266
SYDNEY ROSS
and mercurous chlorides were washed with distilled water until free from barium ion. The lead chloride was washed free from barium ion with ammonium chloride solution, a part of the precipitate dissolving in the process. Each residue was then analyzed for the presence of barium ion and found to be free from this ion. The centrifugates and washings from the silver and merciirous chlorides were treated as in the first experiment, and the amounts of barium ion were determined. The results showed no loss of barium ion. Thus adsorption and occlusion are absent. Postprecipitation was also shown to be absent after 5 days. SUMMARY
No coprecipitation (adsorption, occlusion, or postprecipita tion) of barium ion takes place when the sulfides of the copper and tin groups are precipitat'ed in the presence of ammonium ion. No coprecipitation of barium ion takes place when the chlorides of the silver group are precipitated. REFERENCES
L. J., AND FRANKEL, E.: J. Am. Chem. SOC. 33, 724 (1911). (2) CURTMAN, L. J . : Qualitative Chemical A n a l y s i s , revised edition, p . 298. The Macmillan (1)
CURTMAN,
Co., New York (1938). (3) LEHRMAK, L., BEEN,J., A N D MANES, $1.: J. Am. Chem. SOC.62,1014 (1940). (4) L E H R I A K , L., BEEN,J., AND T\IANDEL, I.: J. Am. Chem. Soc. 63, 1348 (1941). ( 5 ) ZOLOTUKHIN, W. IC.: A& Univ. Vsrogiensis 9,69,84 (1937).
FOARI - A N I EMULSION STABILITIES' SYDNEY ROSS Department of Chemzstry, Stanford Universzty, Californza Receaved J a n u a r y 88, 1948
In another communication (14) various methods of foam measurement are discussed in order to gain some understanding of the factors involved when a foam breaks and how thosr factors are taken into account in different methods, I t is there shown that the Bikerman unit of foaminess (3), defined as the average lifetime of a bubble in the foam, could be measured, using a dynamic foam meter ( 7 ) , only in foams that meet specified conditions and where control of certain variables is undertaken. In static foams, also, there are undoubtedly many factors operating simultaneously, which must be taken into account when considering the stability of the foam. Gibbs (8) lists three causes capable of producing change in liquid films: ( 1 ) The action of gravity on the interior of the film. (2) Suction upon Presented before the Division of Colloid Chemistry a t the 103rd Meeting of the American Chemical Society, Memphis, Tennessee, hpril 20, 1942 (see Abstracts, Section E, page 3).
FOAM AND EMULSION STABILITIES
267
the interior of the film exerted by the liquid mass a t its edge. (3) Evaporation in the upper portions of the film and condensation on the lower portion, the general effect of which is to carry the moisture downward. Previous work that has been done towards establishing a unit of foaminess €or static foams has been frankly empirical and has made no effort to take any theoretical considerations into account. It was discovered experimentally that for many foams the rate of drainage of liquid from the foam obeys the equation
v = Voe-k'
(1)
where V = volume of liquid in the foam after time t , Vo = volume of liquid in the foam when t = 0, t = time, and k is a constant, characteristic for each liquid from which the foam is formed. This equation has been found to hold for such widely diverse substances as beer (4) and saponin solutions ( 2 ) , and the present investigation adds lauryl sulfonic acid to the list. On the basis of an analogy with the unit of foaminess for dynamic foams, Ross and Clark (14) proposed a unit for static foams. This unit, like the Bikerman unit, was originally,designated 2 , but as this might imply an identity of the two units (which the same authors have shown is not the case), it is now proposed to use the symbol Lz for static foams, reserving 2 for the dynamic foams for which it was originally proposed. The unit LZis defined by the general expression LI =
6' v(t)
dt
where the general equation for foam drainage is assumed to have the form
v = Vflf(t) Certain assumptions must be made before it can be shown that this unit is a measurement of the average lifetime of a bubble in the foam; without making any assumption, however, it can be shown to have some physical significance. Since dV
Vof'(t)
dt
and
therefore
LL =
l o --[ vo t d V Yo
(3)
This last expression is the most generally applicable,-hence better for the definition of LI,-and signifies that LLis the average length of time that unit volume of the liquid can remain suspended aloft as foam. On these terms this unit can be contrasted with the Bikerman Z, which has the fundamental sig-
266
(.3TI)SE:I' ItUS':
nifiranirc of ltie average lcnglh of time thnt iurii w!iunc. of the gas remains in the f w i n . For static foam.: the iiiiit, corrrspontling to 2 , liere nanlrd Lg, i$ tlefinrd in rquation 3a :
n-l~orcC is tlie ~ o l u m eof gas in tlie Eonm aftcr time ! and Go i:, t h r initia! volume of ga3 iu thtx foam. mcl Clark method for measuring foaminess and the unit proposrd hu~cx h c n tested by othrr invrstigators (1, 9) and have been found to give rcsults t h a t :we reproduciblr within 3 per cent; -about the same degree of reproclucibility as that reportrd by the most recently published niethods (12).
AIR
FIG.1. Foam meter
The evahiation of Li for foams that obey thc relationship expressed by equation 1 is relatively simple, as in siich cases
Li
=
1
(-1)
Substanrc. the foam stabilities of ivhich have b w n ineastired by this expression includr egg :ilbumin, gelatin, pcptone, saponin, alkyl sulfate, and gum arabic, wing carlion dioxide as the gas with which to proc1iic.e tire foam (9). Although the results are apparently reproducihle, yet it is known (6) that, a t least in one case, that, of egg albumin, t,hc rclationship cxprrssed by equation 1 holds only for a limited portion of t h r total foam life. The rtproducihility of the result can pcrhape be explained when it is remembered that only the central portion of thc total foam life is considered vhen the measurements are made (values of t betneeu GO and 2LO we.). Apparently in many cases anomalies appear both a t the brginning and at the end of the foani lifr. This is well illustrated by scveral csamples of foams forrncd from 0.10 pc~rcrnt solutions of Aerosol OT, The apparatus, in n.hich thc foam is formed and its rate of drainage observed,
FOAM -4XD EMULSION STABILITIES
269
is shown in figure 1. W is a water jacket to ensure constant temperature and G is a sintered-glass membrane of porosity 20-30 microns. Air, previously filtered through glass wool to remove oil droplets that mould be harmful to the foam, is passed into the apparatus at a constant rate. While the foam is being formed, the advance of the foam meniscus up the tube is noted, the time interval for every 5-cc. increase in volume being recorded by depressing a tapping key connected to a calibrated kymograph. The brass drum of the kymograph is run by a Telechron motor turning a t a speed of one revolution per miniite. It was observed that in every case the rate of formation of the foam is constant when the rate of gas flow is constant. 100
40
FIG.2 FIG.2. Foams of 0.10 per cent Aerosol OT FIG.3. Foams of 0.025 per cent Aerosol OT Results for some typical runs with 0.10 per cent Aerosol OT are shown graphically in figure 2, and for 0.025 per cent Aerosol OT in figure 3. The logarithm of the volume of liquid in the foam is plotted against the time. I t will be observed that only in the central part of the curve do the data conform to a straight line. The extent of the straight-line portion of the curve can be varied almost a t will. If the gas is passed into the liquid extremely rapidly and the passage of gas is continued even after all of the liquid has frothed, then the foam collapses rapidly and the straight-line portion of the curve is not reached until near the end of the lifetime of the foam. If, however, the gas is passed in slowly and the foam-liquid miniscus is not allowed to disappear during the passage of gas, the data soon conform to the logarithmic relation of equation 1. A more reliable picture can be realized by considering the numerical values of LI, calculated from a few typical runs. The method of calculating Lt involves only
270
S Y D S E B ROSS
the straight-line portion of the curve. The value of Ti" is found by extrapolation of the straight line to the voliime axif. Li is calculated by the formula
Table 1 contains some calculated values of Ll. Results for various concentrations of lauryl sulfonic acid are shown graphically in figure 4. Here the data are seen to conform 10 equation 1 throughout a greater relative lifetime of the foam. Rut in the case of both these substances, as well as the other substances previondy considered, the rates of drainage at the beginning and the end of the TABLE 1 Foam etabilrtu of 0.10 Der c e n t ~ 0 ~ 7 i t i oofn Aeyosol OT I'r
1'0
CL
7.70
9.00
2.55
'C.
seconds
3.00 2.00
135 193 273
5.m 4.00 3.no
120 162 219
1.40 1.20 1.00
121 151 1S7
4.00
-Bd
1
1
~
~
1
Ll
seconds
207 205 204
I
1
205 200 200 202 200 200
3
no
lb 00 17 00
1, :148 :: 00 13 00 ~
12 00 11 00 io.no 9.00
111 177 260
207 211 209
121 131 141 153 168 1 S7 201 222 245 26G
210 206 201
203 203 205 204 208 211 210
foam life are respectively greater and less than that postulated by equation 1. It is remembered that equation 1 is an empirical equation, yet it is found to be of such general applicability that deviations from it may be regarded as irregular. A possible explanation may lie in the vieiv, communicated to me by Professor J. W. lIcBain, that neither the beginning nor the end of the foam life can be held to be typical of the foam. At the beginning the gravity effect on the drainage must be extremely great and may swamp the other factors: at the end, when there is only a relatively small amount of liquid in the foam, the rate of film collapse may be abnormally sloived by the accumulation of stabilizing material that falls on the last remaining liquid films from all the films that have collapsed on top of tjhem. The work of A h . F. van Acker and others in this laboratory has established the presence of a solid insoluble film, or pellicle, on the surfaces of many apparently soluble detergents. It is desirable to investigate these initial and terminal irregularities more thoroughly. The initial rapid rate of drainage has been explained as duetothe gravity effect on the interior of the film. I t will be remembered that t,his is the
FOAM AND EMULSION STABILITIES
271
first factor considered by Gibbs (8) as important in producing changes in liquid films. According to Gibbs one can obtain “a rough estimate of the amount of motion which is possible for the interior of a liquid film, relative to its exterior, by calculating the descent of water between parallel vertical planes a t which the motion of the water is reduced to zero.” Gibbs uses the experiments of Poiseuille to obtain an equation for the descent of water between parallel planes. The mean velocity of the water (Le., that velocity which, if it were uniform throughout the whole space between the fixed 100
40
Lo TIME IN SECONDS
FIG.4. Foams of lauryl sulfonic acid. Curve A, 0.42 per cent; curve B, 0.21 per cent; curve C, 0.10 per cent.
planes, would give the same discharge of water as the actual variable velocity), relative to the surfaces, is given by the equation
v = 8990’ (6) This is for the temperature 24.5“C. D is the distance in millimeters between the planes, and v is the mean velocity of flow in millimeters per second. The value of the numerical coefficient is uncertain but, according to Gibbs, will probably not exceed 1000. Using a single liquid film, as an approximation to a volume of froth, it is possible to derive an equation for drainage due to gravity, relating the volume drained with the time. Let 1 = vertical height of film in millimeters, IC = horizontal dimension of film in millimeters, D = thickness of the film in millimeters, dx v = - = mean linear velocity of flow in millimeters per second, and dt d V = volume rate of flow in ~ mper - _dvd _ = . second, ~ dt dt
+
272
SYDNEY ROSS
where dVd = .\rolunie of liquid in drained from the film in time dt. In an infinitesimal time dt the original liquid film will contract by a volume (kl.dD) mm.3, assuming no rupture of the film but merely thinning by drainage of fluid. The volume of liquid that drains out of the film will equal (bD.dz) mma3 We can therefore write the equation: 1OOOdVd
=
-kl.dD = kD.dx
This can be expressed usefully as: dTid dz
I
kD 1000
(7)
and dD dx
-
-D 1
A third differential equation can be obtained by rewriting equation 6 as: dx - = 8990’ dt
...
(9)
dx = 8990’. dt
Substituting in equation 8 gives dD
=
-899D3 -1
*
dt
This equation can noiv be integrated
where C iii a constant of integration. of liquid film).
whence
When t = 0, D = DO(initial thickness
F0.4hI AND EMULSIOX STABILITIES
273
133’ combining equations 7 and 9 we obtain:
or dVd = 0.899kD3dt Substitute the expression for D given in equation 10,
or dVd = a(1
+
dt
where a = 0.899kD: cma3set.-'
and D2 b = 2 X 899 -2 set.-' 1 Integrating the equation gives Vd
2a b
= - - (bt
+ l)-l’z + z
where I is the constant of integration. ont) = 0; therefore
When t = 0, then Vd (volume drained
and
Vd =
2a [l 2,
(at
+ 1)-”2]
Substituting back again the values of a and b, -2a=
b
2
x 0.899kD:l 2
x
klDo
-
vo
1000
899D:
klD where V o (initial volume of liquid in cm.a in the film) = 2 Therefore, 1000’ Vd = Vo[l - (bt f 1)-”*]
or
vo vo
1
Vd=-.--..-
(bt
+ l)”?
274
SYDXEY ROSS
The preceding discussion was related to liquid films between masses of gas, but the same considerations apply to liquid films between other liquids. I n the case of emulsions, instead of using Va - Vd to represent the volume of liquid in the film, it is used to denote the amount of emulsified oil left in the emulsion. The data in table 2 were obtained by Dr. Wraeszinski and were printed by A. King (10). The numerical data mere found from the graphs of Figure I of that paper. The range of values of b is within the rather wide experimental error of the original data. E. L. Lederer (11) has developed a formula for the time disintegration of emulsions. I n its integrated form it is:
kt
=
+
I (v)”2 log ___1-
(V)1’2
where Ti is the per cent volume of the separated phase. This equation does not apply to the data in table 2, although it has been found to apply in certain TABLE 2 Rate of demulsifica2ion
Time I” days
CURVE NO. 4
CURVE NO. 5
Per cent emuIs16ed
b e r cent emulsified oil
b
011
______-____ 0 7 14 21 28 63
100 59 49 45 40 26 5
Time in days
____
I
0.267 0.226 0 187 0 187 0.210
a
-
0 4
7 14 20 28 63
100 33 25 .20 14 8
2.05 2.14 2.13 2.50 2.44 2.46
otner cases. Lneesman ana ning (01 tesrea Leaerer s equarion witn cerrain neutral and alkaline emulsions of low stabzlzty and found it to apply. The demulsification of stable neutral emulsions and of acid emulsions did not conform h o ~ e v e r . The emulsions of table 2 are considerably more stable than those that follow the Lederer equation. There xould, therefore, appear to be a t least two different mechanisms in operation, one for stable, the other for unstable emulqions. The Lederer equation is the same as that for a chemical reaction of the one-and-a-half order. The mechanism depends therefore on the interaction of the droplets of the emulsion with each other. Such an interaction would not be possible if the stabilizing film around each emulsified drop were strong because, although kinetic movement would bring the particles momentarily close to each other, they would not coalesce. They mould have to wait until drainage had operated, bringing them into the closest proximity on all sides with their neighbors until, a t a limiting thinness of separating film, coales-
FOAM AND EMULSION STABILITIES
275
cence takes place. By this mechanism of demulsification the stability is greater and is chiefly dependent on the rate of drainage. Perhaps the best indication that the underlying mechanism of Lederer’s equation is a kinetic one is the fact, noted by Lederer, that it gives the same result as Freundlich’s equation for the electrolytic coagulation of colloidal particles. In the case of the emulsions of table 2, a t least, drainage due to gravity is the primary operating mechanism leading to their ultimate separation into two liquid layers. Drainage takes place, as evidenced by creaming, until the peripheries of the oil droplets are in contact. Coalescence will then take place, either spontaneously and immediately after the peripheries are touching, or on application of mechanical or thermal shock. But coalescence cannot occur until, first of all, drainage has brought the droplets together. The separation of the two processes is well illustrated by certain emulsions. One such, prepared in this laboratory by Dr. R. B. Dean, was composed primarily of butyl acetate and water with a trace of Orange OT dye. The emulsion was prepared by shaking and after standing about an hour a thick cream appeared a t the top, although without any visible sign of the separation of the internal phase. It remained in this condition for 2 days without any apparent change and probably would have continued indefinitely in the same state if left undisturbed. At the end of that time, however, the container was knocked sharply against the desk several times and coalescence of the “cream” began to take place immediately. After an hour the emulsion had completely coalesced and separated into two distinct layers, with no trace left of any emulsified oil. There are two processes that occur in the breaking of an emulsion: (1) Druinage or creaming. When two oil droplets are separated from each other, although the system may be thermodynamically unstable, it is practically stable indefinitely, as long &s no agency is a t work to bring the oil droplets together. An emulsion in which the oil phase has the same density as the aqueous phase has been prepared and was found to be extremely stable. When a difference in density does exist, the oil droplets will begin to rise in the fluid. This flow of oil droplets upwards is equivalent to a motion of the water downwards, and hence the phenomenon can be described either as “creaming” or “drainage.” (2) Coalescence. If there is little or no stabilizing agent to prevent coalescence of the oil droplets, then a separation of the emulsion into two liquid layers will take place as soon as drainage has brought the peripheries of the oil droplets into contact. In such a case the rate a t which the emulsion breaks will be determined only by the rate of drainage. This is the case for those emulsions which conformed to the drainage equation, as shown in table 2. With even more stable emulsions, however, the interfacial film between the droplets may be so strong that, even after drainage has occurred, coalescence does not take place. This happens in the case of milk and other highly stabilized emulsions. There coalescence of the oil droplets may have to be engendered by external factors. The situation is more complex when foams are considered. Application of
276
SYDXEY ROSS
equation 11 to the data obtained for foams shows a tendency for the constant b to assume progressively higher and higher values. Figure 5 shon-s the manner in which the reciprocal of b falls off a i t h the time. In some c a w it appearsto be linear a t first, although in other cases this linear relationship i.2.not observed, but in all cases l / b decreases with the time. There are undoubtedly good ieason3 for this decline. I t nil1 be remembered that l / b is given by the equation:
I \vas defined as the vertical height of the film in millimeters, and hence the variation of l / b with time is due to the rupture of the foam films nith time. A lineal relation betneen film rupture and time has been directly observed experimentally for certain non-aqueous foams, where the viscosity of the
FIG.5 . Variation of l / b with time for foams of 0.10 per cent Aerosol OT
liquid mitigates the effect of drainage.' I t is found that equation 11 postulates a yate of drainage from the foam that is actually very much slon-er than the observed drainage. It seems probable that this would be the cme, as equation 11 takes into account only the first of the three causes for drainage from films, mentioned by Gibbs and quoted earlier. When the remaining two, and especially the second, are taken into account, an increased rate of drainage would be obtained by the theoretical treatment. In the case of emulsions, however, only the first of the three factors would be operative in draining. SUMM.4RY
1. The unit of foaminess for static foams is redefined. 2. Foanis of Aerosol OT and lauryl sulfonic acid are shown to conform t o the
usual logarithmic relation for drainage. 3. An approximate equation for drainage of a foam or emulsion is developed theoretically and shown to fit some data O R demulsification. 2
Unpublished data of 311..A . P. Brady, Stanford University.
FLUIDITY OF MIXTURES
277
4. Mechanisms for demulsification of stable and unstable emulsions are postulated. 5. The application of a theoretical drainage equation to data on foam stability indicates a linear relation in some cases between film rupture and time. Thanks are due to Professor James W. McBain for many helpful discussions during the course of this work. REFERENCES (1) AMERINE, M. A., MARTINI,L. P . , AND DE MATTEI,W.:Ind. Eng. Chem. 34,152 (1942). (2) ARBUZOV, K. N., AND GREBENSHCHIKOV, B. N.: J. Phys. Chem. (U.S.S.R.) 10, 32 (1937). (3) BIKERMAN, J. J.: Trans. Faraday SOC.34, 634 (1938). (4) BLOM,J., AND PRIP,P.: Wochschr. Brau. SS, 11 (1936). ( 5 ) CHEESMAN, D. F., AND KING,A , : Kolloid-Z.83,33 (1938). (6) CLARK,G. L., AND Ross, 8.: Ind. Eng. Chem. 32,1594 (1940). C. W., AND MILLER,J. N . : Ind. Eng. Chem. 23,1283 (1931). (7) FOULK, (8) GIBBS,J, W.: The Scientqfic Papers, Vol. I, pp. 300-14. London (1906). (9) GRAY,P. P., AND STONE,J.: Wallerstein Labs. Commun. Sci. Practice Brewing 3, 159 (1940). (10) KING,A.: Trans. Faraday SOC.37, 168 (1941). (11) LEDERER, E. L.: Kolloid-Z. 71,61 (1935). (12) PANKHURST, K. G. A.: Trans. Faraday Soc. 37, 496 (1941). u (13) Ross, S.: Ind. Eng. Chem., Anal. Ed., in press. (14) ROSS, s., A N D CLARK.G . L . : Wallerstein Labs. Commun. Sci. Practice Brewing No, 6,46 (1939).
FLUIDITY OF MIXTURES WHICH OBEY BACHIKSKIf’S LAW‘ F. KOTTLER Kodak Research Laboratories, Rochester, New York Received December 4 , 1948
1. The fluidity of a liquid a t constant pressure may be related either to its volume or to its temperature. For the latter the most useful formula was proposed simultaneously by Andrade (1) and by Sheppard (16) in 1930 and has the form:
log6 = A
- B/T
(1)
where 6 = fluidity or reciprocal viscosity, T = absolute temperature, and A and B = constants. On the other hand, fluidity was expressed as a function of volume first by Bachinskii (2) in 1913, and later by MacLeod (14) in 1923, as follows: 4 = (v
- w)/c
* Communication No. 897 from the Kodak Research Laboratories.
(2)
