Diesel Adsorption to PVC and Iron 

During Contaminated Water Flow and 

Flushing Tests 

Mark A. Kedzierski

NISTIR 7520

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.IR.7520
1

NISTIR 7520

Diesel Adsorption to PVC and Iron During 

Contaminated Water Flow and Flushing 

Tests 

Mark A. Kedzierski

U.S DEPARTMENT OF COMMERCE

National Institute of Standard and Technology

Building Environment Division

Building and Fire Research Laboratory

Gaithersburg, MD 20899-8631

June 2008

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

National Institute of Standards and Technology

James M. Turner, Acting Director

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.IR.7520
1

Diesel Adsorption to PVC and Iron During Contaminated 

Water Flow and Flushing Tests 

M. A. Kedzierski 

National Institute of Standards and Technology 

Bldg. 226, Rm B114 

Gaithersburg, MD 20899 

Phone: (301) 975-5282 

Fax: (301) 975-8973 

ABSTRACT 

This paper presents an experimental and theoretical study of aqueous diesel 

contamination and decontamination of a polyvinyl chloride (PVC) surface and an iron 

(Fe) surface. A test apparatus designed for the purpose of studying adsorption of diesel 

from a flowing dilute diesel/water mixture was used to measure the mass of diesel 

adsorbed per unit surface area (the excess surface density) and the bulk concentration of 

the diesel in the flow using a fluorescence based measurement technique. Both bulk 

composition and the excess surface density measurements were achieved via a traverse of 

the fluorescent measurement probe perpendicular to the test surface. The diesel 

adsorption to each test surface was examined for three different Reynolds numbers 

between zero and 7000. Measurements for a given condition were made over a period of 

approximately 200 h for a diesel mass fraction of approximately 0.15 % in tap water. For 

a Reynolds number of approximately 7000, the largest excess layer thickness was 

approximately 4.4 μm, which was measured on a PVC surface. Averaging over all 

contaminating flow rates and exposure times, the excess layer thickness on the PVC 

surface was approximately 2.0 μm. Reynolds number had little or no effect on the 

accumulation of diesel on an iron surface, which was approximately 0.71 μm. The 

adsorbed diesel on the PVC and iron surfaces was removed by flushing with tap water. 

Models to predict excess layer thickness during flushing and contamination were 

developed. The models predict flushing times to within 7 h and predict the influence of 

pipe surface on contamination level. 

Keywords: adsorption, contaminant, diesel, excess layer, fluorescence, measurement 

technique, sorption, water 
2

TABLE OF CONTENTS 

ABSTRACT....................................................................................................................... 1

LIST OF FIGURES .......................................................................................................... 4

LIST OF TABLES ............................................................................................................ 4

INTRODUCTION............................................................................................................. 5

EXPERIMENTAL APPARATUS AND UNCERTAINIES ......................................... 5

TEST FLUIDS................................................................................................................... 7

MEASUREMENTS AND UNCERTAINTIES .............................................................. 7

Fluorescence/Mass Calibration................................................................................. 7 

Flushing..................................................................................................................... 10 

Air Gap Method ....................................................................................................... 11 

MEASUREMENT RESULTS ....................................................................................... 11

Excess Layer Thickness ........................................................................................... 11 

Contamination Tests ................................................................................................ 12 

Flushing Tests ........................................................................................................... 13 

Gap Test Check ........................................................................................................ 14

MODEL DEVELOPMENT ........................................................................................... 14

Flushing Model ......................................................................................................... 14 

Contamination Model .............................................................................................. 16

FUTURE WORK............................................................................................................ 17

CONCLUSIONS ............................................................................................................. 18

ACKNOWLEDGEMENTS ........................................................................................... 19

NOMENCLATURE........................................................................................................ 20

English Symbols........................................................................................................ 20 

Greek symbols .......................................................................................................... 20 

English Subscripts.................................................................................................... 20 

Superscripts .............................................................................................................. 21

REFERENCES................................................................................................................ 22

APPENDIX A: UNCERTAINTIES .............................................................................. 38

APPENDIX B: MEASUREMENT CORRECTION ................................................... 42

APPENDIX C: MODEL DEVELOPMENT ................................................................ 44
3

Flushing Model ......................................................................................................... 44 

Contamination Model .............................................................................................. 46

APPENDIX D: FLUORESCENCE OF TOLUENE.................................................... 49
4

LIST OF FIGURES 

Fig. 1 Schematic of test loop................................................................................................. 24

Fig. 2 Schematic of spectrofluorometer, test section, and linear positioning device ..... 25

Fig. 3 Schematic of right angle spectrofluorometer.......................................................... 26

Fig. 4 Cross-sectional illustration of test section during contamination and flushing... 27

Fig. 5 Schematic of fluorescence/composition calibration jar ......................................... 28

Fig. 6 Overall calibration of Beer-Lambert Bougher law for diesel on copper disk ...... 29

Fig. 7 Sample F vs. l fit for a PVC data set........................................................................ 30

Fig. 8 Effect of exposure time and flow rate on thickness of the diesel excess layer 

for a 0.15 % bulk freestream mass fraction on a PVC disk.............................................. 31

Fig. 9 Effect of exposure time and flow rate on thickness of the diesel excess layer 

for a 0.15 % bulk freestream mass fraction on an iron disk............................................. 32

Fig. 10 Diesel excess layer thickness as a function of Re for PVC surface and 

water/diesel (99.85/0.15) ....................................................................................................... 33

Fig. 11 Diesel excess layer thickness as a function of Re for iron surface and 

water/diesel (99.85/0.15) ....................................................................................................... 34

Fig. 12 Flushing measurements used to fit coefficients of model..................................... 35

Fig. 13 Modified kinematic viscosity to account for adhesive forces between iron 

and diesel derived for two flow conditions (Re = 3200 and Re = 7000). .......................... 36

Fig. 14 Maximum contamination diesel layer on various pipe surfaces as predicted 

by eq. (22)............................................................................................................................... 37

Fig. A.1 Relative uncertainty of le for 95 % confidence level for iron surface 

xb = 0.15 %............................................................................................................................. 38

Fig. A.2 Relative uncertainty of le for 95 % confidence level for PVC surface 

xb = 0.15 %............................................................................................................................. 39

Fig. A.3 Relative uncertainty of xb for 95 % confidence level for iron surface............... 40

Fig. A.4 Relative uncertainty of xb for 95 % confidence level for PVC surface.............. 41

Fig. B.1 Basis for correction of iron surface measurements made after test 

apparatus repair.................................................................................................................... 43

Fig. D.1 Schematic of experimental setup to measure fluorescence emission of 

toluene on three pipe surfaces: PVC, copper, and iron..................................................... 49

Fig. D.2 Fluorescence emission of toluene on three pipe surfaces: PVC, copper, and 

iron ......................................................................................................................................... 50

LIST OF TABLES 

Table 1 Comparison of flushing model predictions to measurements............................. 23
5

INTRODUCTION 

Since the signing of the Executive Order establishing the Office of Homeland Security, 

Federal agencies have been working on ways to improve the security of the general 

public. In one example, the National Institute of Standards and Technology (NIST) is 

helping the U.S. Environmental Protection Agency (EPA) devise ways to safeguard the 

nation’s drinking water supply. EPA is conducting potable water research with NIST on 

six different efforts. This report describes one of those efforts designed to fundamentally 

understand the attachment and detachment mechanisms of contaminants to solid 

plumbing materials under dynamic water flow conditions. The results of this work 

provide EPA with an investigative tool to support the development of a response to water 

contamination events and a potential detection technique for timely warning of such 

events. 

The purpose of this study is to use a NIST fluorescence based measurement technique 

(Kedzierski, 2006) to add to the existing data on aqueous diesel adsorption to solid 

surfaces and to support the development of flushing and contamination models. In a 

previous study (Kedzierski, 2006), the diesel excess surface density was measured on an 

oxidized copper surface. The present study expands the database to diesel attachment to 

a polyvinyl chloride (PVC) surface and to an iron surface. In this way, we not only gain 

vital fundamental modeling information but we lay the groundwork for a possible early 

detection/monitoring system for sticky contaminants. These efforts have formed the 

foundation for future work that will focus on using the NIST water loop and the 

calibration technique to measure the accumulation and removal of diesel as a function of 

free-stream diesel concentration and contaminated water flow rate. 

Commercial diesel was used rather than a chemically simpler surrogate in order to 

demonstrate the use of the technique with an actual potential contaminant. Diesel was 

also a desirable test contaminant because it has been found to exhibit a strong 

fluorescence. However, because of the complexity and the variability of diesel, the diesel 

for the project was restricted to a single batch. In this way, we can ensure the consistency 

of the properties of pure diesel1

 such as its liquid density and fluorescence characteristics. 

 

EXPERIMENTAL APPARATUS AND UNCERTAINIES 

The standard uncertainty (ui) is the positive square root of the estimated variance ui

2

. The 

individual standard uncertainties are combined to obtain the expanded uncertainty (U), 

which is calculated from the law of propagation of uncertainty with a coverage factor. 

All measurement uncertainties are reported at the 95 % confidence level except where 

specified otherwise. 

Figure 1 schematically shows the flow loop for measuring diesel on pipe substrates. The 

primary components of the loop are the pump, the reservoir, and the test chamber with 

the test section. The inside surfaces of the approximately 96 mm x 1.6 mm rectangular 

flow cross-section of the aluminum test chamber, shown in Fig. 2, were black anodized to 

 

1

 “Pure diesel” is used here to denote that the particular batch of diesel, which will be 

consistently used throughout this project, is not mixed with water. 
6

minimize stray light reflections. The channel was designed to have the same flow area as 

a 13 mm (nominally 0.5 inch) diameter copper pipe. The test chamber had a circular 

cavity to accept the solid pipe test surface. The height of the channel was 1.6 mm so that 

the probe could be flush to the top of the test section while maintaining proximity to the 

test surface for measurement purposes without being an obstruction to the flow. A 

centrifugal pump delivered the contaminated water to the entrance of the rectangular test 

chamber at room temperature. The pump head was removable so that it could be easily 

replaced in order to test a different contaminant. The flow rate was controlled and varied 

by varying the pump speed with a frequency inverter. A heat exchanger immersed in the 

reservoir was supplied with brine from a temperature-controlled bath to maintain the 

entrance temperature to the test chamber at ambient temperature (293.8 K). This was 

done to ensure that the diesel was at the same temperature as it was during the 

fluorescence calibration to avoid the temperature effect on fluorescence (Miller, 1981). 

An additional temperature-controlled bath was used to maintain the fluorescence 

standards at the same ambient temperature. As described in a succeeding section, the 

fluorescence standards were used to calibrate the range of the fluorescence 

measurements. 

Residential copper pipe was used to plumb together the various components of the loop. 

Redundant volume flow rate measurements were made with an ultrasonic doppler and a 

turbine flowmeter with expanded uncertainties of ± 0.12 m3

/h and ± 0.03 m3/h, 

respectively. As shown in Fig. 1, three water pressure taps before and after the test 

chamber permitted the measurement of the upstream absolute pressure and the pressure 

drops along the test section with expanded uncertainties of ± 0.24 kPa and ± 1.5 kPa, 

respectively. Also, a sheathed thermocouple measured the water temperature at each end 

of the test chamber to within an uncertainty of ± 0.25 K. The dissolved oxygen level, the 

conductivity, and the pH, were monitored at the water reservoir with associated B-type 

uncertainties of ± 0.5 %, ± 50 μ Ω/cm, and ± 0.3, respectively. 

 

Figure 1 also shows the inlet and exit taps that were used to flush the test section with 

fresh tap water. In preparation for flushing, the test section was isolated from the rest of 

the test loop by closing valves. Then the fluid was drained from the test chamber and 

returned to the reservoir. Next, a tap water supply was connected to a test chamber port. 

The other test chamber port was connected to a filter to absorb any diesel before it was 

sent to a drain. 

Figure 2 shows a view of the spectrofluorometer that was used to make the fluorescence 

measurements and the test chamber with the fluorescence probe perpendicular to the 

flattened pipe test surface. Figure 3 shows a simplified schematic of the right angle 

spectrofluorometer consisting of a xenon light source, an excitation and an emission 

monochromator, and an emission photomultiplier tube (detector). As sold off-the-shelf, 

the spectrofluorometer was designed to accept 45 mm × 10 mm × 10 mm fluorescent 

samples or cuvettes filled with fluorescent material. The spectrofluorometer was 

modified by replacing the cuvette holder with a special adapter with lenses and mirrors to 

remotely excite and measure fluorescence via a bifurcated optical bundle. Two optical 

bundles consisting of 84 fibers each originated from the spectrofluorometer. One of the 
7

bundles transmitted the excitation light, i.e., the incident intensity (Io), to the test pipe 

surface. The other bundle carried the emission, i.e., the fluorescence intensity (F), from 

the test surface to the spectrofluorometer. The optical bundles originating from the 

spectrofluorometer merge transmitting and receiving fibers randomly into a single probe 

before entering the test section chamber. The sensor end of the fluorescence probe is 

sheathed with a quartz tube to protect it from reacting with the contaminant in the test 

fluid. 

The excitation wavelength (λx) and the emission/detection wavelength (λm) were set to 

434 nm and 485 nm, respectively, for all tests. Further details on the fluorescence 

measurement technique are given in Kedzierski (2006). 

TEST FLUIDS 

Number 2 diesel fuel was used from a single batch throughout the experiment to avoid 

property variations that might be caused by batch variations due to it being a complex 

mixture of hydrocarbons. Kedzierski (2006) provides the measured viscosity and density 

of the pure diesel liquid. A nominally 1.5 % by mass diesel mixture was prepared with 

local Gaithersburg, MD tap water for the exposure/flow rate tests. The measured 

dissolved oxygen level, the conductivity, and the pH, of the water at 24 oC before mixing 

with diesel were found to be, 86.4 %, 358 μΩ/cm, and 7.04, respectively. 

Because diesel and water are not miscible, the suction inlet to the pump was designed to 

entrain diesel from the reservoir and into the water flow. As shown schematically in 

Fig.1, the opening of the pump suction line in the reservoir is situated approximately 

10 mm below the liquid-air interface. The return flow entering the bottom of the 

reservoir ensured good flow mixing of any components of diesel that may have been 

hydrolyzed and settled to the reservoir bottom. Figure 4 depicts the colloidal flow within 

the test section and the fluorescent measurement probe above it for the contamination and 

decontamination test conditions. The size of the droplets in the dispersed flow is 

exaggerated for illustration purposes. Both test conditions are shown to have an excess 

layer thickness (le) of undiluted, potentially hydrolyzed diesel adsorbed to the test 

surface. Because the molar mass of the diesel is unknown, the surface excess density (Γ) 

is defined in this work on a mass basis as (Kedzierski, 2001): 

e d bb Γ = − l x ( ) ρ ρ (1) 

The density of liquid diesel is ρd. The density of the flowing bulk mixture (ρb) is 

evaluated at the bulk mass fraction of the mixture (xb). The surface excess density is 

roughly the mass of diesel attached per surface area. The Γ and le are the primary 

measurements of this study. The le is measured in the y-direction, as shown in Fig. 4, 

with the origin at the fluid-surface interface. 

MEASUREMENTS AND UNCERTAINTIES 

Fluorescence/Mass Calibration

Fluorescence as a means for detecting a contaminant has its advantages in that its 

absorption and fluorescence spectra are like a fingerprint that can be used in its 
8

identification. Consequently, by isolating the wavelength of light that the contaminant 

fluoresces, its intensity can be used to identify its mass. Full detail of the fluorescence 

based measurement technique used in this study is given in Kedzierski (2006) and given 

in brief below. 

 

Two different calibration methods had to be combined due to the additional complexity 

caused by immiscible liquids. Both calibration techniques were used to quantify different 

functional aspects of the Beer-Lambert-Bougher law (Amadeo et al., 1971), which forms 

the basis of the calibration equation. The first method was used to obtain the relationship 

between diesel composition and fluorescence intensity for a fixed light path length (fixed 

probe height above the test surface). The first method would have been sufficient had the 

bulk composition of the flow remained the same as it was charged in the reservoir. Due 

to the immiscibility of the two fluids, the bulk composition of the flow differs from that 

in the reservoir. As a result, a second method is necessary to determine both the 

contaminant mass fraction and the excess layer thickness. The second method that was 

developed in this study relies on a perpendicular traverse of the flow stream with the 

measurement probe. To achieve this, a linear positioning device with a graduated knob 

was adapted to the quartz tube as shown in Fig. 2. The second method (traverse method) 

is used to calibrate the effect of contaminant thickness (path length) and the proximity of 

incident intensity. The traverse method is essential for splitting the total measured 

fluorescent intensity into two components: that from the diesel on the test surface and that 

from the diesel in the bulk flow stream. In this way, the mass the diesel on the test 

surface and the composition of the fluid stream are determined. 

Two standard jars (see Fig. 5) were used as references standards to set the lower (0) and 

upper (100) limits of the intensity signal on the spectrofluorometer for raw measurements 

made at the test section (Fr). A jar that contained only pure water was used to zero the 

intensity. A second jar that contained pure diesel was used to set the intensity on the 

spectrofluorometer to 100. All raw-measured intensities (Fr) were numerically 

normalized by the intensity from the zero-jar (F0) and the maximum-jar (F100) as: 

r 0

100 0

F F F

F F

− = − (2) 

where the intensity of the contamination data was adjusted by no more than 0.3 % to 

account for the small (typically within ± 1 K) difference in temperature between the test 

section and the bath containing the maximum- and the zero-jars (Kedzierski, 2006). The 

maximum correction for the flushing data was approximately 1.5 %, which was larger 

than for the contamination measurements due to the colder temperature of the house tap 

water. 
9

The linear form of the Beer-Lambert-Bougher law (Amadeo et al., 1971) shows that the 

measured fluorescence intensity is related to the incident light intensity (Io), the 

extinction coefficient (ε), the concentration of the fluorescent diesel (c), the path length 

of light (l), and the quantum efficiency of the fluorescence (Φ) as: 

F I cl cl = Φ→ ≤ 2.3 0.05 oε ε[ ] (3) 

The linear criteria for eq. (3) (εcl ≤ 0.05) is satisfied for 78 % of the calibration data, and 

the absorbance (εcl) did not exceed 0.063 for all of the data. As a result, the calibration 

measurements shown in Fig. 6 gave: 1

-1 2 -1 209.23[ ] m

c 2.3 1.04735 m kg lo IM e ε −

− Φ = ⎡ ⎤ ⎣ ⎦ when 

fitted to eq. (3) (Kedzierski, 2006). Using the calibration and expressing the 

concentration in terms of the bulk mass fraction and the bulk liquid density gives the 

calibration of the fluorescence intensity in terms of the mass fraction and path length as: 

1

m

2

209.23[ ]

bb bb

c

2.3 m 1.04735

kg

o l I F lx lx e

M

ε

ρ ρ −

− Φ ⎡ ⎤ = = ⎢ ⎥ ⎣ ⎦

 (4) 

 

Note that the concentration of the fluorescent diesel has been replaced with the product of 

the bulk contaminant (diesel) mass fraction (xb) and the density of the bulk mixture (ρb) 

divided by the molar mass of the contaminant (Mc). The mixture densities were 

calculated from a linear mass weighted basis of the pure fluid specific volumes. 

Because the actual concentration of the diesel entrained in the water flow stream is 

unknown, eq. (4) cannot be directly used to obtain the excess layer of diesel on the pipe 

surface. The Γ and the le must be obtained from additional information that is obtained 

from a perpendicular traverse of the flow stream. As shown in Fig. 2, a linear positioning 

device with a graduated knob was used to traverse and locate the quartz tube relative to 

the test surface and thus measure the path length of the incident light through the fluid. 

Measurements of the fluorescence intensity (F) for various path lengths provided 

sufficient information for obtaining both the bulk mass fraction and the excess layer 

thickness. The methodology for this is explained in the following. 

The total fluorescence signal (F) can be separated into three components along the path 

length while assuming a uniform bulk mass fraction. The total intensity is the sum of that 

contributed by the bulk concentration (Fl(xm = xb)) for the entire path length and that in 

the diesel excess layer (Fle(xm = 1)) minus the intensity that would have been due to the 

bulk concentration but did not occur because it was displaced by the excess layer 

(Fle(xm = xb)) 

e e ( ) ( ) ( 1) F Fx x F x x F x = =− =+ = lm b l m b l m (5) 
10

Substitution of eq. (4) into the components of the above equation and grouping like terms 

gives: 

[ ] -1

c 2.3 F I M lx l x l o b b eb b e d =Φ − + ε ρ ρρ (6) 

Here ρd is the density of liquid diesel. 

For a given probe traverse, the only variable in eq. (6) is the path length. Consequently, 

eq. (6) can be arranged in terms of two regression constants for a single traverse: 

( ) 1 209.23[m ]

0 1

l F A Al e − − = + (7) 

Figure 7 illustrates the fit of eq. (7) for a PVC data set at a Re of 7000. 

Comparison of eqs. (6) and (7), yields the bulk mass fraction as: 

1

209.23m

1 1

-1 2 -1

d c d 2.3 1.04735 m kg

l

b

o

Ae A

x

ρ ε I M ρ

−

−

= = Φ ⎡ ⎤ ⎣ ⎦

 (8) 

and the excess layer thickness as: 

1

m

0 0

e 209.23 -1 2 -1

d c1 d 1 2.3 1.04735 m kg l

o

A A l

ρ ε e IMA ρ A = = −

Φ − ⎡ ⎤ − ⎣ ⎦

 (9)2

As shown in Appendix A, the average uncertainty of le for the measurements with the 

iron and the PVC surface for the contamination measurements was approximately 

± 0.06 μm, and ± 0.1 μm, respectively. The average uncertainty of xb was approximately 

± 0.00008. 

Flushing

The diesel bulk mass fraction of the tap water used during the flushing tests is zero. For 

flushing tests, eq. (8) produced a non-zero bulk mass fraction with a magnitude close to 

the uncertainty of the measurement, i.e., typically 0.008 % (80 ppm). An alternative 

approach for the flushing tests that forces the bulk mass fraction to be zero is to start by 

setting xb = 0 in eq. (6) and taking its derivative with respect to the path length. 

 

2

 The methodology presented here is a refinement of that given in Kedzierski (2006). 

Equations (8) and (9) are more explicit than those presented in Kedzierski (2006), but 

give the same results. 
11

Rearranging the resulting differentiated equation and solving for the excess layer 

thickness yields: 

0 1 1

e 1 -1 2 -1

d c d

1

209.23[m ]

209.23[m ] 2.3 o 1.04735 m kg

dF A A l

dl l

ρ ε I M ρ

−

−

⎛ ⎞ − − ⎜ ⎟ ⎝ ⎠ = = Φ ⎡ ⎤ ⎣ ⎦

 (10) 

Equations (9) and (10) are equivalent for negligible A1, which is the case for flushing. 

However, eq. (10) was used to obtain the le for all of the flushing measurements because 

of its more explicit derivation. The average value of le was used for a given measurement 

probe traverse. As shown in Appendix A, the average uncertainty in le for the iron and 

the PVC flushing tests was approximately ± 0.02 μm, and ± 0.05 μm, respectively. 

Air Gap Method

A secondary methodology was developed that relies on the gradient of F rather than its 

absolute value in order to confirm the measurement of le as obtained from eq. (9). The 

advantage of a gradient approach would be the elimination of a bias error on the 

measurement of F if it existed. As shown in Fig. 4, part of the excitation is reflected 

from the diesel-air interface and is not available to induce fluorescence. Consequently, 

the calibration must be adjusted to account for the air gap during the drained test chamber 

measurements. Kedzierski (2006) provides the derivation of the air-gap le and the result 

is given here as: 

1 ag ag 209.23[ ] m

c

e

mm mm

0.0121[m] kg 0.01156

2.3 m

l

o

dF dF

M e

dl dl l

Ix x ερ ρ

−

− ⎡ ⎤ = =− Φ ⎢ ⎥ ⎣ ⎦ (11) 

MEASUREMENT RESULTS 

Excess Layer Thickness

The test apparatus shown in Fig. 1 was used to submit either a PVC disk or an iron disk 

to exposure tests with fixed bulk concentration of diesel in tap water under varying flow 

conditions. More specifically, contamination measurements over an approximate 200 h 

time period were made for three different Reynolds numbers varying from 0 to 7000: 

b

4 Re

w

m

μ p =  (12) 

where the wetted perimeter of the channel was 195 mm, the viscosity of the mixed bulk 

flow (μb) was calculated using a nonlinear mixture equation, and the mass flow rate (m ) 

was obtained from the turbine meter. Flushing measurements were done for a fixed Re of 

approximately 5000. The range of Reynolds numbers result from using a range of 

volume flow rates that a half-inch diameter tube would experience in typical buildings. 
12

After each contamination tests, the test surface was cleaned with acetone and clean tap 

water. 

Contamination Tests

Figure 8 provides the measured diesel layer thickness on a PVC surface as caused by an 

exposure to a flowing water/diesel (99.85/0.15) mixture, i.e., diesel at approximately 

0.15 % bulk mass fraction (1500 ppm). The exposure time is the duration of the exposure 

test: it is the time that the test surface is exposed to the contaminated flow starting with a 

clean surface. The open circle, square, and triangle symbols represent contamination 

measurements obtained from eq. (9) for the Re = 0, 3200, and 7000 conditions, 

respectively. 

Figure 8 shows that the Re = 3200 and the soak (Re = 0) contamination tests gave similar 

results. More specifically, the excess layer thickness was established immediately upon 

exposure of the PVC surface to the water/diesel mixture and remained nearly constant for 

the 200 h test duration. Only a marginal increase in the time-averaged le was observed 

from approximately 1.32 μm to 1.48 μm when the Re was increased from 0 to 3200, 

respectively. However, an increase in the Re to 7000 resulted in roughly a 142 % 

increase in the time-averaged le over the soak condition to an average value of 

approximately 3.2 μm. In addition, the Re = 7000 condition did not produce a nearly 

constant le with respect to exposure time as did the Re = 0 and Re = 3200 conditions. 

Rather, the Re = 7000 condition gave a maximum diesel thickness of approximately 

4.4 μm at an exposure time of 20 h. With further exposure to 140 h, the diesel thickness 

decreased from this maximum to nearly the thickness at the initial contamination, which 

was approximately 3 μm. For the PVC surface, the approximate average le for the Re = 

0, 3200, and 7000 conditions was 1.32 μm, 1.48 μm, and 3.16 μm, respectively. 

Averaging over all contaminating flow rates and exposure times, the average le for 

xb = 0.15 % on the PVC surface was approximately 2.0 μm. 

Figures 9 gives the measured diesel layer thickness3

 on an iron surface due to exposure to 

a flowing water/diesel (99.85/0.15) mixture, i.e., the same composition as for the PVC 

surface. In general, the flow rate had little effect on the diesel excess layer thickness. 

For the iron surface, the approximate average le for the Re = 0, 3200, and 7000 conditions 

was 0.87 μm, 0.66 μm, and 0.60 μm, respectively. Averaging over all contaminating 

flow rates and exposure times, the average le for xb = 0.15 % on the iron surface was 

approximately 0.71 μm. Consequently, the PVC surface adsorbs approximately 180 % 

more diesel than the iron surface. The average accumulation of diesel on a copper 

surface for xb = 0.2 % was comparable to the PVC surface being approximately 2.3 μm 

(Kedzierski, 2006). 

Figure 10 crossplots all of the contamination excess layer measurements of Fig. 8 as a 

function of Re. Figure 10 shows that the maximum diesel excess layer thickness on the 

 

3

 The soak measurements on the iron surface were corrected as outline in Appendix B To 

account for additional rust resulting when the surface was exposed to air during repair of 

the apparatus. 
13

PVC surface of approximately 4.4 μm occurred between Re of 5700 and 6300. The peak 

le for Re near 3200 was approximately 2 μm, which is approximately 55 % less than the 

maximum le for the Re = 6000 tests. Another 20 % reduction in the peak le on the PVC 

surface was observed when the nominal Re was reduced from 3200 to 0. The peak le for 

the soak tests (Re = 0) was approximately 1.6 μm for the PVC surface. 

Figure 11 crossplots all of the excess layer measurements on the iron surface (Fig. 9) as a 

function of Re. Figure 11 shows that the maximum film thickness of approximately 

1.3 μm occurred for the soak tests on the iron surface. The peak le on the iron surface 

decreases slightly from the soak condition for increasing Re. The peak le on the iron 

surface for Re near 3200 and 6000 was approximately 1.1 μm and 1.0 μm, respectively. 

The dashed lines given in Figs. 10 and 11 indicate the maximum measured excess layer 

for tests on the PVC and the iron surface. The variation in Re for a given set of tests for 

“fixed” Re was caused by an approximate 1 % variation in the water temperature during 

startup and the an approximate 15 % variation in the water flow during the nearly 200 h 

test duration. 

Flushing Tests

The flushing tests that were done after each contamination test are shown in Figs. 8 and 

9. Measurements of le during flushing of the surface after the Re = 0, 3200, and 7000 

contamination tests are represented by the filled circle, square, and triangle symbols, 

respectively. For the PVC surface, most of the flushing measurements are close to but 

less than zero. The average of all the flushing measurements on the PVC surface is 

approximately –0.2 μm. It is likely that an unknown bias error has caused the 

measurement to be less than zero because 0.2 μm is larger than the uncertainty of the le

measurement. The negative thicknesses are interpreted as a clean surface. Consequently, 

the surface is clean nearly immediately after the inception of flushing. Negative 

thickness were observed with the exception of the flushing tests after the Re = 7000 

contamination (of the PVC surface) where the initial le was about 0.6 μm. The le

decreased from approximately 0.6 μm to approximately 0.13 μm after flushing for 

approximately 3.6 h. This corresponds roughly to a 0.13 μm/h removal rate, which is 

similar in magnitude to the flushing diesel removal rate, 0.10 μm/h, found for a copper 

surface (Kedzierski, 2006). 

The le averaged over all exposure times and Re for the flushing test on the iron surface 

was roughly 0.44 mm. The flushing tests after the Re = 7000 contamination were the 

most successful in getting the surface clean (l

e =− ⋅ 0.2 mμ ) assuming that negative 

thickness beyond the uncertainty implies a clean surface. On average, the flushing after 

the Re = 0 and the Re = 3200 tests left similar quantities of diesel on the surface, 0.6 μm 

and 0.8 μm, respectively. These numbers indicated that flushing after the Re = 3200 

contamination tests did not show any diesel removal, while the flushing after the soak 

tests gave only roughly a 0.3 μm diesel removal. However, both flushing tests after 

Re = 0 and the Re = 3200 contamination tests were corrected as outlined in Appendix B. 

The corrected measurements have an estimated uncertainty of ± 0.8 mm. Consequently, 

it is likely that the iron surfaces were flushed clean after Re = 0 and the Re = 3200 
14

contamination tests on the iron surface given that the measurements are within the 

measurement uncertainty and that the non-corrected flushing measurements indicated that 

the iron surface was clean after flushing. 

Gap Test Check

Filled symbols in Figs. 8 and 9, shown between 150 h and 200 h, represent le

measurements that were made at the end of the exposure tests after the test section was 

drained using the air-gap technique as a secondary measurement technique. The average 

uncertainty of the le obtained from the air-gap measurement was approximately ± 400 % 

of the measurement. As a result, it is not surprising that the le obtained from the air-gap 

measurement and that from eq. (9) or eq. (10) ranged between being 300 % smaller and 

200 % larger. It is not clear why the air-gap check gave good agreement with the 

measurements presented in Kedzierski (2006) but failed to provide confirmation of the 

present measurements. 

MODEL DEVELOPMENT 

The derivations of the models to predict the thickness of the contaminant excess layer on 

plumbing surfaces for the contamination and the flushing conditions are presented in 

Appendix C. Each model assumes that transfer of mass to and from the surface occurs 

solely in a direction that is perpendicular to the surface, i.e., in the y-direction shown in 

Fig. 4. The flushing model predicts the thickness of the excess layer as a function of 

time, contaminant transport properties, and flushing Reynolds number. The 

contamination model gives the maximum contaminant excess layer thickness that can 

occur for a given contaminant bulk mass fraction and surface affinity. 

Flushing Model

The model for flushing with contaminant-free water is based on the conservation of 

contaminant mass within the excess layer (le). Because the excess layer is thin, it is 

approximated as stagnate in the axial direction such that the net motion of diesel is solely 

perpendicular from the surface in the y-direction. The model is governed by turbulent 

convection and diffusion of contaminant from the surface. The effect of diffusion is 

modeled by the ratio of the diffusion coefficient (Dwd) to the transition depth (BT) over 

which the concentration difference occurs. The turbulent convection is modeled by the 

contaminant viscosity (νd), the friction velocity ( * u ), and an entrainment constant (KJ) 

that relates the average entrainment velocity ( max v′ / 2 ) to the local axial-velocity (u) in the 

viscous sublayer as: 

J max Kv u ≡ ′ / (13) 

The resulting equation to predict the contaminant excess layer (le) as a function of 

flushing time (t) and initial excess layer thickness (le0) is: 

2 J *

d e 2

e0 D D

1 1 1

K u t l

e

lK K

ν

−

⎛ ⎞

=+ − ⎜ ⎟ ⎝ ⎠

 (14) 
15

where the dimensionless constant KD is a ratio of the convective to the diffusive 

influences: 

2

J * T e0

D

d dw 2

Ku Bl K

ν D = (15) 

For KD = 1, convection and diffusion fluxes of contaminant from the surface are equal at 

the beginning of the flushing. Values of KD larger than 1 indicate that convection is more 

important than diffusion of contaminant from the surface. 

The friction velocity is calculated from an equation given by Kays and Crawford (1980) 

with the average (bulk) axial velocity (and fluid properties) of the flushing water (V) and 

its Reynolds number as: 

0.25

* u V 0.039 Re− = (16) 

Flushing measurements for contamination levels larger than those of the scope of the 

present project were taken in order to establish changes in the measured excess layers that 

were large enough to fit to eq. (14). These experiments flushed diesel from a PVC 

surface with tap water flowing at an Re of approximately 5000. The initial diesel excess 

layer was approximately 31.4 μm. Figure 12 shows the flushing measurements that were 

used to obtain the KJ and Ddw/BT constants from a least squares regression of the Fig. 12 

data to eq. (14). The regression constants are: 

8 8

J K 0.66 10 0.05 10 − − = ×±× (17) 

dw 10 10

T

m m 0.6 10 0.1 10

s s

D

B

− − ⎡ ⎤ ⎡⎤ =× ±× ⎢ ⎥ ⎢⎥ ⎣ ⎦ ⎣⎦ (18) 

Fig. 12 plots eq. (14) using the regressed eq. (17) and (18) constants. The model 

predictions are within ± 4 μm of all the measured le. 

The entrainment constant, KJ, is expected to be less of a function of the properties of the 

contaminant/flushing pair than is the diffusion constant. The ratio of the axial bulk 

velocity to its peak fluctuating component may be nearly constant because the bulk 

velocity is the potential for the fluctuating velocity. Considering this and that Kays and 

Crawford (1980) show that the ratio of the peak fluctuation turbulent velocity 

components is constant, the KJ may be relatively constant for a particular flushing fluid 

and for various Re. It is expected that the KJ presented here would be valid for water and 

liquids with similar kinematic viscosity.4

 Conversely, the Ddw/BT depends on the 

properties of both the contaminant and the flushing fluid. 

 

4

 However, KJ may be altered by the adhesion forces that must be overcome to remove 

the contaminant from the wall. 
16

The required time (t) to flush the surface clean is derived in Appendix C and is presented 

here: 

d

2

J* D

2 1 ln

1

t

Ku K

− ν ⎡ ⎤ = ⎢ ⎥ ⎣ + ⎦

 (19) 

Table 1 compares predictions using eq. (19) with observed values. All of the flushing 

times are predicted to within 7 h and all but one prediction is conservatively 

overestimated. 

Contamination Model

For the contamination case, where a balance between deposition of contaminant on the 

surface and removal of the contaminant from the surface must be achieved, surface 

adhesion requires that a distinction be made between the velocity of the contaminant 

toward the surface (vi) and that away from it (vo). Very near the wall there is an 

additional resistance to flow away from the surface as caused by the attraction of diesel 

molecules to the molecules of the pipe surface. Likewise, for the same region near the 

pipe, the attractive forces induce a reduction in the resistance of flow toward the surface. 

Considering that it is flow that is being modeled, a simply way to approximate this 

behavior is via a modified viscosity. For example, the entrainment velocity (evaluated 

using the properties of the contaminated flow) given in Appendix C (eq. C8) for flow 

approaching the pipe surface becomes: 

[ ]

2

J *e

i

e

d 2 tanh e y l

Kul

v

l

ν δ

= = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

 (20) 

Here, the kinematic viscosity is less than the constant property viscosity (νd) for distances 

from the surface less than the penetration depth, δ, because adhesive forces assist the 

flow of contaminant to the surface within this region. The magnitude of the penetration 

depth is determined by the affinity of the contaminant for the pipe surface. 

Consequently, each contaminant\pipe combination will have its own value of δ. The 

hyperbolic tangent was chosen for its simplicity and because it closely matched what was 

believed to be the required relationship with respect to le. 

Likewise, surface adhesion acts to deter the flow of contaminant from the wall according 

to an assumed hyperbolic cotangent relationship with respect to le. Here the leaving 

velocity is approximated as a local increase in viscosity above the constant property value 

as the pipe surface is approached for distances less than δ: 

[ ]

2

J *e

o

e

d 2 coth e y l

Kul

v

l

ν δ

= = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

 (21) 
17

Figure 13 provides an example of the ratio of the adhesive influenced viscosity to the 

constant property viscosity of diesel (θ) as a function of the distance from the iron 

surface. For this example, the excess layer is 0.5 μm and the penetration depth is 14 μm. 

The viscosity ratio is plotted as a function of y to illustrate the waning and waxing 

influences of the adhesive forces between iron and diesel as a model concept. However, 

as far as the contamination model is concerned, θ is evaluated only at le = 0.5 μm. 

Considering that the exposure time of a pipe surface to a contaminant may not always be 

known, a conservative decontamination response would be to flush for the maximum 

contaminant film thickness (excess layer) for the given concentration of contaminant in 

the flow. The maximum contaminant excess layer, which occurs at steady state where 

the contaminant deposition balances the removal at the wall, can be determined by setting 

the partial derivative of the excess layer with respect to time to zero (see Appendix C) 

and solving the resulting equation for le, yielding: 

[ ] b

e max

b

1

ln

2 1

x

l

x

δ ⎛ ⎞ + = ⎜ ⎟ ⎜ ⎟ − ⎝ ⎠

 (22) 

Equation (22) can be used to determine the maximum possible contamination level and 

used as input to eq. (19) in order to calculate the required flushing time to obtain a clean 

surface. Mathematically, eq. (22) is valid for values of xb between zero and 1; however, 

it has been validated for only dilute solutions. 

Average values of the penetration depth were found by back-substituting the measured 

diesel bulk mass fraction and the measured [le]max into eq. (22) and solving for δ. The δ

was found to be surface dependent: 150 μm, 42 μm, and 16 μm for copper, PVC, and 

iron, respectively. Figure 14 shows the maximum contamination layer for the three pipe 

surfaces as a function of xb as predicted by eq. (22). Because of the presumed stronger 

affinity between copper and diesel, the copper surface has greater contamination levels 

for a given xb as compared to the PVC and iron surfaces. The greater affinity is modeled 

via the larger penetration depth. 

FUTURE WORK

The overall goal of this project is to develop the tools that are necessary for adequately 

responding to a contamination event. These tools have been envisioned to consist of 

measured data, predictive models, and a computer program that embodies the data and 

models. The software would allow the user to input information that is specific to a 

contamination event and to receive estimates of contamination levels and required 

flushing times. Such an all-encompassing goal requires a significantly large effort in 

order to ensure that the software makes reliable predictions for all possible contaminants. 

In order to achieve this task in a reasonably short time, the model must be physically 

based, but yet simple, so that it may be easily adjusted and extrapolated for different 

contaminants. 
18

In this light, the models developed in this project require additional enhancement to 

ensure that the best possible predictions can be provided. Possibly, the major effort 

toward this end will be using measured data to calculate the constants KJ, Ddw/BT, and δ

for potential contaminants (like toluene, see Appendix D) and pipe surfaces. In the 

course of this effort, it will be determined whether or not KJ is merely a function of the 

properties of the flushing fluid. In addition, it can be determined if δ is constant for a 

particular contaminant/surface pair. In the short term, more flushing measurements at 

different initial le are required to validate the flushing constants considering that only one 

data set was used to obtain them. It may be appropriate to lump the diffusion that occurs 

during contamination into the adhesion effect. On the other hand, inclusion of a diffusion 

component in the contamination model may be necessary. These questions can be 

answered with further experimentation and model enhancement. 

CONCLUSIONS 

A detailed account of the continued development of a fluorescence based measurement 

technique for measuring the mass of contaminant on solid surfaces in the presence of 

water flow has been provided. A test apparatus was designed and developed to use the 

fluorescent properties of diesel for the purpose of studying its adsorption and desorption 

to and from plumbing pipe materials. A calibration technique was developed to measure 

both the mass of diesel adsorbed per unit surface area (the excess surface density) and the 

bulk concentration of the diesel in the flow. 

Measurements for a given condition were made over a period of approximately 200 h for 

a diesel mass fraction of approximately 0.15 %. The largest excess layer thickness was 

approximately 4.4 μm, which was measured on a PVC surface for a Reynolds number of 

approximately 7000. The peak contaminant thickness on the PVC surface was shown to 

increase for increasing Re. Averaging over all contaminating flow rates and exposure 

times, the excess layer thickness on the PVC surface was approximately 2.0 μm. 

Reynolds number had little or no effect on the accumulation of diesel on an iron surface, 

which was approximately 0.71 μm. On average, the PVC surface adsorbed 

approximately 180 % more diesel than the iron surface. Both the PVC and iron surfaces 

were readily flushed with tap water. 

Models to predict excess layer thickness on plumbing surfaces during flushing and 

contamination were developed. The flushing model predicts the thickness of the excess 

layer as a function of time, contaminant transport properties, and flushing Reynolds 

number. The required time to flush clean given an initial contaminant thickness can also 

be calculated. All of the flushing times were predicted to within 7 h. The contamination 

model gives the maximum contaminant excess layer thickness that can occur for a given 

contaminant bulk mass fraction and surface affinity. The contamination model accounts 

for the relative affinity between pipe surface and contaminant by predicting greater 

contamination levels on the PVC than on the iron surfaces. Together, the two models can 

be used as tools to develop a response to a contamination event. 
19

ACKNOWLEDGEMENTS 

This work was funded by the U.S. Environmental Protection Agency (EPA) under 

contract #DW-13-92167701-0, with the guidance of project manager Mr. V. Gallardo. 

Thanks go to the following NIST personnel for their constructive criticism of the first 

draft of the manuscript: Dr. S. Treado, and Dr. P. Domanski. Thanks goes to Dr. K. Cole 

of NIST’s Biochemical Science Division for his constructive criticism of the second draft 

of the manuscript. Furthermore, the author extends appreciation to Mr. D. Wilmering 

and Mr. J. Wamsley for taking the measurements and conquering the difficult machining 

and design problems encountered in the project. 
20

NOMENCLATURE 

English Symbols

A regression constants in eq. (7) 

BT diffusion length, m

c concentration, mol m-3 

c mass concentration, kg m-3

Dwd diffusion coefficient, m2 s-1

F fluorescence intensity 

Fc corrected fluorescence intensity measurement 

Fr raw fluorescence intensity measurement 

Io incident intensity, V 

KD dimensionless number convection to diffusion eq. (15)

KJ entrainment velocity ratio eq. (13)

l path length, m 

le thickness of excess layer, m 

M mass of excess layer, kg 

Mc molar mass of contaminant, kg mol-1

m mass flow rate, kg s-1

Re Reynolds number 

pw wetted perimeter of channel, m 

t time, s 

T temperature, K 

u local axial velocity, m s-1

u* friction velocity, m s-1

U expanded uncertainty 

ui standard uncertainty 

v local velocity in y-direction, m s-1 

v’ turbulent fluctuating velocity in y-direction, m s-1

V bulk axial velocity, m s-1

x mass fraction of diesel 

y coordinate perpendicular to pipe surface, m 

Greek symbols

δ penetration depth, m

Γ surface excess density, kg m-2

ε extinction coefficient 

θ ratio of modified to constant viscosity 

λ wavelength, m 

μ dynamic viscosity, kg m-1 s-1

ν kinematic viscosity, m2 s-1 

ρ mass density of liquid, kg m-3

Φ quantum efficiency of fluorescence 

English Subscripts

0 zero reference jar 

100 maximum reference jar 
21

a ambient 

ag air gap 

b bulk 

d pure diesel 

e excess layer 

i inlet 

l liquid 

le excess layer 

m emission, mixture 

ng no air gap 

o outlet or exit 

s solid surface 

Tb reference bath temperature 

TT test section temperature 

x excitation 

w tap water 

Superscripts

- average 
22

REFERENCES 

Amadeo, J. P., Rosén C., and Pasby, T. L., 1971, Fluorescence Spectroscopy An 

Introduction for Biology and Medicine, Marcel Dekker, Inc., New York, p. 153. 

Guilbault, G. G., 1967, Fluorescence: Theory, Instrumentation, and Practice, Edward 

Arnold LTD., London, pp. 91-95. 

Herman, B., 1998, Fluorescence Microscopy, 2nd ed., Springer-Verlag New York, Inc., 

pp. 69 –71. 

Kays, W. M., and Crawford, M. E., 1980, Convective Heat and Mass Transfer, McGrawHill, New York, NY. 

Kedzierski, M. A, 2006, “Development of a Fluorescence Based Measurement Technique 

to Quantify Water Contaminants at Pipe Surfaces During Flow,” NISTIR 7355, U.S. 

Department of Commerce, Washington, D.C. 

Kedzierski, M. A., 2003, ”Effect of Bulk Lubricant Concentration on the Excess Surface 

Density During R134a Pool Boiling with Extensive Measurement and Analysis Details,” 

NISTIR 7051, U.S. Department of Commerce, Washington, D.C. 

Kedzierski, M. A., 2002, ”Use of Fluorescence to Measure the Lubricant Excess Surface 

Density During Pool Boiling,” Int. J. Refrigeration, Vol. 25, pp.1110-1122. 

Kedzierski, M. A., 2001, ”Use of Fluorescence to Measure the Lubricant Excess Surface 

Density During Pool Boiling,” NISTIR 6727, U.S. Department of Commerce, 

Washington, D.C. 

Miller, J. N., 1981, Volume Two Standards in Fluorescence Spectrometry, Chapman and 

Hall, London, pp. 44-67. 

Reader, J, Corliss, C. H., Wiese, W. L., and Martin, G. A., 1980, "Wavelengths and 

Transition Probabilities of Atoms and Atomic Ions", NSRDS-National Bureau of 

Standards #68, U.S. Department of Commerce, Washington. 

Schlichting, H., 1979, Boundary-Layer Theory, McGraw-Hill, New York, pg. 591. 

Schwarzenbach, R. P., Gschwend, P. M., and Imboden, D., M., 2003, Environmental 

Organic Chemistry, 2nd ed., Wiley, NJ, pp 281-283. 

Simplex, 2006, http://www.simplexdirect.com/FuelSupply/mainten04.html 

Tennekes, H., and Lumley, J. L., 1982, A First Course in Turbulence, MIT Press, 

Cambridge, MA, p. 160. 
23

Table 1 Comparison of flushing model predictions to measurements 

Surface Re le0 (μm) KD Flushing time 

for clean eq. 

(19) (h) 

Observed 

flushing 

time for no 

change (h) 

PVC 0 1.5 0.29 6.4 ≈ 0

PVC 3200 1.5 0.29 6.4 ≈ 0

PVC 7000 2.5 0.49 9.7 ≈ 8

Iron 0 1.0 0.20 4.3 ≈ 0

Iron 3200 1.0 0.20 4.3 ≈ 0

Iron 7000 0.5 0.10 2.3 ≈ 5
24

Fig. 1 Schematic of test loop
25

Fig. 2 Schematic of spectrofluorometer, test section, and linear positioning device 
26

 

Fig. 3 Schematic of right angle spectrofluorometer (Kedzierski, 2006) 
27

 

Fig. 4 Cross-sectional illustration of test section during contamination and flushing 
28

 

Fig. 5 Schematic of fluorescence/composition calibration jar (Kedzierski, 

2006) 
29

Fig. 6 Overall calibration of Beer-Lambert Bougher law for diesel on copper disk 

(Kedzierski, 2006) 
30

 

Fig. 7 Sample F vs. l fit for a PVC data set 
31

Fig. 8 Effect of exposure time and flow rate on thickness of the diesel excess layer 

for a 0.15 % bulk freestream mass fraction on a PVC disk 
32

Fig. 9 Effect of exposure time and flow rate on thickness of the diesel excess 

layer for a 0.15 % bulk freestream mass fraction on an iron disk 
33

Fig. 10 Diesel excess layer thickness as a function of Re for PVC surface and 

water/diesel (99.85/0.15) 
34

Fig. 11 Diesel excess layer thickness as a function of Re for iron surface and 

water/diesel (99.85/0.15) 
35

Fig. 12 Flushing measurements used to fit coefficients of model 
36

Fig. 13 Modified kinematic viscosity to account for adhesive forces between 

iron and diesel derived for two flow conditions (Re = 3200 and Re = 7000). 
37

 

Fig. 14 Maximum contamination diesel layer on various pipe surfaces as 

predicted by eq. (22) 
38

APPENDIX A: UNCERTAINTIES 

Figure A.1 shows the relative (percent) uncertainty of the diesel excess layer thickness 

(Ule) as a function of le for the iron test surface. Measurements of le on the iron surface 

with uncertainties larger than 10 % were discarded. Of the retained measurement sets, 

the average uncertainty in le for the contamination and the flushing tests was 

approximately ± 8 %, and ± 4 % of le, respectively. Overall, the average uncertainty of le

on an absolute basis for the iron surface contamination and flushing tests was 

approximately ± 0.06 μm and ± 0.02 μm, respectively. 

 

Fig. A.1 Relative uncertainty of le for 95 % confidence level for iron surface 

xb = 0.15 % 
39

Similarly, Fig. A.2 shows the relative (percent) uncertainty of the diesel excess layer 

thickness (Ule) as a function of le for the PVC test surface. For the PVC surface, 

contamination and flushing measurements le with uncertainties larger than 10 % and 

20 %, respectively, were discarded. Of the retained measurement sets, the average 

uncertainty in le for the two lowest Re contamination tests and the Re = 7000 

contamination tests was approximately ± 6 %, and ± 3 % of le, respectively. Overall, the 

average uncertainty of le for the measurements with the PVC surface for the 

contamination measurements was approximately ± 0.1 μm. The average uncertainty in le

for the PVC flushing tests was approximately ± 17 % of le, which was approximately 

± 0.05 μm. 

Fig. A.2 Relative uncertainty of le for 95 % confidence level for PVC surface 

xb = 0.15 % 
40

Figure A.3 shows the relative (percent) uncertainty of the bulk freestream diesel mass 

fraction (Uxb) as a function of xb for the iron test surface. Of the retained measurement 

sets, the average uncertainty in xb for the contamination tests was approximately ± 4 % of 

xb. Overall, the average uncertainty of xb on an absolute basis for the iron surface was 

approximately ± 0.006 % (± 60 ppm). 

 

Fig. A.3 Relative uncertainty of xb for 95 % confidence level for iron surface 
41

Figure A.4 shows the relative (percent) uncertainty of the bulk freestream diesel mass 

fraction (Uxb) as a function of xb for the PVC test surface. Of the retained measurement 

sets, the average uncertainty in xb for the contamination tests was approximately ± 5 % of 

xb. Overall, the average uncertainty of xb on an absolute basis for the PVC surface was 

approximately ± 0.008 % (± 80 ppm). 

Fig. A.4 Relative uncertainty of xb for 95 % confidence level for PVC surface 
42

APPENDIX B: MEASUREMENT CORRECTION 

This appendix outlines how two flushing tests and one contamination test were corrected 

to account for additional rust resulting when the iron surface was exposed to air during a 

one-time repair of the apparatus. The bottom of the quartz probe housing became ajar 

just prior to the flushing tests that were done after the Re = 3200 contamination tests. 

Due to exposure of air during the repair, rust developed on the iron test surface causing a 

reduction in the measured fluorescence intensity. Consequently, flushing tests after 

Re = 0 and the Re = 3200 contamination tests were corrected as were the soak 

contamination measurements. 

The correction was accomplished by comparing repeated contamination measurements 

before repair and after repair for the same bulk mass fraction of diesel and the same 

Reynolds number. Figure B.1 shows the excess layer as a function of exposure time for 

Re = 7000 and xb = 0.0015 for contamination tests before and after the test apparatus 

repair. The correction was devised to adjust the fluorescence intensity by a constant such 

that the average le of the before and after data sets were equal. Given that both data sets 

appeared to exhibit random trends with respect to time, it was assumed that a steady state 

between contaminant deposition and removal had been achieved for the entire data set. 

For this reason the entire data range for both data sets were used to obtain an average for 

each. 

Because the oxidation of the iron had relatively ceased once it was re-immersed in the 

test water, the effect of the rust on the signal intensity was expected to be constant. In 

order to ensure that the adjustment to the intensity (ΔFc ) was a constant, the effect of the 

increased incident intensity with increased proximity to the surface was accounted for by 

the exponential term in the expression for the corrected fluorescence intensity (Fc): 

1 209.23[m ]

c c

l F Fe F −

= +Δ (B.1) 

The correction was found to be: c Δ = F 0.001and the exponential term came from the 

calibration given in eq. (4). Once the intensity was corrected, Fc was used in place of F

in the determination of le. The estimated uncertainty of le on an absolute basis for the 

corrected measurements was approximately ± 0.8 μm. 

 
43

Fig. B.1 Basis for correction of iron surface measurements made after test 

apparatus repair 
44

APPENDIX C: MODEL DEVELOPMENT 

The derivations of the models for the prediction of the thickness of the contaminant 

excess layer on plumbing surfaces for the contamination and the flushing conditions are 

presented in this appendix. Each model assumes that transfer of mass to and from the 

surface occurs solely in a direction that is perpendicular to the surface. The flushing 

model predicts the thickness of the excess layer as a function of time, contaminant 

transport properties, and flushing Reynolds number. The contaminant model gives the 

maximum contaminant excess layer thickness that can occur for a given contaminant bulk 

mass fraction and surface affinity. 

Flushing Model

The flushing model is based on the conservation of contaminant mass within the excess 

surface density layer. Because the excess layer is thin, it is approximated as stagnate in 

the axial direction such that the net motion of diesel is solely perpendicular from the 

surface in the, y-direction. From the corresponding continuity equation, the rate of 

change of change of mass (M) in the excess layer with respect to time (t) is equal to the 

mass flow of contaminant ( md  ) from the excess layer-flushing water interface: 

io d

M

mm m

t

∂ = − =− ∂   (C1)5

The mass of the excess layer can be represented by the product of the contaminant 

density (ρd), the surface area of the excess layer-water interface (A), and the thickness of 

the excess layer (le), i.e.: 

M = = Γ A Al ρd e (C2) 

The diesel is transported from the surface via convection and diffusion. For turbulent 

flushing, convection of the diesel from the interface between the excess layer and the 

flushing water is caused by the pumping action of the fluctuating y-velocity component, 

[ ] e y l v = , that entrains diesel from the excess layer into the bulk water flow. Diffusion also 

occurs perpendicular to the surface because of the difference in diesel mass concentration 

between the excess layer ( d c ) and the water ( wc ). The following equation approximates 

the diffusion with an expression for equimolal diffusion (McCabe and Smith, 1976) that 

contains a diffusion coefficient (Dwd) and a transition depth (BT) over which the mass 

concentration difference occurs. The total mass flux of diesel from the excess layer is the 

sum of the convective and the diffusive components: 

[ ] ( ) d wd

d dw

T e y l

m D

v c cc

A B = = +−  (C3) 

 

5

 Here mi  and mo  are the mass flow rates of contaminant entering and leaving the excess 

layer control volume, respectively. No flow enters the excess layer from the plumbing 

surface. Consequently, mi  is zero. 
45

The effect of upstream diesel entrainment is assumed to not significantly increase the 

mass concentration of diesel in the flushing water. As a result, the cw is approximated as 

zero. In addition, the diesel excess layer is neat diesel, i.e.: 

d dd d c x = = ρ ρ (C4) 

The average entrainment velocity (v) is approximated by half the magnitude of the 

maximum fluctuating component of the turbulent y-velocity ( max v′ ): 

max

2

v

v ′ = (C5) 

From the law of the wall, the axial velocity component in the viscous sublayer is 

(Tennekes and Lumley, 1982): 

2

*

max

d

u

u yu

ν = ∝ ′ (C6) 

whereνd is the kinematic viscosity of the diesel, max u′ is the maximum fluctuating 

component of the turbulent axial velocity component, and * u is the friction velocity given 

by Kays and Crawford (1980): 

0.25

* u V 0.039 Re− = (C7) 

Where V is the bulk average velocity of the flushing water in the axial direction and Re is 

the Reynolds number based on the hydraulic diameter evaluated for the properties of the 

flushing water. 

Kays and Crawford (1980) also show that the fluctuation turbulent velocity components 

may be related by a constant max max Kv u ≡ ′ ′ / . If it is assumed that max u′ is proportional to 

the axial velocity, i.e., max u Ju ′ ≡ , and the constant J is lumped into the constant KJ

6

, 

max v′ can be written as: 

[ ] [ ] 2

2 max J* d

J *e

/

2 22

e e

e

yl yl

y l

v Ku y Kul

v

ν

ν

= =

=

′ ⎡ ⎤ ⎣ ⎦ == = (C8) 

 

6

J max K KJ v u ≡ ≡ ′ /
46

Substitution of eqs. (C2), (C3), (C4) and (C8) yields the following first order partial 

differential equation that governs the removal of the excess layer (le) during flushing: 

2

e J * e dw

d T 2

l Kul D

t B ν

∂

+ =−

∂ (C9) 

multiplying both sides of the differential equation by the integrating factor 

2 J *

2

K u t

e ν gives: 

2 J *

d

2 2 J* J*

d d

2

e 2

2 2 e J * e dw

d T 2

K u t

Ku Ku t t

l e

l Kul D

e e

t Bt

ν

ν ν

ν

⎛ ⎞

∂ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ ∂ ⎝ ⎠ ⎜ ⎟ + =− =

∂ ∂ ⎝ ⎠

 (C10) 

Separating and integrating the last two terms of the above equation and ensuring that 

le = le0 at t = 0 yields: 

2 J *

d d dw d dw 2

e e0 2 2

J* T J* T

2 2 K uD D t

l le

Ku B Ku B

ν ν ν

−

− ⎛ ⎞

= ++ ⎜ ⎟ ⎝ ⎠

 (C11) 

The required time to flush le0 to le = 0 can be determined by setting le to zero in the above 

equation and solving for the elapsed time t: 

d

2 2

J * J * e0 T

d dw

2 1 ln

1

2

t

K u Kul B

D

ν

ν

⎡ ⎤ ⎢ ⎥ − = ⎢ ⎥ ⎢ ⎥ + ⎢ ⎥ ⎣ ⎦

 (C12) 

Contamination Model

For the contamination case where a balance between deposition of contaminant on the 

surface and removal of the contaminant from the surface must be achieved, surface 

adhesion requires that a distinction be made between the velocity of the contaminant 

toward the surface (vi) and that away from it (vo). Very near the wall there is an 

additional resistance to flow away from the surface as caused by the attraction of diesel 

molecules to the molecules of the pipe surface. Likewise, for the same region near the 

pipe, the attractive forces induce a reduction in the resistance of flow toward the surface. 

Considering that it is flow that is being modeled, a simply way to approximate this 

behavior is via a modified viscosity. For example, the entrainment velocity (evaluated 

using the properties of the contaminated flow) given in eq. (C8) for flow approaching the 

pipe surface becomes: 
47

[ ]

2

J *e

i

e

d 2 tanh e y l

Kul

v

l

ν δ

= = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

 (C13) 

Here, the modified kinematic viscosity is less than the constant property viscosity (νd) for 

distances from the surface less than the penetration depth, δ. The magnitude of the 

penetration depth is determined by the affinity of the contaminant for the pipe surface. 

Consequently, each contaminant\pipe combination will have its own value of δ. The 

hyperbolic tangent was chosen for its simplicity and because it closely matched what was 

believed to be the required relationship with respect to le. 

Likewise, surface adhesion acts to deter the flow of contaminant from the wall according 

to an assumed cotangent relationship with respect to le. Here the leaving velocity is 

approximated as a local increase in viscosity above the constant property value as the 

pipe surface is approached for distances less than δ: 

[ ]

2

J *e

o

e

d 2 coth e y l

Kul

v

l

ν δ

= = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

 (C14) 

For the case where diffusion is negligible, the balance between the deposition and 

removal of contaminant at the wall becomes: 

i o i bd o d ( ) [] [ ] e e yl yl

M mm v x v A

t

ρ ρ = =

∂ =− = − ∂  

 (C15) 

Substitution of M from eq. (C2) reduces the above mass balance to: 

[] [ ] e

i bo e e yl yl

l

v xv

t = =

∂ = − ∂ (C16) 

Substitution of vi and vo into eq. (C16) gives the following first order differential equation 

for surface contamination from a bulk flow with a contaminant mass fraction of xb: 

2

e J *e b

d e e

1

2 tanh coth

l Kul x

t ν l l

δ δ

⎛ ⎞ ⎜ ⎟ ∂ ⎛ ⎞ = − ⎜ ⎟ ∂ ⎛⎞ ⎛⎞ ⎝ ⎠ ⎜⎟ ⎜⎟ ⎝ ⎠ ⎝⎠ ⎝⎠

 (C17) 

Considering that the exposure time a pipe surface to a contaminant may not always be 

known. A conservative decontamination response would be to flush for the maximum 

contaminant film thickness (excess layer) for the given concentration of contaminant in 

the flow. The maximum contaminant excess layer, which occurs at steady state where 

the deposition balances the removal at the wall, can be determined by setting the partial 
48

derivative of the excess layer with respect to time to zero in eq. (C17) and solving the 

resulting equation for le, yielding: 

[ ] b

e b max

b

1

ln 0 1

2 1

x

l for x

x

δ ⎛ ⎞ +

= → →< < ⎜ ⎟ ⎜ ⎟ − ⎝ ⎠ (C18) 
49

APPENDIX D: FLUORESCENCE OF TOLUENE 

This appendix presents the fluorescence of a potential next contaminant to study using 

the fluorescence measurement technique presented in this report. Figure D.1 

schematically shows the test setup to measure the fluorescence emission of toluene on 

PVC, copper, and iron surfaces. Each emission was measured with the 

spectrofluorometer instrumented with two fiber optical bundles orientated nearly 

perpendicular to each other at the test surface. The excitation bundle was orientated at a 

slight angle from the horizontal with respect to the toluene film that was on the test 

surface. The emission bundle was perpendicular to the test film and surface. 

The toluene film was confined to each test surface by an open-ended quartz box that was 

sealed around the 10 mm x 30 mm outside perimeter of the base with modeling clay. In 

order to achieve a repeatable film thickness of approximately 1 mm, single drops of 

toluene were dropped onto the surface until it was fully wetted. 

Each emission spectrum was produced with a constant excitation wavelength of 355 nm. 

Figure D.2 shows the fluorescence emission of toluene on three pipe surfaces: PVC, 

copper, and iron. Figure D.2 shows that the surface materials do not significantly affect 

the emission spectrum. Each emission spectrum has approximately the same shape and 

the same peak wavelength. The tests show that maximum signal intensity for toluene is 

found between 375 nm and 425 nm and that toluene is a potential contaminant candidate 

that can be detected with the measurement technique that is presented in this report. The 

uncertainty of the mean intensity and wavelength measurement for this particular 

experimental setup was approximately ± 20 %, and ± 2 nm, respectively. 

Fig. D.1 Schematic of experimental setup to measure fluorescence emission of 

toluene on three pipe surfaces: PVC, copper, and iron 
50

 

Fig. D.2 Fluorescence emission of toluene on three pipe surfaces: PVC, copper, and 

iron