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ABSTRACT

A STUDY OF FOAM FRACTIONATION IN THE
SODIUM LAURYL SUIFATE AND WATER SYSTEM

by Kenneth Edward Hastings

Foam fractionation was studied in a batch column with

no external reflux and compared to the following mathemati-

cal description of the process.

where:

0‘

#331105

- C (61‘) 0%) (1)

b

concentration of surfactant in broken down foam
concentration of surfactant in gassed bulk solu-
tion

bubble diameter

gas flow rate in the foam

liquid flow rate in the foam

surface excess (a constant in the model region)

The above equation was derived by writing a material bal-

ance on the solute about a column of foam with the following

assumptions: excess solute on the liquid-gas interface is cone

stant, foam bubbles are spherical, internal reflux has negli-

gible effect, and the gas-liquid interface of the bubbles is

in equilibrium with the bulk of the liquid.

The experimental equipment consisted of a round bottom

flask containing bulk solution into which air was bubbled to

produce foam which rose through a column, was collected over-
head, and collapsed. The overhead product was returned to
the bulk liquid to replenish surfactant thereby keeping the
system in steady state. The air used in these experiments was
filtered and saturated with water. Conductivity measurements
were used to measure the concentrations of products from the
column and the bubblecfiameters were measured photographically.
The data were correlated in the form of a plot of sep-
aration, Cf - Cb’ as a function of G/RD which yields a straight
line as predicted by equation (1). However, the line does
not pass through the origin, Cf - Cb being equal to zero when
G/RD is 144. As a second test of equation (1), surface excess
was calculated from the slope (6T) of equation (1) and com-
pared to surface excess calculated from the following Gibbs

equation (2).

l d
T2";ta—13Qr (2)

where:

a surface excess of surfactant
= universal gas constant

a temperature

= surface tension

Get-HM

82 a surfactant concentration

Surface excess calculated from equation (1) was 0.728 x 10-10

gm moles/cmz, compared to the value calculated from equation

10

(2) which was 5.46 x 10- gm moles/cmz.

A STUDY OF FOAM FRACTIONATION
IN THE SODIUM IAURYL
SULFATE AM) WATER SYSTEM

BY

Kenneth Edward Hastings

A THESIS

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

MASTER OF SCIENCE

Department of Chemical Engineering
1964

 

.-
' ‘ --'

 

 

To
SUSAN

ii

ACKN OW LEM: MEN TS

The author would like to express deep appreciation
to Dr. Donald K: Anderson, Department of Chemical Engin-
eering, and Dr. James L. Dye, Department of Chemistry,
Michigan State University, for their cooperation and
guidance in the preparation of this thesis.

Appreciation is also extended to the Dow Chemical
Company, Midland, Michigan for financial support, and
to Mr. Andrew W. Seer, glass blower, for helping in the

design and construction of the equipment.

iii

' TABLE OF

LIST OF ILIUS'I'F’LATIONS . .
INTRODUCTIV’N. . . . .
THROTTYooooooo...
KEP‘QRILY‘NTAL METHODS. . .
I’XP' RITUCNTAL RVSULTS . . . .
CONCL’SIONS . '. . . . . .
APl-"z‘NDIX. . . . . . . . .
A. Tables of Data
B. Nomenclature .

BIBIOSRUDHY. . . . . . .

C 01‘! TEN TS

Page

LIST OF ILLUSTRATIONS

Figure Page

1. Diagram of Foam.Fractionation Apparatus . . . 6
2. Platinum Conductivity Cell. . . . . . . . . . 12

3. Calibration Curve for the Conductivity
C811. 0 e o e e. e e e e e e e e o e e e o o e 13

4. Surface Tension as a Function of Sodium
Iaurvl Sulfate Concentration. . . . . . . . . l7

5. Column Wall Bubble Diameter as a
Function of Surface Tension . . . . . . . . g 19

6. Column Variables as a Function of
Surface Tension . . . . . . . . .g. . . . . . 2O

7. Comparison of Experimental Data with
Theoretical Equation. . . . . . . . . . . . . 21

INTRODUCTION

Interaction forces between molecules are greater for
a liquid than for a gas. Molecules in the liquid which are
within a few molecular diameters of the gas-liquid inter-
face are subject to different environmental forces than mole-
cules well within the bulk of the liquid. These environmen-
tal surface forces decrease with the addition of a surface
active solute; that is, a solute which concentrates at the
surface.. Since surfactants concentrate at the gas-liquid
interface, a partial separation can be achieved by removing
the surface from the bulk liquid by some means. For instance,
a knife edge could be used as a mechanical means to skim off
the surface of a liquid, but this is not practical. The sim-
ple process of generating a foam is an excellent means of
producing large surface area and removing this generated sur-
face from the bulk of the liquid in the Same operation. It
is upon this principle that foam fractionation is based.

Foam fractionation utilizes a quantity of feed solution
which is bubbled to produce foam and residual solution. The
foam is partially drained, collected overhead, and broken down
to form a solution of higher surfactant concentration than

the original feed solution.

3

Foam fractionation is different from froth flotation
although both involve the gassing of a liquid. Froth flo-
tation is an old established procedure in mineral dressing.
The surface characteristics of one solid are modified so
that particles will more readily attach themselves to air
bubbles than other solids will. Froth flotation involves
the gassing of a liquid which contains suspended solids,
while foam fractionation involves the gassing of a liquid
which has surfactant dissolved in it.

Present interest in foam fractionation has increased
over the past ten years because of the increased usage of
non-biodegradable detergents. Synthetic detergents are
used in large quantities in industry and in the home, and
these detergents polute the country's streams, rivers, and
lakes. Foam fractionation might serve as an excellent tech-
nique for removing these surfactant contaminates. Another
possible use for foam fractionation is in the separation of
cations (9 and 10). A detergent sometimes has an affinity
for a particular cation and forms a surface active complex
with the non-surface active ion. This complex can then be
separated from other cations in the bulk solution by foam
fractionation.

Past work - The adsorption of ionic surfactants and

 

their gegenions at the air-water interface of aqueous solu-
tions were studied by Roe and Brass (8). They gathered sur-

face tension data on many surfactants (potassium laurate,

4

potassium palmitate, dodecylamine hydrochloride, and sodium
dodecyl sulfate). They found surface excess to be a con-
stant over a wide range in concentration just below the
critical micelle concentration.

Concentrations of foams and their residual liquids were
examined by Kevorkian and Gaden (4). Clean air saturated
with water to the extent of 88, 91 or 96% was bubbled into
aqueous solutions of isobutyl alcohol in a batch foam frac-
tion column with no external reflux. The concentrations of
alcohol in the top and bottom products were determined. Posi-
tive and negative enrichments were found by varying the per
cent saturation of air with water. This shows that in cases
where foam fractionation is undesirable a change in operating
conditions might make it desirable.

Schnepf and Gaden (9) studied a batch column with no
external reflux. Non-surface active metal ions (strontium
and cesium) were found to be separable from water in dilute
solutions when a surfactant was used to form a surface active
complex with the metal ion.

A continuous column with central feed and no external
reflux was examined by Schoen and Mazella (10). Metal ions
(strontium, cobalt, and beryllium), in dilute concentrations,
were separated from water by complexing them with a surface
active agent. The data was correlated by plotting CF/CR

versus F/LD.

where:

x metal ion concentration in feed stream

‘11

a metal ion concentration in residual stream

volumetric foam rate

brand
u

: volumetric liquid feed rate
D = average foam bubble diameter

Brunner and Lemlich (1) studied a batch column with and
without external reflux. Column data were obtained for humidi-
fied nitrogen bubbled into Aresket-3OO in water. The column
without reflux was used as a one-theoretical plate separator
for comparison to the column with reflux. Their experimental
evidence indicates that reflux increases separation for any
given set of column operating conditions.

The author of this thesis made a study of a batch column
with total external reflux. It was discovered that most of
the separation took place between the bulk of the liquid and
the foam. Small separations in the foam were easily eXplained
by the change in density of the foam.

The present study was carried out in a batch foam frac-
tionation column with no external reflux, as shown in Figure 1.
In order to have the system in steady state, the top product

was returned to the flask of bulk liquid.

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THEORY

The foam in a batch foam fractionation column consists
of bulk solution at the concentration of liquid in the flask
and surface excess. Surface excess is the amount of solute
at the surface'in excess of what would be present if the
bulk concentration extended to the surface, and is expressed
as excess solute per unit area of surface. This surface ex-
cess is described by the Gibbs equation (3) which is first
stated for a non-dissociating surfactant (equation 1) and

then is corrected for dissociation (equation 2).

T l. dQ

2"}?d1n02 (1)

O
N

l d®

T2 ' - Zrt d In C2

(2)

a. :1:
”(DIG-N

N
c+

where:
T a surface excess
= universal gas constant

temperature

‘ec'O-HN
II

a surface tension

concentration of surfactant

N
I

Z = average number of particles that the surfactant

dissociates into

8
The only effect of the surfactant dissociating is the cor-
rection factor, Z, in the denominator of equation (2) to
correct the derivative of surface tension with respect to
the logarithm of concentration for this ion effect.

The above equations (1 and 2) were derived from ther-
modynamic considerations of a solution in static equili-
brium and should only be applied to surfactant concentra-
tions well below the critical micelle concentration. In
this region, the surfactant molecules exist as independent
entities. They only feel the effect of environmental water
molecules and are not influenced by other surfactant mole-
cules.

For an isothermal gas-liquid interface, surface excess
(T2) is constant over a range in concentration where the
derivative of surface tension with respect to the logarithm
of concentration is a constant. This range in concentration
is defined as the model region for this thesis.

_gpplication‘gf,theorx‘tg'a foam fractionation column.

 

The surface—active solute which is carried 'up with the foam
'in a foam fractionation column will be treated mathematically
as two separate contributions. The first is solute which
would have been carried up in the bulk solution if no sur-
face excess was present and the second is surface excess.

A material balance may now be written around the model foam

fractionation column.

9
Input - Output = Accumulation
Under steady state conditions, accumulation is zero.

Therefore,

 

 

 

 

 

 

{Surfactant entering [Surfactant enteriné FSurfactant'
due to liquid en- due to surface ex- leaving in
trained in the en- 4' cess at the gas-liq " the top' =
tering foam quid interface of product.

_ J1 _the foam JI L J‘)

RC .G(—-§—)T-Rc-o (
o' D f‘ 3)
where:

Cb a concentration of surfactant in the flask

C_f a concentration of surfactant in the broken down
foam

8 diameter of average (bv area) bubble

a gas flow rate in the foam

a net liquid flow rate in the foam

850435

a surface excess
Equation (3) may be rearranged into the following form:
cf - ob s (6T) 1%]; (4)

The assumptions used in the model for deriving equation
(3) are the following:
1) Surface excess of the surfactant is constant because the
bulk concentration is in the concentration range where a plot
of surface tension versus the logarithm of concentration forms
a straight line.
2) Bubble diameters are spherical in shape.

lO

3) Internal reflux (drainage) which drains back into the
flask has the same concentration as liquid in the flask.
This assumption implies:

a) The liquid entrained in the foam has the same con-

centration as liquid in the flask.

b) Bubbles do not coalesce as they rise up the column

since this would change the surface to volume ratio

and, thus, the concentration.
4) The gas-liquid interface of a bubble comes to equilibrium
with the bulk liquid around it before the bubble leaves the
pool of liquid and enters the column of foam.

In equation (4), the separation (Cf - Cb) is shown to
be proportional to (G/RD) with the proportionally constant
being (6T). All of the acove parameters can be measured
experimentally except the area averaged bubble diameter (D).
However, this Can be measured approximately by photographic

means 0

EXPmII-J‘EN TAL METHODS

Standard solutions of sodium lauryl sulfate, or po-
tassium chloride in distilled water were prepared by weigh-
ing out the salt on a sartorius selects balance and adding_
it to a measured volume of water. A wet test meter was
checked by positive displacment and found to be accurate to
within 2-3%. At one hundred times the normal column gas
flow rate, the relative humidity of the air leaving the
humidification section was 98%. An electric timer was used
to measure gas and liquid flow rates.

Surface tensions of sodium lauryl sulfate solutions of
different concentrations in water against air were deter-
mined by the use of a Ceno-DuNouy Tensiometer in conjunc-
tion with a four centimeter platinum ring. The experimental
surface tension of water distilled in metalm 70.7, com-
paring favorably to the literature value for highly distilled
water of 71.9 dynes/cm.

Bottom and top product concentrations were measured
using a platinum electrode cell (Figure 2) in conjunction
with a conductivity bridge (Industrial Instruments Inc.,
model RC-lSB) at a frequency of 1000 cps. Figure 3 is the
calitration curve of conductance as a function of sodium

lauryl sulfate concentration which was used to obtain product

11

12

Cork
Cell

Leads to conductivity bridge

 

Safety clamp Stopcock

 

 

‘\ Rubber stopper

 

 

 

Suction line

 

 

 

W

Suction flask

Figure 2 Platinum conductivity cell

 

 

 

 

   

 

13
70..
60d_
“\A 507+
C)
.4
N
,,
La
3 2+0”
0
O
3
.p
U
:3
rd
a
8 30..
20‘ Region
10. ll
0“ 4 # i. % 1‘
0.h 0.8 1.2 1.6 p 0

. 3
Concentration of Sodium Lauryl Sulfate (gm moles/cm x 10

6)

Figure 3 Calibration curve for the conductivity cell.

14
concentrations from conductance readings. Special care was
taken in measuring conductance readings. The cell was always
filled with distilled water when stored. The cell constant
was checked with a standard potassium chloride solution
(0.0200 molar aqueous KCl, specific conductance 2 0.002768

1 cm'l) at regular intervals to make certain it remained

ohm"
constant. Solutions to be measured were used to rinse out

the cell as many as six times before a reading was taken.

This method was continued until successive readings remained
constant.

A Nikon F Reflex Camera was used to take pictures of
a one square centimeter section of wall bubbles, and the nega-
tives were enlarged to three and one-half by four and one-
half inches. These pictures were then enlarged on a Koda-
graph Microprint Reader. The overall magnification of the
complete process was about 200 times. To determine the area
averaged bublle diameter for a particular run, a randomly
selected zone of bubbles was selected and the squares of the
measured bubble diameters were averaged. ‘

The experimental column equipment and accessories were
set up as shown in Figure 1. The prescribed amounts of so-
dium lauryl sulfate and distilled water were added to the
round bottom flask of the column. Air was bubbled into the
column for stout one and a half hours while the column

variables were adjusted. Over a period of two hours, the

top and bottom product sampling ports were flushed out and

15

the equipment was allowed to come to steady state, after
which measurements of gas flow rate were made with a timer
and a wet test meter. Repetitive samples of top and bottom
products were taken until successive readings remained con-
stant. Photographs were then taken of the bubbles, and the
liquid flow rate, R, was determined by timing the collection
of 50 ml. of top product. It was necessary to determine

the liquid flow rate last, since this disturbed the steady

state operation.

EXPERIMENTAIaRESULTS

.The surface tension data measured here are shown in
Figure 4 as a function of sodium lauryl sulfate concentra-
tion. The slope of the curve was found to be a constant
between the concentration limits of 0.226 x 10'"6 and 1.38
x 10"6 gm moles/cm3 H20. The corresponding surface tensions
were 54 and 29 dynes/cm, respectively. The straight line
portion of the curve had a negative slope equal to 13,52.
Using equation (1) for a non-dissociating surfactant, a

10 gm moles/cm2 was calcu-

surface excess, Tg, of 5.46 x 10-
lated.

The diameter of burbles formed at the sparger are a
function of the system geometry, rubble formation pressure
which is approximately the pressure in the liquid around the
sparger, and surface tension of the surfactant solution. In
this work, system geometry and bubble formation pressure were
constant. Thus, the average bubble diameter formed at the
sparger should be a function of surface tension only. The
model assumes the average bubble diameter not to change from
the sparger to the top product tank. Therefore, the average
Lulble diameter in the column is a flinction of the surface
tension of the liquid in the flask; Since no experimental

luhble diameters were availalle for the first fourteen runs,

16

17

7O

60‘

50.

    
 

ho” Model Region

 

30.

Surface Tension (dynes/cm)

20.,

lo 0

 

l
I

1.0
3 6
Concentration (gm moles/cm. H20 x 10 )

 

P.)
O J;

03 0.1+ 0.5 0.7

Figure h Surface Tension as a function of sodium lauryl sulfate
concentration. Region of constant slope obeys the Gibbs
equation.

18
bubble diameters were read from Figure 5 which shows the
experimental relation between average bubble diameter and
surface tension for runs 15-17 and 20-25. Runs 18 and 19
are omitted since they fall outside of the model region
for constant surface excess.
Equation (3} can be rearranged into the following

form:

 

G

Since bubble diameter is a function of surface tension
and T is a constant, from equation (5) surface tension

can be written as a function of (G/R(Cf - 0%)).

G
¢ . ¢[R(Cf _ 22.07] (6)

The relationship between G/R(Cf - Cr) and surface tension

 

is shown in Figure 6. As expected from equation 5 and 6,
the shape of the curve is similar to that of Figure 5.
Correlation g: the separation gagg; Equation (4) indi-
cates that the data should be correlated by a plot of sep-
aration versus G/RD. This plot is shown in Figure 7. Bub-
ble diameters used in calculating G/RD were determined ex-
perimentally as well as from Figure 5. According to equa-
tion (4), the slope of a straight line through the data of
Figure 7 should be equal to six times surface excess. Sur-
face excess c.lculated in this manner (To) was found to he

10 10

0.728 x 10- compared to the value of 5.46 x 10- gm

moles/cm2 found from surface tension data.

19

 

 

 

0-OS+L
0.0h9_
E?
ii
H 0'03‘r
G)
.p
8
CU
-H
O
.3
.0 4-
,0
.3 0.02.L
0.014,
0 +9 : ti 4 % : 9+
10 20 30 he so 60 70

Surface Tension (dynes/cm)

Figure 5 Column wall bubble diameter as a function of surface
tension.

-6)

(cm3 HQO/gm moles x 10

Column Variables G/R (cf - Cb)

350»

300

 

20

 

 

+-
+
250.
4-
2004
1.
150‘
+
100‘ .+
+++
+
504
0 i + t _l .4
12 2h 36 h8 60

Surface Tension (dynes/cm)

Figure 0 Column variables as a function of surface tension.

Test to see if a correlation does exist.

Separation Cf - Cb (gm moles/cm3 x 106)

21

 

 

 

 

 

 

 

0-1751r
+
0.1501“
0.125%?
0.100"
0.075r
B
.1...
0.050.. Legend
mBubble diameters taken
. from figure 5
+.Experimental bubble
0.025«- diameters
0‘ i J. ‘r J: 4
120 euo ‘360 1.80 600

Variable Group G/R D (cm-J)

Figure 7 Comparison of experimental data with theoretical equation.

22

Discussion 2; errors. There are many factors which

would cause To to be less than T¢.

a. The high flow rates could have prevented the bub-
bles from coming to equilibrium with the liquid
around them, therefore causing a low Tc.

b. The surfactant actually dissociates into either a
weak or a strong electrolyte and the surface ex-
cess T. should be smaller than the calculated value.

0. Measuring liquid flow rate in the foam is a disturb-
ance to the system since it drops the liquid level
in the column. This decreases the liquid flow rate
and proportionally decreases the calculated surface
excess.

d..If gas bubbles coalesced as they rose up the column,
then the ratio of surface area to volume of gas in
the foam would decrease. Since surface area was
experimentally measured at the base of the foam col-
umn, the separation measured at the tcp of the column
and therefore surface excess Tc would be less.

e. If the concentration of drainage from the foam to
the bulk liquid in the flask was greater than the
concentration in the flask, the separation would be
smaller than predicted, thus lowering To.

In examining Figure 7, the model predicted that the ex-

perimental straight line should pass through the origin. In-

23
stead, (G/RD) had a value of 144 when the separation was
zero. One reason for this discrepancy could have been that
at high gas flow rates the bubbles were not in equilibrium
with the bulk liquid around them when they entered the foam.
The equation of the best straight line through the ex-

perimental data is the following:
C -C .A(-C’-)+B
f b RD
~10 gm moles
’x84o37x10
cm
6

B - o0.0629 x 10' gm moles/cm3

CMNCEUSIONS

The mathematical description of the batch foam frac-
tionation column of this thesis correlated experimental
data in the form of a straight line as predicted theore-
tically. The extrapolated line was predicted to pass through
the origin, but actually passed through a point where the
6

gm moles/cm3 H20 when the

gas flow rate divided by the liquid flow and bubble diameter

separation was ~0.0629 x 10-

was zero. The lepe of the experimental line was d.37 x 10-10

gm moles/cmz, compared to the predicted slope of 32.8 x 10-10
gm moles/cmz.

Dissociation of sodium lauryl sulfate in water was not
taken into account in the calculation of surface excess from
the Gihts equation, and this would lower the value consider-
ably. Coalescence of Eubhles near the top of the column and
liquid drainage in the foam caused the experimental slope to
he lower than the predicted value. The net rate of liquid
entrained in the foam with respect to the gas flow rate, and
the lack of attainment of equilibrium between bubbles and the
liquid around them, as they entered the column of foam, prob-

ably caused the extrapolated straight line not to pass through

the origin.‘

24

APPENDIX

26

TABLE I - Experimental data for the batch foam fractionation
column with concentrations in the model region.

Run

\omqmawm

10
12
139%
14##
15
16
I7

1944
20
21'
22
23
24
25

42
###

H HMS

~

en’ 71,0

in Foam

0.367
0.705
0.733
0.549
0.482
0.316
0.767
1.132
0.348

0.1782
0.2045

0.691
1.114
1.047
1.950
1.817
1.462
0.583
0.379
0.432
0.292
1.198

wa

atmosphere.

Cb

($464109

0.334
0.653
0.649
0.522
0.412
0.251
0.673
1.010
0.327

0.1748
0.1749

0.631
0.979
0.963
1.747
1.652
1.292
0.523
0.358
0.405
0.259
1.093

Points taken from Fig. 5.
Points outside of model region

Gas temperature 75.2° to 77.5°

Rate
G42}
( Ml

an.

382.0
440.0
149.0
235.0
176.8
152.1
147.0
149.7
315.5
657.0
270.0
271.0
156.7
543.0
113.1
170.1
170.5
238.5
411.0
282.5
281.0
130.7

Concentration Concentration Gas Flow Liquid
in Bulk

Flow
Rate

R

M1 )
min 0
44.4
74.8
15.2
39.4
16.14
14.28
12.40

16.34

44.8 '

97.8
27.3
37.1
13.4
66.5
9.76
15.93
11.78
31.0
64.4
37.7
31.4
13.91

Bubble
Diameter

D
(cm)

0.03556
0.02836
0.0283?
0.0297“
0.0319?
0.0432?
0.02815
0.0255?
0.03553
0.0548”,
0.05485
0.0298
0.0273
0.0264
0.0280
0.0340
0.0252
0.0308
0.0289
0.0371
0.0404
0.0221

and a pressure of one

27:
TABLE II - Calculated grougsumn of variables for the latch foam

 

9 Points outside 01 model region.

fractionation

Run Difference Gas Rate G Surface

(cf-0b) Liquid Rite (m‘y ‘E‘D‘l' Tension

In Concentration % (“mm 10‘") cm".1 ((1 rnee)
Wmc‘) D' . m )

1mensionless

- 2 0.033 8.60 261.0 242.0 48.2
3 0.052 5.88 113.1 208.0 39.6
4 0.084 9.78 116.5 346.0 39.6
5 0.027 5.96 7221.0 201.0 42.3
7 0.070 10.93 156.0 343.0 45.4
8 0.065 10.66 164.0 247.0 51.8
9 0.094 11.84 126.0 421.0 39.2
10 0.122 9.16 75.0' 359.0 33.9
12 0.021 7.04 335.0 198.0 48.2
13% 0.0034 6.72 1975.0 123.0 56.5
14% 0.030 9.88 321.0 180.0 56.5
15 0.060 7.30 122.0 245.0 40.0
16 0.135 11.70 86.6 429.0 34.3
17 0.084 8.16 97.2 309.0 34.6
18? 0.203 11.60 57.1 414.0 26.8
19% 0.165 10.07 64.5 314.0 27.6
20 0.170 14.47 85.0 573.0 30.7
21 0.060. 7.70 128.0 250.0 42.4
22 0.021 6.38 304.0 220.0 47.3
23 0.027 7.50 278.0 202.0 45.8
24 0.033 8.95 271.0 221.0 51.9
25 0.105 9.39 89.0 424.0 32.4

28

TABLE III - Surface tension of sodium lauryl sulfate in

distilled water from 77.0 to 78.3°F.

Concentration of Scale Correction Surface
Sodium Lauryl Sulfate Reading Factor Tension
(ma—a 355.299) (5‘?) {-949
0.1637 5.67 27.6 0.9005 24.8 '
0.1328 4.60 26.9 0.8988 24.2
0.0976 3.38 28.0 0.9016 25.2
0.0655 2.27 29.8 0.9061 27.0
0.0531 1.842 30.0 0.9067 27.2
0.0390 1.352 32.0 0.9115 29.2
0.0262 0.908 36.6 0.9225 33.8
0.0212 0.735 40.5 0.9314 37.7
0.01561 0.541 44.3 0.9395 41.6
0.01048 0.363 49.0 0.9491 46.5
0.00849 0.294 53.3 0.9578 51.1
0.00624 0.216 55.8 0.9625 53.7
0.00419 0.1452 59.1 0.9687 57.3
0.00339 0.1175 60.3 0.9712 58.5
0.00250 0.0866 62.1 0.9744 60.5
0.00 0.0000 71.4 0.9907 70.7

y 29
TABLE IV - Conductance of sodium lauryl sulfate in water

at 7705 2." 1.0°F.

Concentration of Conductance
Sodium Lauryl Sulfate

les 6 -l 5
(W) (fly-L0 x 10 ) (ohms x 10 )
”1 2 cm H20

0.20168 6.98 ' 179.5
0.16990 5.89 153.9
0.1410 4.89 131.9
0.10084 3.49 . I 96.9
0.08495 2.94 82.0
0.0705 , 2.44 69.1
0.0605 2.10 59.7
0.05042 1.745 51.3
0.04248 1.471 44.2
0.0352 1.22 ' 36.2
0.0302 1.046 . 31.6
0.0251 0.874 26.7
0.0148 0.513 16.4
0.01260 0.436 14.3
0.0074 0.256 8.95

0.000 0.000 ’ 1.01

- "'30
‘TABLE V _ Butble diameters for different operating con-
ditions in the batch foam fractionation column.

Smallest Bubble Largest Bubble Area Averaged Number of

in Sample in Sample Bubble Bubbles

Run Diameter in Sample
(cm) (cm) (cm)

15 0.0163 0.0419 0.0298 40
16 - 0.0206 0.0356 0.0273 50
17 0.0198 0.0395 0.0264 50
18 0.0167 0.0390 0.0280 50
19 0.0238 0.0452 0.0340 50
20 0.0170 0.0417 0.0252 50
21 0.0237 0.0447 0.0308 48
22 0.0207 0.0395 0.0289 50
23 0.0222 0.0645 0.0371 50
24 0.0232 0.0744 0.0404 50
25 0.0123 0.0319 0.0221 50

I? OLEN CLA TURE

 

Symbols

. . 1es
C 3 Concentration of surfactant in solvent (SE—E%——-)

cm
D = Bubble diameter in foam (cm)
. cm
6 a Gas flow rate in foam (sec)
r = Universal gas constant (8.3144 x 107 0K gir$6183
3

n . Liquid flow rate in foam (gala)
t-n Temperature of surface (°K)
T a Surface excess (gm moles/cm2)
Z . Average number of particles per molecule of sodium lauryl

sulfate (dimensionless)

Greek Svmbol

 

0 a Surface tension of surfactant in solvent (dyne/cm)

Subscripts

O '3’ H) O H N H

Solvent

Surfactant

Input (material balance)

Output (material balance)

Foam in column

Bulk solution in round bottom flask
Surface tension data

Column data
31

BIBLIWHEAPHY

1.

2.

3.

8.

9.

10.

33

BIBLIOGRAPHY

Brunner, C. A., and Lemlich, R., I&EC Fundamentals,
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Kevorkiarl’ V0, and Gilden, E. Lo, Jr., A. I. Ch. E.
Journal,.3, No. 2, 180 (1959).

Langmuir, 1., J. Am. Chem. 806., 39, 1848(1917).

Lewis, G. N., and Randall, M., ”Thermodynamics,“
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N. Y., 1961.

Lewis, W. K., Squires, L., and Broughton, G., ”Indus-
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1943.

Roe, C. P., and Brass, P. 0., J. Am. Chem. 300., 16,
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Schoen, H. M., and Mazella, 0., Industrial Water and
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