FOAM DRAIS.4GE
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FOAM DRAIKAGE' GILBERT D. RIILES, LEO SHEDLOVSKY, ASD JOHN ROSS
Colgate-Palmoliae-Peet Company, Jersey C i t y , New Jersey Received November $1, 1944
The rates of drainage of liquids through foams have been mentioned in several papers dealing with the measurement of foam properties ( 1 , 2 , 3 , 5 ) . Frequently, a relationship has been postulated between foam drainage rates and foam coalescence. In previous reports, the types of foams measured were often heterogeneous with respect to bubble size, and sufficiently unstable so that coalescence of bubbles occurred during the course of the experiments. In order to avoid such variables, we have studied some of the flow characteristics of liquids through foams of relatively uniform bubble size and of sufficient stability so that no appreciable coalescence occurred when the measurements were made. Our present study has been restricted to the determination of rates of liquid f l o through ~ foams as a function of the amount of liquid held in the foam lyith the liquid uniformly distributed throughout a column of foam a t constant temperatures, and to an investigation of some of the effects of varying temperatures, bulk and surface viscosity, and bubble size. Some typical measurements of drainage rates in homogeneous stable foams have also been made. EXPERIMENTAL
Procedure Rate of $ow of liquid through f o a m s of uniform liquid concentration: The drainage apparatus (figure 1) vas filled with foam by passing filtered air which had been preheated to the temperature of the bath by a metal-coil heat exchanger, which is not shown in the diagram. As soon as the column was filled with foam, the solution a t the same temperature was introduced a t the top of the column a t a fixed rate. This rate was measured directly by taking the time required to collect a known volume. The outlet tube (D) \vas adjusted t o maintain the foam-liquid interface at a constant level. Khen this rate became constant, the volume of liquid in the foam was obtained by stopping the flow at the inlet tube and draining the column of foam. In some cases the electrolytic conductivity through the foam was measured with a 60-cycle conductivity bridge2 with a precision of i 1 per cent. A linear relationship between the amount of liquid held and the conductance was found on calibrating solutions containing 1 per cent of sodium sulfate and the foamstabilizing constituent. On this basis, the conductivity could be used to determine when the volume of liquid in the foam reached a steady state as n-ell as the amount of liquid in the foam. The volume oi the foam column x i s 295 cc. Presented before the Division of Colloid Chemistry and the Division of Physical and Inorganic Cheinistry a t the 108th Meeting of the American Chemical Society, S e w York City, September 13, 1944. Industrial Instruments conductivity bridge, model RC.1B.
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GILBERT D. MILES, LEO SHEDLOVSKT, A S D JOHN ROSS
and the cell constant wits 3.5. When the volume of liquid in the foam was measured directly, no addition of sodium sulfate was made.
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Q
CONDUCTIVITY BRIDGE
;ii""1 /
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--.e
SOLUTION HEAT EXCHANGE
e
4 d
e FIG.1. Foam drainage apparatus
Rate of drainage of liquid f r o m foams: The drainage of liquid from the foam was started when the column contained a uniform concentration of liquid throughout. The flow of liquid into the foam x a s stopped, and the drainage
95
FOAM DR.II?U'AGE
rate followed by weighing fixed increments of liquid on a torsion balance. Following these rates by weighing the liquid is more precise than by making volume measurements.
Sfeasurement of bubble size The rate of flon- of air through the orifice (0.15 mm. diameter) was determined by mexsiiring the time to fill the column nith foam. -\ls before, the volume of liquid in the foam was obtained by draining the foam. The difference betn-een the volume of the column and the liquid held gives the gas volume. The volume of the bubbles was obtained by collecting bubbles made under the same conditions as above in a conical vessel containing the solution, for a short period of time. The bubbles at the surface of the liquid were collected within an inverted petri dish provided with an opening on the periphery. The petri dish was placed about in. below the liquid level. The bubbles could be slowly released through the opening and counted by tilting the petri dish.
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MATERIALS
The sodium lauryl sulfate was prepared by a method previously described (4). The lauryl alcohol was purified by distillation. Syntes ill is a commercial preparation consisting of the sodium salts of sulfated monoglyceride and sodium sulfate. Igepon T is a commercial preparation for n-hich the following formula is given : CI7H&OS (CH3)C2H4S03Na.This product also contains sodium sulfate. RESULTS
Rate ojjlou! of ltquid through f o a m s : Figure 2 s h o w three typical curves for the rate of flow of liquid through the foam against the volume of liquid held in the foam. The solutions n-ere chosen to cover a range of rates of flow for comparable amounts of liquid in the foam. The open and solid circles indicate two separate runs with 0.25 per cent Igepon T solution and indicate the extent of reproducibility which was obtained. If the logarithms of the two variables of the above data are plotted against each other, the points fall on a straight line (figure 3) and this leads t o a relationship of the form y =
(1)
CY"L
where y = rate of f l o of ~ liquid through the foam (cubic centimeters per minute), = volume of liquid in the foam (cubic centimeters), and "a" and "n" are constants. The following equations were obtained for three solutions tested:
.2:
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I
0.25 per cent sodium lauryl s u l f a t e . , . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.1 per cent sodium lauryl sulfate lauryl alcohol.. . . . . . . . . . . . 0.25 per cent Igepon T solution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ I I
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y = 0.24r1.5 y = 0.06~~,~ y = 0.42~'.~
R a t e of drainage of liquid f r o m foam: A series of curves for the rates of drainage of solutions of 0.25 per cent sodium lauryl sulfate and 0.1 per cent sodium lauryl
96
GILBERT D. MILES, LEO SHEDLOVSKY, AND JOHN ROSS
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sulfate lauryl alcohol were determined, starting with various fixed amounts of liquid in the foam. The data for a typical experiment for each solution are shown in figure 4, where the volumes of liquid left in the foam are plotted as a function of time.
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30
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C C . LIQUID I N FOAM
FIG.2. Rate of flow of liquid through foam
Xs a much simplified approsirnation, let us c o n d e r the rates of f l o in ~ these drainage experiments analogous to the drainage of a liquid in a vertical capillary tube. If L = the height of the liquid in the capillary at time f, and s the capillary rise due to surface tension, from Poiseuille’s la\.\-we have:
FOAM DRAINAGE
where
kt = (L (L
L-s - Lo) + s In -
- Lo)&
Lo - s
= u
- u0 = -vd
mhere 1.' = volume of liquid left in the foam a t time t , T', liquid, and V~ld = volume of liquid drained.
(4)
(5) = initial volume of
FIG.3. Log cubic centimeters of liquid in foam uersus log rate of flow of liquid through foam.
When s is small compared to L ,
s In ( L - s) = s In L
(6 ) and Lo - s = constant. Collecting all the constants in equation 4, this leads to an equation of the form
98
GILBERT D. MILES, LEO SHEDLOVSKY, AND JOHN ROSS
To test whether the data conform to such an approximate equation, a value of a was estimated from three points on the curve (figure 4) and then (1’ a log V ) plotted against t (figure 5). The points fall reasonably well on a straight line except for the lon-er and extreme upper portions of the curve. The data for
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0.1%
GG. L I Q U I D IN FOAM FIG.1. Rate of drainage of liquid froiii foam
the two runs sh0w.n in figures 4 and 5 are typical of a series of ten experiments. This equation is merely a first step in considering the drainage characteristics of the foams tested, since the analogy to flow of a liquid in a tube n-ould be expected to have limitations for foams. From figure 5 the following equations are obtained for the curves ahown in
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FO.4M DR.2IN.4GJS
figure 4:for the 0.25 per cent sodium lauryl sulfate solution whcrc I'o = 6.9 CC., 1' - 21.7 log 1- 10.8 = 0.138t; and for the 0.1 per cent sodium lauryl aulfatc solution lauryl alcohol, where 1, = 25.3 cc., I' - 27.6 log 1' 15.2 = O.057t.
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