= fluxR= total retardation factor: R = 1 + pK/0
Rm
= retardation factor of dynamic region: Rm = \+fpK/6m/?lm= retardation factor of stagnant region:*im= l+(l-f)pK/Olm
Sm,Sim = adsorption in dynamic and stagnant regions, respectively Og/g)/= time (days)^= pulse period (days)T= pore volume T = vat/L = vmt$ILT!
= dimensionless pulse period: Tt = vJ-JL
va= average pore-water velocity (cm/day): va = q!6vm= average pore-water velocity in dynamic region: vm =<?/0m(cm/day)x= dimensionless distance: x = zILz= distance (cm)a= mass transfer coefficient (I/day)a= dimensionless mass transfer coefficient: a = aLlq

ft
e

J»=
^
p

= 4>RJRwater
content: 9 = Om+0im (cm3/cm3)= mobile water content (cm3/cm3)
immobile water content (cnr/cirr)= fractjon mobi,e water. ^ = eje— b,^ density (g/cm3)

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