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This is to certify that the
thesis entitled

TRANSFER OF VOLATILE CHEMICALS ACROSS THE AIR-
WATER INTERFACE UNDER DIFFERENT WIND CONDITIONS
presented by

Sinisa Sirovica

has been accepted towards fulfillment
of the requirements for

 

Master of Science Jegreein Civil Engineering

Major professor

Date May 17, 1982

0-7639

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TRANSFER OF VOLATILE CHEMICALS ACROSS THE AIR-
WATER INTERFACE UNDER DIFFERENT WIND CONDITIONS

by

Sinisa Sirovica

’ /

(A. {a h/
- ' ‘

A THESIS

Q / {"7

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Civil and Sanitary Engineering

1982

ABSTRACT

TRANSFER OF VOLATILE CHEMICALS ACROSS THE AIR-
WATER INTERFACE UNDER DIFFERENT WIND CONDITIONS

BY
Sinisa Sirovica

Mass transfer across the air-water interface was
studied for a wide range of wind conditions. The study
was aimed at the evaluation of the liquid and gas phase

mass transfer coefficients, k2 and k respectively, as

9
defined by Whitman's two film theory. Wind-tunnel
experiments were performed to simulate field conditions.
Values of kl were determined using toluene as a volatile
agent and values of kg were determined from water
.evaporation measurements. Two independent methods were
applied for the evaluation of the coefficients and yielded
consistent results. The effect of temperature was
considered. A linear relation was obtained between k2 and
the shear velocity u* for u* > 0.10 m/s. A linear
relationship was also found between Kg and u* for the

.. experimental range considered. A comparison of to values

obtained in the laboratory with field data showed an

underprediction in kg by approrimately 25%.

To My Parents

Ankica and Borivoje

ACKNOWLEDGEMENTS

I would like to express my gratitude to my major
advisor, Dr. Reinier-J. B. Bouwmeester, for his help and
guidance throughout this work.

Special thanks to Dr. John A. Eastman for his
contributions prior to and during the course of the
experiments. Thanks also to Dr. M. L. Davis and
Dr. D. C. Wiggert for helping me with my training in
engineering.

I am grateful to Mr. D. Harms for his assistance
in computer programming.

Financial support for this study was provided by

the Environmental Protection Agency.

iii

.Chapter

TABLE OF CONTENTS

1 O O I NTRODUCTI ON C O O O O C O O O O O O O O O O O

2.0 THEORY . . . . . . . . . . . . . . . . . . . .

3.0 EXPERIMENTAL PROCEDURES . . . . . . . . . . .

wwww
O O O

3.5 Humidity measurements . . . . . . . .

PMNI—J

Wind tunnel facility .
Experimental setup . .
Velocity measurements .
Toluene measurements . .
3.4.1 Toluene application .
3.4.2 Toluene measurements in air

3.4.3 Toluene measurements in water

4.0 CALCULATION PROCEDURES . . . . . . . . . . . .

4.1 Horizontal flux method . . . . . . . . .
4.2 Depletion method . . . . . . . . . . . .

5.0 RESULTS AND DISCUSSION . . . . . . . . . . . .

5.
5.

5.
5.
5.

1
2

3
4
5

Velocity calculations . J . .
Determination of k values .
5.2.1 Horizontal lux method
5.2.2 Depletion method . . .
Temperature correction . . .
Determination of k values

Comparison of kg wlth field data.

6.0 CONCLUSIONS AND RECOMMENDATIONS . . . . . . .

APPENDICES

A.

B.
C.

Measurement of toluene concentrations
in air and water . . . . . . . . . . .
Insrumentation and equipment . . . . .
Tables and experimental data . . . . .

BI BLIOGRAPHY O O ' O O O O O O O O O O O O O O O O 0

iv

Page

13

13
15
17
18
19
20
21
21

23

23
27

29

29
33
33
40
40
45
48

51

53
69
71

75

Table

A1
A2
C1

C2

LIST OF TABLES

Velocity Parameters . . . . . .

Calibration data for toluene in air

Calibration data for toluene in CS2

Toluene experimental data . . .

Water vapor experimental data .

Figure
l.

10.
ll.

12.
13.
14.
15.
16.

LIST OF FIGURES

Relation between partial pressure and
mole fraction of a solute in solution . . .

Schematic of the two-film model of
volatilization from the surface of
water bodies . . . . . . . . . . . . . . .

Plot of Solubility, Vapor Pressure
and Henry' s Constant (20°C) . . . . . . . .

Environmental Wind Tunnel, Fluid Mechanics
Laboratory, Michigan State University . . .

Experimental Setup . . . . . . . . . . . .

Vertical wind velocity distribution
at station 1 . . . . . . . . . . . . . . .

Vertical wind velocity distribution
at station 2 I O O O O O O O O C O O O O 0

Examples of measured concentration profiles

Measured concentration, C , vs.
calculated concentration, C1 . . . . . . .

vs. U1 for station 1 and 2 at 20°C
(horizontal flux method) . . . . . . . . .

Kg vs. u* for station 1 and 2 at
20°C (horizontal flux method) . . . . . . .

Kt vs. U10 at 20°C (depletion method) . . .

*
vs. u at 20°C (depletion method) . . .

K2

K2 vs. Temperature for U10 = 7.62 m/s . . .

Kg vs. Ulo for station 1 and 2 . . . . . .
*

Kg vs. u for station 1 and 2 . . . . . . .

14
16

30

31
34

35

37

38
41
42
44
46
47

Figure
17.

Al.

A2.
A3.
A4.

A5.

*
Kg vs. u for field and laboratory data

Schematic drawing of a gas
chromatographic system . . . . . . . .

Typical chromatogram . . . . . . . . .
Permeation tube calibration system . .
Permeation tube weight loss vs. time .

Internal standard calibration . . . . .

54
57
59
60
64

"1WD

7:213")

LIST OF SYMBOLS

Description
Surface area of water (m2)
Concentration of toluene in water (mol/m3, mg/m3)

Concentration of toluene in air (mol/m3, mg/m3)

Concentration of toluene at the interface

(mol/ma, mg/ma)

Initial toluene concentration in water
(mol/m3, mg/m3 )

Water vapor concentration at height of 10 cm
(mol/m3 , mg/m3 )

Saturated water vapor concentration (mg/m3)
Water evaporation rate (g/m2.hr, cm/3hrs)
Chemical potential in gas phase (atm)
Chemical potential in liquid phase (atm)
Henry's constant (atm.m3/mol)

Mass transfer coefficient (mZ/s)

Liquid phase mass transfer coefficient (m/hr)
Gas phase mass transfer coefficient (m/hr)
Mass transfer coefficient at z = 10 cm
Water depth (m)

Toluene mass flux (mol/mz.s)
Partial pressure (atm)

Partial pressure at interface (atm)

Film resistance

Description
Universal gas constant (atm.m3/mol°K)
Absolute temperature (0K)
Shear velocity (m/s)
Wind velocity (m/s)
wind velocity at 10 cm (m/s)
wind velocity at 8 m (m/s)

Concentration of toluene at the interface
(mole fraction)

Distance to the upwind edge (m)
Distance above the water surface (cm)
Surface roughness length (cm)
Power-law exponent

Gamma functiOn

l . 0 I NTRODUCTI ON

The transfer of volatile chemicals across the
air-water interface occurs by molecular and turbulent
diffusion. The development of a full understanding of
this process and hence the prediction of transfer rates
for any chemical under different environmental conditions
presents a problem that has not yet been fully elucidated.
When a natural water body is in contact with the
atmosphere, the following questions are important. In
which direction does the transfer take place? How fast is
it occurring? What factors enhance it or reduce it? The
answer to these questions requires an understanding of
wind-wave interaction, chemistry and the transfer process
itself.

One aspect of the transfer process is the
volatilization of aqueous pollutants from natural waters
into the atmosphere. This process affects pollution
levels in the aqueous environment. For example, it was
found that some hydrocarbons and chlorinated hydrocarbons
in natural water are predominantly eliminated by
volatilization to the atmosphere (Dilling et a1, 1975;
Mackay and Leinonen, 1975; Schwarzenbach et al., 1979)

The transferof a chemical from one phase to the
other has been investigated by studying the turbulent flow

behavior in the region close to the water surface and

-1... --- -

-2-

several mass transfer models have been proposed. Because
of the complex and not fully understood nature of the
volatilization process, these proposed models embody many
simplifying assumptions. The simplest is the two-film
theory model. Although the model is a gross
simplification of the actual diffusion process that takes
place, it nevertheless has been found useful in predicting
transfer rates on either side of the interface. (Liss and
Slater, 1974;Liss, 1975; Mackay and Leinonen, 1975).

It is reasonable to make a distinction between two
hydrodynamic regimes of the air-water interface: one
regime for turbulence generated by flow in open channels
and the other regime for water turbulence produced by the
wind. The former is typical for rivers and streams, the
latter is typical for lakes and ponds. Present
understanding of the mass transfer process across the
surface of natural waters, although not complete, has
reached a stage where the effects of rivers and streams
are fairly well understood (e.g. Dobbins, 1962; Fortescue
and Pearson, 1967; Ueda et al., 1977), but the effects of
wind are less understood. In order to determine the
transfer rate it is essential to obtain values of the mass
transfer coefficient for a wide range of wind conditions.

The general objective of this research is to
develop expressions describing quantitativily the effects

of wind on the mass transfer of aqueous pollutants across

-3—

the air-water interface of stagnant natural waters (e.g.

lakes and ponds). The specific objectives of this study

are :

1. To quantify the wind-wave interaction for a wide range
of wind conditions in terms of wind velocity, surface
shear stress;

2. To develop a method of measuring concentrations of
chemicals in air and water that will permit evaluation
of transfer rates;

3. To develop relations between the mass transfer
coefficient and parameters obtained from the first
objective;

4. To compare our laboratory results to existing

experimental results obtained in the field.

2.0 THEORY

The two-film model originally develOped by Whitman
and Lewis (1924) assumes that there exists a thin film of
stagnant fluid on either side of the gas-liquid interface.
The transfer process in these films occurs by molecular
diffusion. Outside the films turbulent motion is present
in the form of eddies and transfer then occurs by
turbulent diffusion. The turbulent mixing in the gas and
liquid region outside the films is assumed to maintain the
concentrations of the bulk at a constant value. It is
further assumed that the concentrations on either side of
the interface are in equilibrium and that Henry‘s law is
applicable. Under these steady-state conditions the
transfer rate depends on the molecular diffusivity, film
thickness of each phase and on Henry's constant. The
model does not incorporate any relationship between the
fluid dynamics at the interface and the transfer process.
Nevertheless, the two-film model is useful in describing
processes at the interface and for calculations of mass
transfer rates.

Figure 1 shows a typical plot of partial pressure
versus mole fraction for an environmental pollutant. Most
pollutants in natural waters are present in very small
concentrations. Hence Henry's law should be applicable;
i.e. the chemical at the interface exerts a partial

-4-

" Vapor pressure

   
 
    
     

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/ Pv
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Partial Pressure, pi

 

 

 

Mole Fraction, Xi

Figure 1. Relation between partial pressure and mole fraction
of a solute in solution.

-6-

pressure Pi (atm) which is proportional to the
concentration Xi (mole fraction) at the interface.
Mathematically,

Pi = HXi, (1)
where H is Henry's constant for a given chemical

The two-film model is shown schematically in

Figure 2. The model assumes no resistance to transfer
across the interface and as a result the concentrations at
the interface are in equilibrium. The driving force of
mass transfer is the difference in chemical potential of
each phase. Chemical potential of each phase is expressed
as follows:

Fg = CgRT (2)
for the gas phase and,

FR = can (3)

for the liquid phase,
where F is chemical potential (atm),

C is concentration of chemical (mol/ma),

T is absolute temperature (0K),

H is Henry's constant (atm.m3/mol),

R is the gas constant (atm.m3/mol.°K).
The subscripts g and 2 stand for gas and liquid phase
respectively. At equilibrium,

chT = C£H. (4)
Apart from difference in chemical potential

between gas and liquid phase the rate of transfer is also

Distance

Turbulent transport

 

 

 

air
Molecular transport
J_— stagnant 5 film I
air/water
interface
Molecular transport C9v
water

Turbulent transport

 

 

 

Concentration or Partial Pressure

Figure 2. Schematic of the two-film model of volatilization
from the surface of water bodies.

-8—
affected by the resistance to transfer within each film.
Knowing how the chemical partitions gives an idea as to
which film governs the transfer process. If a chemical
partitions mostly into the gas phase then it is the liquid
film which governs the transfer process and vice versa if
the.chemical partitions mostly in the liquid phase, the
gas film governs the transfer process. Chemicals with
high H values ( >10‘btm.m3/mol) tend to partition into the
gas phase while those with low H values ( <10'btm.m3/mol)
tend to partition into the liquid phase (Mackay,1979).
For intermediate values of H chemicals tend to partition
more equally between the two phases so that both films
play a significant role in the transfer process. A plot
of vapor pressures versus solubility for various compounds
is shown in Figure 3. The diagonal lines have constant H
values and the more departure from the central diagonal
line ( H = 10‘“ atm.m3/mol) the more the transfer is
governed by one film only.

The air-water exchange kinetics can be treated as
two resistances in series, in which each film has its own
resistance to transfer. The flux through each film must
be the same as there can be no accumulation or depletion
of the chemical at the interface. This mass flux N
(mol/m2.hr) can be expressed in terms of a resistance r
with a chemical potential F as the driving force. For

transfer from the liquid phase to the gas phase,

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(FR-Fi)/r£, ’ (5)
and I

N

F.-F r . 6)
( 1 g)/ g (
The subscripts 1,1,9 stand for liquid phase, interface and

gas phase. Eliminating F yields

N = (Pg-Pg)/rt, (7)
where rt is the total resistance,
rt = r£+rg. (8)

N can also be expressed in terms of mass transfer
coefficients k2 and k9 (m/hr). These coefficients are

defined by

77
ll

w/(Ci-cg), (9)
and

k2

Using equations (2), (3), (5), (6), (9) and (10), the

N/(C£-Ci)' (10)

relations between the mass-transfer coefficient and the

resistance are

r = RT/k , (11)
9 g
and
r2 = H/kg. (12)
Substitution of equations (11) and (12) into equation
(7) yields
'Cz-C RT/H
N ._. W (13)
9
or
N CzH/RT-Cg

 

= (14)
l/kg+H/RTE§

-11-

Hence prediction of transfer rates across a
gas-liquid interface requires the knowledge of three
parameters if the film model is to be used. These are H,
kg and kz. H can be estimated from chemistry handbooks
giving the chemical vapor pressure and solubility at a
given temperature or can be obtained experimentally.

Values for kg can be obtained experimentally by
considering water as the transferring agent. In that case
the liquid phase resistance is nil and kg can be evaluated
from
kg = N/(ClH/RT-Cg). (15)
Values of k, can be obtained experimentally by selecting a
"liquid phase controlled compound" (e.g. toluene, H = 6.7 x
ldfiatm.m3/mol). The expression for kg then becomes

kfi = N/(Ck-CgRT/H). (16)

Once mass transfer coefficients have been obtained
experimentally in the laboratory for specific compounds,

they can be used to predict those of other compounds by

the following relations:

kg k2 /M' (17)

kg k§/M/M , (18)

where M' is the molecular weight of the compound of

and

interest and M is the molecular weight of the compound

used in the experiments.

-12-

The laboratory results can be applied to field
conditions using the shear stress exerted by the wind as a
criterion for similarity. This concept is illustrated in

Section 5.5.

3.0 EXPERIMENTAL PROCEDURES

A series of wind tunnel experiments were performed
to determine the liquid phase and gasthase mass tranSfer
coefficients. Toluene was chosen as the volatile chemical
to determine the k2 coefficients. This compound with its
high Henry's law constant, has a high chemical stability,
has relatively non-toxic properties and is detectable at
low concentrations in water as well as in air. The kg
coefficients were determined using the water vapor flux
from the water surface.

This chapter describes the wind tunnel facility,
the experimental setup and the measuring procedures. All

specific information concerning instrumentation used is in

Appendix B.
3.1 Wind Tunnel Facility

The experiments were performed in the
Environmental Wind Tunnel at the FluidMechanics
Laboratory of Michigan State University. The wind tunnel
is shown schematically in Figure 4. It is of the open-
circuit type with a 12 m test section. An axial fan is
employed to draw ambient air through the tunnel. The mean
velocity can be adjusted continuously from 1 m/s to 12 m/s

using a variable speed control system. The revolutions of

-13-

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-15-

the fan are monitored by a digital frequency counter so
that velocities can be reproduced precisely. The entrance
conditions consist of flow straighteners made from
cardboard. The straighteners dimensions are 60 cm in
length with an outside diameter of 5 cm and an inside
diameter of 4.7 cm. The straighteners are mounted on an
adjustable plastic frame installed in the tunnel such that
the bottom row of straighteners is positioned just above
the water surface. A plastic sheet covers the bottom
straighteners preventing them from getting wet. The
tunnel has a constant width of l m and a maximum height of
1.25 m. The ceiling is adjustable so that longitudinal
pressure gradients can be adjusted. The bottom of the
tunnel and the lower part of the side walls are sealed and
water resistant permitting a maximum depth of 25 cm. The
wind tunnel is equipped with a probe support carriage.

The vertical position can be set remotely by a stepping
motor control system. Vertical positions of probes can be

read with an accuracy of 10"+ m.
3.2 Experimental setup

The experimental arrangement is shown in Figure 5.
Prior to all experiments the tunnel was cleaned with soap
and water. It was then filled with 2.5 m3 of tap water

which gave a water depth of 22 cm. The two experimental

-16-

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stations were positioned at 6.75 m and 9.25 m,
sufficiently far downwind to yield approximately uniform
wind and wave conditions. Wind velocities, toluene
concentrations in air and water and humidities were
monitored at these two different fetches. A venting
system was installed to maintain the background toluene
levels and humidity low.

The temperature of air was monitored in the free
stream and that of water at 10 cm below the surface, both
at a fetch of 9.25 m.

The following experiments were performed at both
stations :

1. Velocity measurements to determine the surface shear
stress and other parameters of the velocity profiles.
2. Toluene measurements to evaluate kl.

3. Humidity measurements to evaluate kg.
3.3 Velocity measurements

Wind velocity profiles were measured at a fetch of
6.75 m and 9.25 m. The profiles were measured for wind
speeds varying from 1 to 10 m/s.

The following procedure was used to obtain
velocities at discrete points in a vertical profile.
1. A pitot tube was mounted on the probe support carriage

and connected to a pressure transducer.

-13-

2. The recorded pressures were converted by the pressure
transducer to an electrical signal and read as a voltage
on a digital voltmeter.
3. The pitot tube was traversed first upwards and then
downwards up to 40 cm above the water surface.
4. The pressure change with distance traversed was
instantanuously recorded on an x-y plotter both for the
upward and downward profiles.
5. The upward and downward profile were used to
correct for a lag between the pressure readout and the
actual pressure at the pitot tube. An algorithm was
developed to obtain velocities from the pressure plots.
Details of the calculation procedure are given in
Bouwmeester(l982).

The pressure transducer was calibrated using a
differential manometer equipped with a micrometer dial
gage so that water height differences as small as 10'“ in.

could be recorded.
3.4 Toluene measurements

A total of thirteen runs were performed with wind
speeds varying from 1 to 10 m/s. Before a series of runs
were started, toluene was applied to the water. An
experimental run consisted of setting a wind velocity,

taking a water sample, sampling the air at one station,

-19-

taking a second water sample, sampling the air at the
other station and finally, taking a third water sample.
Water and air temperatures as well as the background
toluene concentration were monitored continuously during
the runs. Details of each experimental step are given

below.
3.4.1 Toluene application

Dissolving toluene in water presented a problem
due to its low dissolution rate. Therefore a special
technique was developed for the toluene application.
Namely a water jet was used to disperse the toluene into
fine particles making it dissolve more readily. The
complete application procedure was as follows:

1. 60 m1 of toluene was mixed with 180 m1 of ethanol.

2. The mixture was transferred to a separatory funnel.
3. A submersible pump installed in the tunnel provided a
strong jet of water.

4. The neck of the separatory funnel was placed in the
water such that the tip was just in front of the water
jet. The tip was slanted slightly to prevent the water
from "shooting up" the funnel.

5. A tenth of the mixture was then released very slowly,
the water jet being rotated around the tip of the funnel.

In this way the mixture was dispersed into fine particles

-20-

providing for rapid dissolution of the toluene.

6. This application was carried out at ten equidistant
points to distribute the toluene uniformely over the full
lenght of the channel.

7. Prior to a series of experimental runs the wind-tunnel
was operated for two hours to enhance uniformity of the

toluene concentration in the water.
3.4.2 Toluene measurements in air

Air was sampled for 30 minutes at five vertical
positions, one station at one time. Four positions were
close to the water surface and one was higher in the free
stream to monitor the background concentration of toluene
(See Figure 5). The air was led through charcoal tubes
installed vertically to compact the carbon granules and,
hence, to prevent channeling. The tubes contained two
compartments and checks were made to verify that all the
toluene was collected in the first compartment (See
Appendix A, Section 3.1). The flow rate was set at about
1 l/min and monitored with an orifice-manometer system.
This flow rate was sufficiently low to capture all
toluene in the first compartment. After sampling the
tubes were capped, stored in the refrigerator and analyzed
within 48 hours. The collected toluene in the charcoal

tubes was analyzed using gas chromatography as described

in Appendix A.

-21-

3.4.3 Toluene measurements in water

The water was sampled before and after each air
sampling. One water sample consisted of several aliquots
taken at various points between the two stations giving a
total volume of 100 ml. When discharging the aliquots
into the sample bottle, care was taken to submerge the tip
of the pipet under the water. This was done to prevent,
any losses of toluene occurring during the discharge. Ten
ml of CS2 were immediately added to the water sample. The
solution was shaken sufficiently long to complete the
toluene extraction from the water. Subsequently the

samples were analyzed using gas chromatography as

described in Appendix A.
3.5 Humidity measurements

Humidity measurements were obtained using the dry
and wet bulb technique. Two thermistors were mounted on
the probe support carriage to measure the dry-bulb and
wet-bulb air temperatures. Both thermistors were
calibrated to measure temperature via a digital voltmeter.
The thermistor recording the wet-bulb temperature was

covered with a wick which was kept wet. Each measurement

-22-

consisted of traversing the pair of thermistors along a
vertical profile. Dry and.wet bulb temperatures were
recorded at ten points along the profile. A total of
seven measurements were taken at each station with wind
speeds varying from 2 to 10 m/s. The water temperature

was monitored continuously during the experiment.

4 . 0 CALCULATION PROCEDURES

The liquid phase mass transfer coefficients, k£,
as defined by equation (15) were determined by two
independent methods. One method is based on a mass
balance of toluene in the air above the water surface and
is called the horizontal flux method. The other method is
based on the relation between the depletion rate of
toluene in the water and the toluene emission across the
air-water interface; the so called depletion method. The
gas phase mass transfer coefficients, kg, as defined by
equation (16) were determined by the horizontal flux

method only. A detailed description of both methods is

given in the following two sections.
4.1 Horizontal flux method

The liquid and gas phase mass transfer
coefficients k2 and kg were determined using equations
(15) and (16) given in Chapter 2. This required the
measurement of the mass flux across the air-water
interface. In the horizontal flux method this flux is
determined by applying a mass_balance i.e., the increase
in horizontal mass flux between the upwind edge and a
station is equal to the mass leaving the air-water

interface between the upwind edge and that station. By

-24-

measuring concentration profiles at the upwind edge and at
the station the increase in horizontal flux enables the
determination of the average mass flux across the
air-water interface.

The calculation of this mass flux involved the use

of a simplified form of the convection-diffusion equation,

ac_ 3 ac
UK‘E‘KE) (19)

where x is distance to the upwind edge,

2 is height above the water surface,

U is local wind velocity; U = U(z),
C is local concentration; C = C(x,z),
K is mass transfer coefficient; K = K(z).

The boundary conditions are :

C+0forz+°°,N=0forx<0,and

N=['-g%] forx.>_0 _ (20)
z=0

average mass flux across the air-water

where N
interface.

The solution for the concentrations is obtained
following a procedure given by Pasquill (1974). The area
source [represented by equation (20)] is considered as the
superposition of an infinite series of line sources. The
first step is then to determine the analytical solution
for a line source. This is done as follows:

1) The velocity profile is appoximated by the power-law

-25..

formula,
U = U10 (z/o.1)“ (21)

where U10 is the velocity at a height of 0.1 m above

the water and a is the power-law exponent.

2) The profile of the mass transfer coefficient above the
water is approximated by

K = K10 (z/o.1)l'a (22)

where K10 is the mass transfer coefficient at a height of
0.1 m. K10 is evaluated using the Reynolds analogy
assumption of equating the mass transfer coefficient to
the momentum transfer coefficient.
Thus
K10 = ku*z, (23)
where k is von Karman's constant (= 0.4),
u* is shear velocity

Equations (l9),(20) and the above expressions for

K and U

10 10'
C(xiz) = Nr/U10P(s) [UlO/rzKlox] exp [-Ulozr/rzKlox] (24)

yield the following closed form solution

l+2a

where r

s (a+l)/r
F is the gamma function.

The solution for an area source is now obtained by

integrating along the x-direction from the upwind edge to

the point of consideration; i.e.,

x
C(x,z) =~/‘ Nr/UloF(s)[UlO/r2Klox] exp [-Ulozr/rzKlox] dx (25)
0

-26-

The calculation of the mass flux N was carried out
as follows. First the solution for C(x,z) was obtained by
setting N equal to unity. Denoting this solution by
C1(x,z) and denoting the actual concentration measured
experimentally by C2(x,z), the unknown flux N was
determined by relating C2 to C1.

The evaluation of Cl required the following
parameters : 010' u*, x, and z. U10 and u* were obtained
graphically by plotting the measured velocity profiles on
semilog paper. The coordinates x and 2 were those of the
various samplers. The calculation of Cl using equation
(25), was carried out on a computer. The calculation
procedure included the numerical integretion of line
source solutions. The line sources were equally
distributed over the area, except for the section directly
in front of the point of consideration which had a denser
‘distribution of line sources. This was done to avoid
numerical errors due to discretization.

With a known mass flux, N, and known
concentrations in the water and air, kg and kg were
determined using equations (15) and (16).

As the chemical potential of toluene in the air
was several orders of magnitude smaller than that in the

water (CgRT/H << Cg) equation (16) in Chapter 2 could be

-27-

simplified to

4.2 Depletion method

The mass flux N across the air-water interface can

be expressed by equation (14) in Chapter 2.

N = k£(C£-P/H), (27)
where P = CgRT, the terms having the usual meaning.
A mass balance in an unsteady state model, assuming only
volatilization losses, yields

Vdcg/dt = -NA, (28)
where V is the volume of water in the wind tunnel and A is
the surface area exposed to volatilization. Eliminating N
using equation (27) and using L = V/A, where L is the
water depth in the wind-tunnel, we get

dC£/dt = -k£(C£-P/H)/L. (29)
Integrating equation (29) to express the toluene
concentrations as a function of time t and denoting the
initial concentration by CR0, gives

C

1
For a low solubility compound, such as toluene

P/H + (cg -P/H)exp(-k£t/L). (3o)
0

(P/H << Cfi), equation (30) simplifies to

C

£ Cgoexp(-k£t/L), (31)

so that

x
ll

(L/t)ln(C£o/C£). (32)

_28-

Equation (32) can be used to calculate k1 by

measuring the change in toluene concentration with time.

5.0 EXPERIMENTAL RESULTS AND DISCUSSION

The primary objective of this study was to develop
relations between wind conditions and liquid phase and gas
phase mass transfer coefficients. Relations were obtained
and u* and between k and u*. Comparison is

z 9
made between the two theoretical methods used and the

between k

effect of temperature is discussed. Comparison of

experimental k results with existing field results is

9

also made.
During the experiments the background toluene

concentration was kept low by keeping an exhaust fan

running. The maximum concentration ever recorded was 2

ppm well below the maximum permissible level of 200 ppm.
5.1 Velocity measurements

Figure 6 and 7 show plots of measured wind
velocity profiles above the mean water level at stations 1
and 2, respectively. A straight line was drawn
through the logarithmic portion of each profile. The
velocity parameters 010 and u* were determined from these
profiles. The power law exponent as defined in equation

(21), and U10 and u* are listed in Table 1.

-29-

 

_30-

    

 

 

 

3o ‘ CL
1
25-
C)
20 - 0
C)
15* 0
O
15: C)
C, 10- C)
N 9-
,7 a. o
9
a) 7'
H C)
a: 6-
4.)
g 5-
: C)
It!
2 4-
9
° U </)
‘3 3- C) 10 m s
a) O 1.10
g o 2.24
13 o 3.40
.2 D 4.59
o 2- Q 5.61
A 6.68
A 7.75
O 8.90
D
1 I l I 1 I I I I I I
0 2 4 6 8 10

Figure

6.

Wind Velocity, U (m/s)

Vertical wind velocity distribution at station 1.

2 (cm)

Distance above mean water level,

 

 

-31_

     

 

3.) ,g
_ 6?
C)
20 - O
D
O
15'
C)
C)
10 - O
9 ..
8...
C)
7‘ <>
6—
5— (D
4-
0 U (W8)
3_ 10
O 1.09
G)2.27
C) 3.34
D 4.38
2- Q 5.44
0 6.64
A 7.48
O 8.52
O
1 l I I I l I l l I I
0 2 4 6 8 10

Figure 7.

Wind velocity, U(m/s)

Vertical wind velocity distribution at station 2.

Table 1.

Velocity Parameters

 

*

 

STATION 1

 

 

STATION 2

 

U10 U
(m/s) (m/S) a
1.10 0.047 0.117
2.24 0.095 0.116
2.82* 0.127 0.124
3.40 0.158 0.129
4.59 0.265 0.164
5.61 0.367 0.190
6.68 0.470 0.207
7.75 0.570 0.218
8.90 0.680 0.228
10.03* 0.780 0.235
1.09 0.055 0.141
2.27 0.110 0.135
2.80* 0.163 0.166
3.34 0.215 0.186
4.38 0.315 0.212
5.44 0.410 0.225
6.46 0.505 0.235
7.48 0.595 0.240
8.52 0.695 0.247
9.56* 0.790 0.251

 

 

 

* Velocities marked with an asterisk were
obtained by interpolation.

 

-33-

5.2 Determination of k8 values

Values for k2 were determined using the two
methods described in Sections 4.1 and 4.2. The two
methods are independant of each other. Therefore a

comparison of the k values obtained with both methods

1
provides a means to check the consistency and accuracy of
the experiments.

The experimental data of toluene concentrations in

the air and in the water is listed in table C1 of Appendix C.

These results together with the velocity data are used to

obtain kl values under different wind conditions.
5.2.1 Horizontal flux method

The evaluation of kl values using the horizontal
flux method consisted of two steps. First the
convective-diffusion equation and measured toluene
concentrations in the air were used to calculate the mass
transfer rate across the air-water interface. Then kg was
obtained from the ratio of mass transfer rate to measured
aqueous toluene concentration [equation (26)].

Figure 8 shows an example of a series of measured
concentration profiles (Runs 7 and 8). A plot of these

measured concentrations, C versus the corresponding

2 I
calculated concentrations, C

1, is presented in Figure 9.

-34-

 

 

 

 

 

 

 

 

RUN 7 RUN 7
Station 1 Station 2
50 P 0 5° ' 0
40 ' 40"
E _
’g 30 * 3 30
o
" N
N 20 - 20’-
C) C)
10 - 10 ’
. c0 0 o
O I L I l g 0 L I I I I I I
l 2 1 2 3
Toluene.Concentration Toluene Concentration
(mg/m3) (mg/m3)
RUN 8 RUN 8
Station 1 Station 2
SOI- c) 50" C)
40 ' 40"
8
30 . - 30 t
A N
E 20 - 20 -
N O O
10" C5 10" c)
O a I I l J 0L O I I I l I
0.5 .1 1.5 0.4 0.8
Toluene Concentration Toluene Concentration
(mg/m3) (mg/m3)

Figure 8. Examples of measured concentration profiles.

-35-

3)

C2 (gr/m

 

 

 

STATION 1
STATION 2
STATION 1
STATION 2
.E
0 l l l l L l
0.2 0.4 0.6

CI (gr/m3) x 10-2

Figure 9. Measured concentration, C2' vs. calculated
concentration, Cl'

-36-

A best fit straight line was drawn through each series Of
points. The slope of this line is equal to themass flux
across the interface. The toluene concentration in water
used to calculate k1 was the average Of the concentrations
prior to and after the air sampling. The k1 results for
all the runs are plotted in Figure 10 versus U10 and in
Figure 11 versus u*. It is noted that some of the kl
values in these figures were adjusted to a temperature Of
20°C; see Section 5.3. .

Results from Figure 10 indicate that for U10 < 2
m/s k8 is relatively small and that wind has little
effect. In this range the water surface is calm and any
transfer appears to be controlled by molecular diffusion
and water currents with no or little turbulence. For this
range of velocities values Of k2 do not exceed 0.03 m/hr.

For 010 > 2 m/s k increases substantially up to

1
approximately 0.4 m/hr at 010 = 10 m/s. The increase is
fairly linear. This behavior is consistent with the
observation made by Wu (1975) that the wind induced drift
current is turbulent for this velocity range.

Another interpretation of the sudden increase in
kfi could be based on the following. It was Observed
during the experiments that the first ripples started
occurring around 2 m/s coinciding with the increase in the

transfer rate. A study by Banner et al.(l975) has shown

that wave breaking may occur at the onset of ripples.

-37-

.Acoauofi stm amazoNfiHosv Uocm an N can H cowumum MOM

-mxe-oflo

OH

D

.m> ax

 

<)<]

N ZOHBdBm AV

H ZOHfidfim

nu

.oH masons
o
4H.o
X.
~O
. m.
I N o my
a.
I m.o
1 v.0

 

-33-

 

.AmVOgflm-h NDHH HMHCONHHOSV. UOON “M N GEM H COHHMHW HOW 5 .m> ax oHH mhfimflh
¥
Am\8v 5
.1
oo.H om.o oo.o oo.o o~.o
.- q q - . - _ q q . G.» O
00
o O
m 23.25 0 . O
H 23.33 0 0 To
0
Au
0 H.
G O .0
G 0 m5 m
o 8
co m
AV
0 .
O m o
AV
0 O
AV

v.o

 

-39-

This can explain the increase in transfer around a U10
value of 2 m/s.

A contributing factor to the increase in kg is the
enhancement of interfacial area due to wave growth. This
is appreciable above a U10 value of 4 m/s. ApprOximate
calculations indicated that the increase in area was at
maximum 10 %.

Whithin experimental error there is no difference
between the k2 values at the two stations. Apparently,
the variation in mass transfer rate with fetch is not so
significant. The original intention was to evaluate k2
for the section between the two stations but due to
relatively large experimental errors this proved to be
unfeasible.

Results from Figure 11 indicate that k is also

2
correlated to u*. For u* < 0.1 m/s little transfer is

taking place. Above that value the transfer rate

increases fairly linearly up to a k2 value of

approximately 0.35 m/hr at u* = 0.75 m/s. Using linear
regression analysis the following relation was determined

for k2 as a function of u*:

k2 = 0.45u* - 0.010, (33)

where k2 is in m/hr and u* is in m/s.

-40...

5.2.2 Depletion method

Values for k2 were also Obtained using the
procedure described in Section 4.2. The kg results for
all the runs are plotted in Figure 12 versus U10 and in
Figure 13 versus u*. Some of the kl values have again
been adjusted to a temperature of 20°C; see Section 5.3.

Results indicate that whithin experimental error
the k2 values predicted by the depletion method do not
differ from the ones predicted by the horizontal flux
method. One would expect the depletion method to
underpredict the horizontal flux method due to the effect
of wind tunnel side walls. However the results seem to
indicate that the side wall effect is negligible. The
results support the conclusion that a linear relationship
exists between k~ and U10 for the U range of 2-10 m/s

2 10
and between k1 and u* for the u* range of 0.1-0.75 m/s.

5.3 Temperature correctiOn'

Due to the high evaporative cooling Of the water
during the runs with velocities between 6.5 m/s and 10
m/s, it was necessary to correct for the effect of
temperature on the transfer process. The maximum change
in temperature that occurred during a series of runs was

from 209C to 15°C.

ca a

.-oonuma eonumaomo- Ooom no : .m> x .NH wagons

 

-41-

axE So
w v N
. . _ q . - o. O
O
O
O
I_H.o
O
O X.
~O

IN.c I,
m
mu m.

Im.o

I¢.o

 

_42_

a

 

Aconums cowumammvv Doom no «a .m> x .ma Tasman
. axe- .9
o.H m.o w.o v.o ~.o
_ - _ q . . - O O
O
O
O
I H.o
x.
0 ~0
I ~.o MN
m
O O (
O
I m.o
O
O
I v.o

 

-43-

The experimental procedure was identical to the
other experiments except that no air samples were taken.
The wind speed was kept constant with Ulo = 7.62 m/s and
u* = 0.583 m/s. This speed was representative for the
range mentioned above. The temperatures were monitored
with time. The range covered was from 28°C to 15°C and,
during that time water samples were taken periodically.
The kfi values were Obtained using the depletion method and
the results are shown in Figure 14. A best fit straight
line gave the following equation :

k2 = k£u+ 0.010(T2-Tl), (34)
where kmlis the uncorrected mass transfer coefficient

Equation (34) was used to adjust the measured k2
values to those for a temperature of 20°C. The results
show that k increases by l cm/hr for each°C rise in

8

temperature. As equation (34) was Obtained for U10 = 7.62

m/s, some error is introduced by applying it to the U10
range from 6.5 m/s to 10 m/s. The author believes these

errors are small and not significant to alter the general
trend of the k£ plots. Additional experiments would have

to be conducted to more completely investigate the effect

of temperature.

_44_

on

.m\9 ~o.a

Avov ouaumuomfios
mm

oaD wow musumwmmeou .m>

om

 

 

 

.va mwsmflm

(aw/m) ”x

-45-

5.4 Determination of k9 values

Values for kg were determined using the horizontal

flux method described in Section 4.1. Instead of toluene
concentrations in air, water vapor concentrations in
conjuction with the velocity data were used to Obtain the
water evaporation rate. Table C2 in Appendix C summarizes
the results Of seven experimental runs.

Values Of k as defined by equation (15), were

9!

determined by taking for C the water vapor concentration

9
at a height Of 10 cm. Denoting this water vapor

concentration by C10 and CzH/RT by Cs(the saturated water
vapor concentration), equation (15) becomes

k = E/(CS-C ), (35)

10
where E is the water evaporation rate (g/m2.hr).

The kg results for all the runs are plotted in
Figure 15 versus U10
experimental method was not used for wind velocities

and in Figure 16 versus u*. The

< 3m/s because of inadequate evaporative cooling of the
wet bulb. Results indicate that for the experimental
range covered k.g is a fairly linear function Of U10 and
u*. Again no difference is Observed between station 1 and
station 2. The relation between kg and u* using linear
regression analysis was

h: = 131.3u* + 16.3 (36)

J

where kg is in m/hr and u* is in m/s.

0

 

.N can H GOHumum Mom oHD .m> x .mH owanm
faxes ado
OH m o m
_ _ u - _ H _
o.
m onnkBm G
H 23.53 0 I on
O
G
x.
@ I ow 5
w
o u.
G I ow
o o
I o
O m
o o
I as

 

.m can H :oHumum How : .m> ox .oH musmHm
a.

 

-47-

Exfi- s
a.
o.o o.o To ~.o
— _ _ _ 4 _ - - D
a 23.28 a . om
H 23.28 0 I
O
o
I oo 69.
o O )
w
o u
o
I om
nu
mu
0
o o I 2:
nu

 

-48—

5.5 .Comparison of k with field data

9

The evaporation equation developed by Marciano et
al.(l954) was used to compare our laboratory data tO field
data. This equation is

E = 6.25x10‘“08(PS—98), (37)
where E is evaporation in cm/3hrs,
U8 is wind speed in knots at 8 m,
P3 is the saturated water vapor pressure in mb, and
P8 is the water vapor pressure at 8 m in mb.
Equation (37) was used to Obtain an expression for kg
which could be compared to equation (36).

The following assumptions were made:

1. the surface shear stress u* is used to relate the wind
conditions in the wind tunnel to those in the field;

2. the humidity and velocity profiles are logarithmic;

3. the relation between u* and surface roughness length,

2 is given by (Charnock; 1955)

0!

zo/(u*2/g) = 0.0156. (38)
Using these assumptions, equation (37) yields the
following expression for kg

kg = 5.207 08 2n(8/zO)/2n(1/zo) (39)
where 20 is related to u* by equation (38) and U8 is

related to u* by

* *2
U8 = 2.5 u in (5031/u ) (40)

-49-

Equations (36) and (39) are given in Figure 17. The
laboratory data underpredicts the field data. A similar
result was Observed by Easterbrook (1968). From our
results it appears that in the field situation the water
evaporation is approximately 25% greater than in the
laboratory wind tunnel. This may be explained by the

limited fetch of the laboratory experiments.

—50_

 

o
.ouoo snouononofl can oaman now a .m> x .AH masons

i.

Am\E- s

k.
m.o w.o v.c N.o

- - - J . - - . 4
\
\

I cm
I OOH X.
b.
,‘m’
/
U.
u.
I 9.:

can
4

 

6.0 CONCLUSIONS AND RECOMMENDATIONS

The experimental results presented and discussed
support the following conclusions:

1. Both RI and k9 increase linearly in the U

10
range of 2-10 m/s and in the u* range Of 0.1-0.75 m/s;

’2. At a Ulo Of 2 m/s the sudden increase in
toluene mass transfer rate may be attributable to wave
breaking occuring at the onset Of ripples;

3. The variation in mass transfer rate with fetch
was not Observed;

4. NO difference in predicting mass transfer
rates exists between the two theoretical methods used;

5. Temperature affects the transfer process
considerably;

6. Water evaporation in the field is approximately
25% higher than in the wind tunnel for the same wind '
conditions.

No attention was paid to the effects of surface
active agents. These are known to play an important role
and are permanently present in most natural waters. Only
a two component system, toluene and water, was considered
for this study. In natural waters more than one pollutant
is usually present so it would be Of interest to test a

system containing several components. In this way the

effect of chemical reactivity on the transfer process can

-51..

-52-

be investigated. It would also be of interest to have a
wind tunnel with a larger fetch so that the horizontal
flux method could be applied to a section in which the

surface conditions are more uniform.

APPENDIX A

APPENDIX A
MEASUREMENT OF TOLUENE CONCENTRATIONS IN AIR AND WATER

1. Introduction

A method has been developed to measure toluene
concentrations in air and water. For water concentrations
a sample Of water is mixed with carbon disulphide (C52);
the toluene present in the water partitions to the C52 and
the resulting solution is analysed with a gas
chromatograph. For air concentrations the air is passed
through a charcoal tube where the toluene adsorbs onto the
charcoal. The charcoal is mixed with CS2, the toluene
again partitioning to the C52 which is then analyzed in
the same way.

This report describes briefly the basic principles
Of gas chromatography and outlines procedures for the
establishment of toluene concentration standards and

calibration curves.
2. Theory of Gas Chromatography

A gas chromatograph (G.C.) separates volatile

components present in a liquid or gas sample. It consists

-53-

-54-

Of three main parts, an injection port, a column and a
detector. In conjuction with it a strip chart recorder
and a chromatograph data system are commonly used as shown

in Figure Al.

Thermostat!

    
 

lnioction
Port

Flow
Controller Comm 1

  
  

Curler
Ga

Bottle Enlarged Cm. Section

Figure Al. Schematic drawing of a gas chromatographic
system.

2.1 Injection port

Liquid or gas samples are introduced with a
syringe. This is done instanteneously so as to have a
"plug" flow onto the column. The injection port is heated
resulting in almost immediate vaporisation of liquids.
These vapors are carried to the column by a non-reactive

gas (e.g. nitrogen).
2.2 Column

The column tubing, normally in a coiled form, can
be made from copper, stainless steel, aluminim and glass.
The column contains a packing material which may be a dry
solid coated with a liquid film. The packing material

constitutes the stationary phase of the column whereas the

 

-55-
gas transported through the column makes up the moving gas.
phase. When the carrier gas transports the injected
sample through the column different components Of the
sample transfer in and out of the stationary phase. As
the exchange rate depends on molecular weights, different
components have different retention times and, therefore,
separate out in the column making it possible to analyze‘
them individually. The exchange rate between stationary
and moving gas phase is also temperature and carrier gas
flow rate dependent. This permits the adjustment of
retention times. In general a higher temperature and a
higher flow rate result in a shorter retention time and

lower resolution.
2.3 Detector

The detector indicates the presence and measures
the amount of components in the gas leaving the column.
This is converted into an electrical signal by several
possible methods. A suitable method for organic compounds
is the use Of a flame ionisation detector (FID). The FID
Operates on the principle that the conductivity of a gas
is directly proportional to the concentration of charged
particles within the gas. The effluent carrier gas is
mixed with hydrogen and burned with air forming ions and
electrons. These then pass through an electrode gap,
decreasing the gap resistance thus varying the resistance
across the gap. The particular usefulness of the FID is

in its lack of response to the CS used as a solvent,

2
while its response to toluene is excellent.

-56-

2.4 Strip chart recorder

These are nearly always used in conjuction with
the G.C. to obtain permanent records of the results. The
results come out as a chromatogram i.e. a series of peaks
each peak identifying the resistance variation across the
electrode gap caused by the ionisation of a particular
compound. The area under the peak is an indication of the
amount (i.e. mass) of the component present in the sample.
A typical chromatogram resulting from one single

injection is shown in Figure A2.
2.5 Chromatogram data system

This device is used to automatically quantify a
chromatogram with preset parameter values. The most
important are retentiOn times and area counts under peaks.
It can be used to perform other calculations such as
internal standard calculations which will be discussed in

Section 3.2.
3. Calibration

In order to Obtain a calibration curve relating
mass of toluene to area under a peak in a chromatogram it

was necessary to prepare a series of standards. Two

-57..

Peak 1: C82

Peak 2: Benzene

Peak 3: Toluene

 

Figure A2. Typical chromatogram

-58—

methods were applied; for the first one known amounts of
toluene were dissolved in water and then extracted in C52;
For the second one an additional step was introduced
involving an adsorption-desorption process and employing a
constant toluene emission device and a charcoal tube.

This second method involved procedures similar to those
used for the measurement of toluene in air. The first
method, on the other hand, was similar to that for the

evaluation of toluene concentrations in water.
3.1 Procedures and results for toluene in air

A toluene permeation tube was used as a source
with a constant release rate being only dependent on
temperature. The permeation rate was determined by
measuring weight losses over different lenghts of time.
For this purpose the tube was installed in a controlled
temperature air bath at 50°C. Air was drawn past the tube
to remove the toluene. A schematic of this system is.
shown in Figure A3.

The weight loss was recorded over a period of
several weeks and the results are shown in Figure A4.
From this graph a toluene permeation rate of 46 ug/hr was
obtained.

The calibration permeation tube was now used to

create calibration standards using the experimental setup

Air from Lab

\l/

Effluent Port
~(front panel)

Permeation
Chamber
(50°C)

 

 

Charcoal Tube
Installed here

1

-59-

 

 

 

 

Scrubber

Glass Bead
Rotameter

 

Flow Control

 

 

'x/

 

Vacuum
Pump

 

 

I

To Lab

Figure A3. Permeation tube calibration system.

 

-50-

 

 

.490
g 480
O
O
O
6‘
H
I
4...)
I:
U)
.,.I
0)
3
470
460 I l 4 I l l
0 200 400 600

Figure A4.

Time (hrs)

Permeation tube weight loss vs. time.

-61..

shown in Figure A3. The procedure used to get a
calibration standard is outlined below.

.The released toluene was adsorbed onto the
‘charcoal tube for a selected lenght of time. The flow
rate of approximately 1 liter/min was measured by a
rotameter. This flow rate prevented any toluene from
escaping capture in the charcoal tube.

.The charcoal tube was then removed and the
charcoal was transferred into vials containing 2 ml CS2
and a small amount of benzene. The benzene served as an
interal standard.

.The toluene was then desorbed from the charcoal
using a commercial shaker for a period of 30 minutes. The
calibration standards, namely the CS2 containing known
amounts of toluene and benzene, were now obtained.

.One ul of the calibration standard was injected
into the G.C. under the following conditions:

Injection port temp: 180°C

FID detector temp: 250°C

Column temp: 60°C

Column pressure: 16 psi

Sensitivity: 10'11

Attenuation: l6

Nitrogen carrier flow rate: 2 ml/min

Nitrogen make-up flow rate: 25 ml/min

Hydrogen flow rate: 30 ml/min

-62..

Air flow rate: 300 ml/min
Column manufacturer: Supelco
type: 2-3710, glass capillary, grade AA
lenght: 30 meters
coating: SP-2100
used in splitless mode

The peaks for toluene and benzene were recorded in
the chromatogram and the evaluation of areas under peaks
was carried out employing a data analyzer. The data
analyzer was used to calculate the areas as shown by the
stripped line in Figure A2.

A total of 6 calibration standards were obtained
by installing charcoal tubes for different lenghts of
time. The results are given in Table A1.

Figure A5 shows a plot of column 8 versus column 9.

The slope of the calibration line obtained is called the

cub
.- a '

relative response factor (RRF) and is defined as:

mass of toluene x area under benzene peak
area under toluene peak mass of benzene

From Figure A5, RRF = 0.598
The mass of toluene in an unknown sample is then

calculated from the formula:

area under toluene peak,

Mass of toluene = RRF x
(area under benzene peak')‘Mass Of benzene

Some additional notes on the calibration procedure

are given below:

-63-

 

 

 

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ax» ax» -a- -o- Nmo axos -axoa- -oa- -aaes .oz

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mead mend nouns .Hou mum:

 

 

 

 

 

.Hou .ocou

 

 

 

 

.uHm :H ososHou you want COHumunHHmo .H< pomB

 

-54-

.COHDMHQHHMO cumvcmun HmcumucH

cumucmn\ocoaHou OHumu moms
m.~ N m.H H m.c

N¢ OHQMB
H< OHQMB

 

    
 

 

.md musmHm

m.H

SUGZUBQ/SUSUIOQ 0133.91 UOIQPIQUSOUOD

-55-

All glassware used was cleaned with acetone to remove
any organic residue that might affect results.

The charcoal tubes were positioned vertically to
compact the granules and reduce the possibility of
channelling.

The charcoal tube was installed such that the air
entered directly without passing through any tubing
or any other material that might adsorb some of the
toluene.

The charcoal tubes contained two compartments. The
first one containing 400 mg and the second 200 mg of
granulated carbon. Both compartments were analyzed
and it was found that 99% toluene adsorption occurs
in the first compartment, i.e. no or minute traces of
toluene are measured in the second compartment.
Thirty minutes shaking produced full extraction and
no change in toluene concentration were observed for
longer shaking periods.

Benzene was found to be appropriate as an internal
standard for the G.C. analysis; it improved the accu-
racy of toluene concentration analysis significantly.
Two m1 of CS2 were used for desorption as that would
maximize the toluene concentration and still keep all

of the charcoal in the vial covered with C82.

_66-

3.2 Procedure and results for toluene in water

Water samples were taken in 100 ml aliquots. When
discharging the aliquots into the sample bottle care was
taken to submerge the tip of the pipet under the water.
This was done to prevent any losses of toluene occuring
during the discharge. Ten ml of CS2 were added to each
water sample. The mixture was then shaken manually for a
period of about 30 seconds. This was repeated at least
six times. The procedure resulted in complete extraction
of toluene from the water. A check was made by performing
a second extraction with C82 and no or minute traces of
toluene were observed. Three toluene calibration
standards were prepared by dissolving toluene in CS2
containing the internal standard benzene. Upon analysis
the results shown in table A2 were obtained.

These results are plotted also in Figure A5. We
can infer from these results that within experimental
error full extraction occurs from the charcoal. The
Handbook of Chemistry and Physics indicates that some C82
dissolves in water thus making toluene concentrations
higher than predicted. This was checked by adding water
to a solution of C52 containing known concentrations of
benzene and toluene. After a period of shaking no change
in benzene and toluene concentrations were observed.

Hence, either no measurable amount of C52 dissolves in

-67—

.mcHDDOHm uHEuom Ou moEHu m couscom w

 

 

 

«AM¢HO.NV «HommH-Hv
ano.m mvmm.m Nmmmm mvamm mm o.omH m
mem.o mmmm.c mmmnm wmcHw mm o.mH N
mmbo.o mmmo.cr hHmmm qub mm m.H H
b\u n\u madnson osmsHou H\mE .Nsmn H\mE .HO» .0:
comm .Ocou mucsoo monfl mucsoo bond .Ocoo .OGOU onEmm
.Nmo an dadoaon non oboe aoaoownaamo .md wands

-68..

water or the same portion of C52, benzene and toluene
dissolve in water making no change in benzene and toluene
concentrations. In either case the results are not

affected by the partitioning.

APPENDIX B

APPENDIX B

INSTRUMENTATION AND EQUIPMENT

Velocity measurements:

United Sensor Pitot Static Tube

Datametrics Pressure transducer, Model 590D

Dwyer Differential micromanometer

Toluene measurements:

Varian gas chromatograph, Model 3700

Varian data analyser, Model CDS lll

Varian recorder, Model 9176

Supelco glass capillary column, 2-3170
(grade AA, SP2100, 30 meters long)

Tractor permeation tube calibration system
Supelco air pollution control charcoal tubes
(NIOSH large size 200/400 mg)

Sartorius top loading electronic balance,
Model 1265 Mp

Hamilton 10 ul syringe

Supelco developing vibrator, Model SKC
Developing vials with teflon-lined septum caps
(3.7 ml)

Dynacol toluene permeation tube, lenght 18 cm,

type ME

-69-

-70..

Humidity and temperature measurements:

- YSI thermister, Model 702A

- YSI thermivol signal conditioner, Model 740A
Air Sampling System (non commercial):

Orifice, non commercial, diameter 1/64”.

APPENDIX C

-71-

 

 

 

 

 

 

 

 

Table Cl. Toluene experimental data.
Height Measured Height Measured
above air above air
water conc. water cone.
(cm) (mg/m3) (cm) (mg/m3)
RUN 1 48.2 0.39 RUN 1 48.6 0.30
STATION 1 13.7 1.48 STATION 2 14.1 1.63
U10 3 1.10 m/s 6.1 1.90 U10 - 1.09 m/s 6.5 2.15
C11) 8 10.67 mg/l- 4.1 2.00 C1b - 10.50 mg/l 4.6 2.68
Cla 8 10.50 mg/l 2.1 2.31 Cla 8 10.35 mg/l 2.5 2.72
RUN 2 48.2 0.59 RUN 2 48.6 0.64
STATION 1 13.7 1.17 STATION 2 14.1 1.39
U10 8 2.24 m/s 6.1 2.01 U10 - 2.27 m/s 6.5 2.07
C1b = 9.61 mg/l 4.1 2.52 C1b a 10.35 mg/l 4.6 2.26
C1 I 8.98 mg/l 2.1 3.39 C I 9.61 mg/l 2.5 2.56
a la
RUN 3 48.2 1.02 RUN 3 48.6 0.65
STATION 1 13.7 1.55 STATION 2 14.1 1.23
U10 - 2.82 m/s 6.1 2.28 U10 = 2.80 m/s 6.5 1.82
C1b = 8.98 mg/l 4.1 3.00 C1b - 8.05 mg/l 4.6 2.44
C = 8.05 mg/l 2.1 4.19 C I 7.19 mg/l 2.5 3.01
la la
RUN 4 48.2 0.84 RUN 4 48.6 0.96
STATION 1 13.7 1.14 STATION 2 14.1 1.60
U10 8 3.40 m/s 6.1 1.90 Ulo - 3.34 m/s 6.5 2.63
C1b - 6.10 mg/l 4.1 2.43 Clb 8 7.19 mg/l 4.6 3.22
C - 5.22 mg/l 2.1 3.24 C - 6.10 mg/l 2.5 4.12
la la
RUN 5 48.2 1.35 RUN 5 48.6 0.98
STATION 1 13.7 1.79 STATION 2 14.1 1.36
U10 - 4.59 m/s 6.1 2.42 U10 - 4.38 m/s 6.5 2.14
C1b = 5.22 mg/l 4.1 3.08 C1b - 3.90 mg/l 4.6 2.50
C = 3.90 mg/l 2.1 4.00 C - 2.88 mg/l 2.5 2.93
la la
RUN 6 48.2 2.90 RUN 6 48.6 1.85
STATION 1 13.7 3.45 STATION 2 14.1 2.96
U10 - 5.61 mVs 7.9 4.10 U10 8 5.44 m/s 6.5 4.15
Clb I 9.64 mg/l 4.1 5.41 C1b I 6.23 mg/l 4.6 4.35
C - 6.23 mg/l 2.1 7.94 C 8 4.53 mg/l 2.5 5.07
la la
RUN 7 48.2 1.08 RUN 7 48.6 1.82
STATION 1 13.7 1.46 STATION 2 14.1 2.40
Ulo = 6.68 m/s 6.1 1.88 U10 8 6.46 m/s 6.5 3.06
C1b = 2.63 mg/l 4.1 2.06 C1b = 4.53 mg/l 4.6 3.33
C1a = 1.77 mg/l 2.1 2.41 C1a = 2.63 mg/l 2.5 3.74

 

 

_72..

Table C1 (continued)

 

Height Measured Height Measured

 

 

 

 

 

 

 

above air above air
water oonc. water conc.
(cm) (mg/m3) (cm) (mg/m3)
RUN 8 48.8 0.76 RUN 8 49.4 0.49
STATION 1 14 . 3 O . 97 STATION 2 15 . 1 0 . 62
010 I 7.75 m/s 8.5 1.14 010 I 7.48 m/s 7.4 0.76
Clb I 1.77 mg/l 6.7 1.18 Clb I 0.98 mg/l
Cla I 0.98 mg/l 4.6 1.40 Cla I 0.63 mg/l
RUN 9 48.8 0.19 . RUN 9 49.4 0.32
STATION 1 14.3 0.21 STATION 2 15.1 0.39
010 I 8.90 m/s 8.5 0.25 010 I 8.52 m/s 9.3 0.46
C1b I 0.33 mg/l 6.7 0.26 C1b I 0.63 mg/l 7.4 0.48
C I 0.21 mg/l 4.6 0.29 C I 0.33 mg/l 5.4 0.53
1a 1a
RUN 10 48.8 0.136 RUN 10 49.4 0.081
STATION 1 14.3 0.149 STATION 2 15.1 0.089
U10 I 10.03 m/s 8.5 0.166 U10 I 9.56 m/s 9.3 0.093
C1b I 0.21 mg/l 6.7 0.178 C1b I 0.11 mg/l 7.4 0.111
Cla I 0.11 mg/l 4.6 0.187 C1a I 0.07 mg/l
RUN 11 48.9 8.49 RUN 11 49.1 4.17
STATION 1 14 . 3 9 . 30 STATION 2 14 . 7 4 . 87
U10 I 10.03 m/s 6.7 11.94 010 I 9.56 m/s 6.9 5.64
C1b I 13.19 mg/l 2.6 12.04 C1b I 5.65 mg/l 3.0 6.02
C1a I 5.65 mg/l C1a I 2.53 mg/l
RUN 12 48.9 1.02 RUN 12 49.1 1.73
STATION 1 14.3 1.16 STATION 2 14.7 2.10
010 I 7.75 m/s 6.7 1.32 010 I 7.48 m/s 6.9 2.48
C1b I 1.67 mg/l 2.6 1.62 C1b I 2.53 mg/l 3.0 2.63
C1a I 1.17 mg/l C1a I 1.67 mg/l
RUN 13 48.9 0.388 RUN 13 49.1 0.242
STATION 1 14.3 0.402 STATION 2 14.7 0.344
U10 I 5.61 m/s 6.7 0.523 U10 I 5.44 m/s 6.9 0.403
C1b I 1.17 mg/l 2.6 0.745 C1b I 0.96 mg/l 3.0 0.600
C1a I 0.96 mg/l C1a I 0.66 mg/l
Clb: Toluene concentration in water before air sampling.
C : Toluene concentration in water after air sampling.

la

-73-

Table C2. Water vapor experimental data.

 

 

 

 

 

 

Height Measured Height Measured
above air above air
water conc. water conc.

(cm) (gr/m 3) (cm) (gr/m 3)
RUN 11 0.8 8.25 RUN 11 0.7 8.44
STATION 1 1.8 7.52 STATION 2 1.6 7.85
U10 I 2.82 m/s 2.7 7.11 U10 I 2.80 m/s 2.5 7.34
4.6 6.62 4.5 6.88
6.5 6.39 6.4 6.57
10.4 6.15 10.2 6.23
14.2 6.01 14.0 6.12
18.0 5.95 17.8 5.97
33.8 5.92 33.7 6.05
RUN 12 0.8 8.43 RUN 12 1.0 8.40
STATION 1 1.8 7.73 STATION 2 2.0 7.88
U10 I 3.40 m/s 2.7 7.33 U10 I 3.34 m/s 2.9 7.49
4.6 6.81 4.8 6.99
6.5 6.47 6.7 6.80
10.4 6.17 10.5 6.38
14.2 6.02 14.3 6.17
18.0 5.97 18.1 6.08
27.5 5.84 33.7 6.11
RUN 13 1.1 8.17 RUN 13 1.3 8.03
STATICN 1 2.1 7.71 STATION 2 2.3 7.85
U10 I 4.59 m/s 3.0 7.41 U10 I 4.38 m/s 3.2 7.65
4.9 7.04 5.1 7.24
6.9 6.71 7.0 6.97
14.5 6.27 10.8 6.57
18.3 6.16 18.5 6.12
33.8 6.02 33.7 5.96
RUN 14 1.8 7.74 RUN 14 1.6 7.93
STATION 1 2.7 7.54 ‘STATION 2 2.6 7.57
U10 I 5.61 m/s 3.7 7.37 Ulo I 5.44 m/s 3.5 7.39
5.6 7.10 5.4 7.15
7.5 6.84 7.4 6.98
11.3 6.53 11.2 6.70
15.1 6.43 15.0 6.55
18.9 6.32 18.8 6.37
33.8 6.21 33.7 6.36
RUN 15 2.8 7.55 RUN 15 2.9 7.47
STATION 1 3.7 7.45 STATION 2 3.9 7.51
U10 I 6.68 m/s 4.7 7.45 U10 I 6.46'm/s 4.8 7.46
6.6 7.27 6.7 7.33
8.5 7.05 8.6 7.14
12.3 6.88 12.4 6.92
16.1 6.80 16.2 6.68
19.9 6.75 20.1 6.57
p 34.2 _6.00‘;_ .33 7 Q 6.38

 

-74-

Table C2 (continued)

 

 

 

Height Measured Height Measured
above air above air
water conc. water conc.
(cm) (gr/m3) (cm) (gr/m3)
RUN 16 3.1 7.65 RUN 16 3.2 7.72
STATION 1 4 . 1 7 . 62 STATION 2 4 . 2 7 . 55
U10 I 7.75 m/s 5.0 7.53 U10 I 7.48 m/s 5.1 7.54
6.9 7.41 7.0 7.34
8.8 7.31 8.9 7.21
12.6 7.15 12.8 7.04
16.4 7.06 16.6 6.85
20.3 6.98 20.4 6.73
34.2 6.87 33.7 6.49
RUN 17 3.7 7.63 RUN 17 3.9 7.39
STATION 1 4.7 7.76 STATION 2 4.8 7.39
U10 I 8.90 m/s 5.7 7.66 U10 I 8.52 m/s 5.8 7.45
7.6 7.57 7.7 7.31
9.5 7.53 9.6 7.22
13.3 7.38 13.4 7.04
17.1 7.28 17.2 6.93
20.9 7.21 21.0 6.80
34.2 7.13 33.7 6.69

 

BIBLIOGRAPHY

BIBLIOGRAPHY

L. Banner and W. K. Melville. On the Separation of Air
Flow Over Water Waves. Journal of Fluid Mechanics
77, 825-842, (1975).

Bouwmeester. Alternative procedure for the evaluation
of velocity profiles. Michigan State University,
to be published (1982).

Charnock. Wind stress on a water surface. Quart.J.
Roy. Meteorol. Soc., 81, 639-640, (1955).

L. Dilling, N. B. Tefertiller and G. J. Kallos.
Evaporation Rates and Reactivities of Methylene
Chloride, Chloroform, 1,1,l-Trichloroethane,
Trichloroethylene, Tetrachloroethylene and Other
Chlorinated Compounds in Dilute Aqueous Solutions.
Envir. Sci. Technol., 9, 833 (1975).

E. Dobbins. BOD and Oxygen Relationships in Streams. J.
of the Sanitary Engineering Division, Am. Soc. of
Civil Engr., 90, 43, (1962).

.C. Easterbrook. A study of the effects of waves on
evaporation from free water surfaces. U.S. Dept.
Int. Bur. Recl. (1968).

.E. Fortescue and J. R. A. Pearsons. On Gas Absorption
into a Turbulent Liquid. Chem. Engng. Sci., 22,
1163-1176 (1967).

S. Liss. The exchange of gases across lake surfaces.
Proc. First Speciality Conf. on Atmospheric
Contribution to the Chemistry of Lake Waters 83,
Intern. Assoc. Great Lakes Res. (1975).

S. Liss and P. G. Slater. Flux of Gases Across the
Air-Sea Interface. Nature 247, 181 (1974).

. Mackay and P. J. Leinonen. Rate of Evaporation of Low
Solubility Contaminants from Water Bodies to
Atmosphere. Envir. Sci. Technol. 9, 1178 (1975).

Mackay and A. T. K. Yuen. Transfer Rates of Pollutants
Between the Atmosphere and Natural Waters.
Proceedings in Atmospheric Input of Pollutants to
Natural Waters, September 9-14, 1979, Washington,
D.C., ed. S. J. Eisenreich, Ann Arbor Science
Publ. Lim. (1979). '

-75-

-76-

J. J. Marciano and G. E. Harbeck. Mass-Transfer Studies;
Water Loss Investigation; Lake Hefner Studies
Technical Report. Geological Survey Professional
Paper 269. U.S. Government Printing Office,
Washington, D.C. (1954).

F. Pasquill. Atmospheric Diffusion. Wiley and Sons, New
York, (1974).

R. P. Schwarzenbach, E. Molnar-Kubica, W. Giger and S. G.
Wakeham. Distribution, Residence Time, and Fluxes
of Tetrachloroethylene and 1,4-Dichlorobenzene in
Lack Zurich, Switzerland. Envir. Sci. Technol.,
13, 1367 (1979).

H. Ueda, R. Moller, S. Komori, and T. Mizushina. Eddy
Diffusivity Near the Free Surface of Open Channel
Flow. Int. J. Heat Mass Transfer, 20, 1127 (1977).

W. G. Whitman and W. K. Lewis. Principles of Gas
Absorption. Industrial and Engineering Chemistry,
16, 1215 (1924).

J. Wu. Wind-Induced Drift Currents. J. Fluid Mechanics,
68, 49 (1975).