Heifferich. F. G., "ion Exchange," Chapter 6, McGraw-Hill, New York, N. Y . , 1962. Heifferich, F. G., J. Phys. Chem. 69, 1176 (1 965). Heifferich. F. G., Sheii DeveioDment Co.. Houston.. Tex... orivate _ ~ -cornrnu- - nication, 1972. inczedy, J., "Analytical Applications of Ion Exchangers," English translation by A. Pail, p 68, Pergamon Press, New York, N. Y . , 1966. Levenspiel, O., "Chemical Reaction Engineering," p 346, Wiiey, New York. N. Y . . 1962. Seiim, M. S., Seagrave. R. C., ind. Eng. Chem., Fundam. 12, 14 (1973).
Sherwood, T. K., Pigford, R. L., "Absorption and Extraction," pp 72-74, McGraw-Hill, New York, N. Y., 1952. Weisz, P. B., Goodwin, R. D., J . Catal. 2, 397 (1963).
~
Receiuedfor review October 11,1972 Accepted September 10,1973 T h i s work was supported b y the Engineering Research Institute, Iowa State University, Ames, Iowa.
Surface Shear Viscosity and Related Properties of Adsorbed Surfactant Films Lalit Gupta and Darsh T. Wasan" Department of Chemical Engineering, lllinois lnstitute o t Technology, Chicago, 111. 60616
The adsorption and accumulation of surface-active agents at fluid-fluid interfaces results in additional, intrinsic, hydrodynamic resistance to flow of which surface shear viscosity is a measure. The results of a study of the surface shear viscosity of a number of soluble surfactant systems are presented. None of the nonbiodegradable, single-component soluble surfactants investigated yielded significant surface shear viscosities. However, lauric acid and lauryl alcohol, practically insoluble in water by themselves but solubilized by .sodium lauryl sulfate, yielded significant surface shear viscosities at certain concentrations and proportions. Relatively insoluble substances or such substances solubilized by other substances will usually cause significant surface shear viscosity at liquid-gas interfaces.
Introduction An understanding of many engineering operations such as distillation, gas absorption and desorption, and liquidliquid extraction is contingent on a thorough study of the role of the interfaces across which transport occurs. In this context, interfacial properties and the dynamic effects of surfactants thereon assume importance. The significance of interfacial shear viscosity has been recognized in several instances such as foam fractionation, formation and stability (Kanner and Glass, 1969; Leonard and Lemlich, 1965; Mannheimer, 1969; Miles, et al., 1950; Shah, 1972; Shih and Lemlich, 1967; Whitaker, 1966), emulsion stability (Oldroyd, 1955; Sherman, 1953), suspension polymerization (Joly, 1964; Kanner and Glass, 1969), film permeability (Cadenhead, 1969; Joly, 1964, 1972a,b), tanning (Joly, 1964), Marangoni instability (Scriven and Sternling, 1964; Sternling and Scriven, 1959), lung surfactant systems (Scarpelli, 1968), films flowing down solid walls (Whitaker, 1964; Whitaker and Jones, 1966), bubble and drop behavior (Bupara, 1966), and mass transfer operations (Lewis, 1954a,b). Surface-active agents tend to accumulate and adsorb at the interfaces between their solutions and the adjacent solid, liquid, or gaseous phases. Such accumulation at fluid-fluid interfaces results in additional, intrinsic, hydrodynamic resistance to flow. Interfacial shear viscosit y is a measure of this resistance. It is defined as the ratio of the interfacial shear stress to the interfacial shear rate and has the dimensions ( M / T ) ,or in the cgs system g/sec or surface poise (S.P.). The concept of interfacial shear viscosity originated more than a hundred years ago (Plateau, 1869). Since then, interfacial shear viscosity and its measurements have received considerable attention (Joly, 1964; Pintar, 1968). The earlier observations of interfacial shear viscosi26
Ind.
Eng. Chem., Fundam., Vol. 13, No. 1, 1974
t y were made at liquid-gas interfaces and were mainly
concerned with insoluble monomolecular films. These studies are reviewed by Gaines (1966), Kanner (1968), and Joly (1956, 1964, 1972a,b). It is only in recent years that attempts have been made to extend interfacial shear viscosity measurements to liquid-liquid interfaces (Gupta, 1970; Wasan, 1971; Wasan, et al., 1971) and to films at liquid-gas interfaces adsorbed from surfactant systems (Eirich, 1967; Joly, 1964). A survey of the literature on the surface shear viscosity of soluble surfactant films at liquid-gas interfaces revealed only isolated pieces of work (Brown, et al., 1953; Israel, 1968; Joly, 1964; Karam, et al., 1967; Lorinc, 1969; Mannheimer, 1969; Mannheimer and Schechter, 1970; Ross and Epstein, 1958; Trapeznikov and Dokukina, 1970; Voce1 and Ryan, 1971; Vora, 1970) in the field. Often, the reported values are close to the sensitivity of the measurement technique. In certain cases the surfactants used were not 100% active or underwent degradation. Also, in most cases, the lack of a mathematical analysis permitting an exact relationship between surface viscosity and experimentally measured variables does not justify full confidence in the reported values of surface viscosity. An experimental program was therefore undertaken to gain insight into the kind of surfactants that would yield significant surface viscosities. Having identified such systems, measurements would then be made of other properties like surface tension, surface potential, and light scattering ratips to shed light on the characteristics of interfacial films.
Surface Shear Viscosity. Surface shear viscosity was determined by the so-called deep-channel viscous traction interfacial viscometric technique (Burton and Mannheim-
STAT ION A R Y PA R ALL EL CHANNEL WALLS
er, 1967; Mannheimer and Schechter, 1970; Pintar, et nl., 1971;Wasan, et al., 1971). Basically it consists of two concentric, stationary vertical cylinders and a rotating flatbottomed dish containing the liquids (see Figure 1). The cylinders are so placed that they almost touch the bottom of the dish. The dish is rotated, causing the fluids in the channel between the cylinders to rotate. The stationary channel walls tend to shear the fluids, thereby enhancing the effect of the interface. For laminar, Newtonian, timeindependent flow in the channel, the velocity in the channel can be readily written down as (Pintar, e t al., 1971)
V = 4
A , cosh na(D - X ) cosh nnD
;E, n -1
+ n x E sinh nx(D - X) + n x E sinh nxD sin nxY (1)
where
An
=
{’-1/(2Ri + 1)
( n odd) ( n even)
’OVtNG
Here X = dimensionless x coordinate = x/yo, Y = dimensionless y coordinate = y/yo, V = dimensionless velocity = u / D b , D = dimensionless depth = x/yo, E = dimensionless surface viscosity = t / q y o , Ri = dimensionless radius of inner channel = rj/yo, Ob = centerline velocity at floor = (r, y 0 / 2 ) w o , 9 = bulk viscosity, t = surface viscosity, and wo = angular dish speed. For deep channels (D > ZIT), sinh nTD = cosh nnD e n a D / 2 .Furthermore, a t the interfacial centerline, that is, X = D and Y = 0.5,only the first term in the infinite series for velocity is significant (Pintar, et al., 1971). Consequently, the interfacial centerline velocity (VJ can be written as
+
8e-”D (1 x E ) (2) x(l T E ) For a given Newtonian surface viscosity ( E ) and a given dimensionless depth ( D ) , the velocity Vc is constant. In dimensional terms this implies that U c / & is constant, that is to say t , / t , = constant (31
v, =
+
+
where to and .tc are times required for one revolution of the dish and a particle on the interfacial centerline, respectively. For pure interfaces, E = 0. Using an asterisk to represent such interfaces, we have from eq 2
8e-“D -
(4)
V,*/V, - 1
(5)
v,* =
x
From eq 3 and 4 it follows that
xE
=
Equation 5 relates the surface shear viscosity to experimentally determinable velocities Vc* and Vc for the pure and impure interfaces. In terms of particle revolution times, the surface shear viscosity is given by
aE
=
t,/t,*
-1
(6)
Experimental Techniques Determination of Surface Shear Viscosity. It has been shown (Gupta, 1970; Mannheimer and Schechter, 1970; Pintar, 1968; Pintar, et al., 1971) that curved interfaces in the channel result in an error of less than 1070 in the calculated values of interfacial velocities and shear viscosities. The present work, as we shall see, deals with systems generally exhibiting high surface shear viscosities (0.001to 1.0 s.P.) for which this error is insignificant. Fur-
v ‘ ( r i t y \ Wo V * ( RitY) / ( R i t 0.5)
Figure 1. Cartesian representation of channel
thermore, maintenance of flat interfaces in the channel requires the construction of a step or ledge (Mannheimer and Schechter, 1970) in the channel walls. Such a ledge was machined into the channel walls of the interfacial viscometer built in our laboratory, but it made experimentation more difficult. Liquids have to be introduced extremely slowly, and consequently no time-dependent data can be taken a t low surface ages. Also, evaporation of liquid will cause the liquid level to fall below the ledge and the interfacial profile to assume a curved shape. It was therefore decided to ignore curvature effects in this work. Figure 2 shows the cross section of the viscous traction interfacial viscometer. The motive power is provided by a %-hp Servo-Tek “100 B” series precision adjustable-speed drive system which is infinitely adjustable from zero to 90 rpm. A 5:l Boston worm gear, which reduces the rated speed to 18 rpm, permits improved manipulation of lower speeds. A 1-in. diameter steel shaft connects the gear to the turntable. The stainless steel dish is centered automatically when the pin projecting from its bottom is inserted into the receptacle provided in the shaft. The dish is fastened onto the turntable with the help of four bolts. The canal assembly which houses the stationary cylinders rests on four sleeves placed around support posts attached to the working platform. The height of the sleeves is such that the gap between the bottom of the channel walls and the dish bottom is l/S4 in. Such a small gap, however, has no effect on the interpretation of data (Pintar, et al., 1971). The canal assembly is centered when a pin is inserted through the top plate of the assembly into a receptacle fixed to the bottom of the dish. The canal assembly is held in position by tightening four nuts on the support posts. A Starrett micrometer depth gauge with a range of 3 in. and an accuracy of 0.001 in. is attached to the top plate of the canal assembly. It permits measurement of the depths of liquids in the channel. For conducting solutions, the micrometer is used in conjunction with a microammeter and a battery in series. For making velocity measurements, an Edmund erectimage, direct measuring microscope No. 70,266,which has a field of view of 3/4 in. and a magnification of 6x at a working distance of 4’/8 in., is used to observe Teflon particles introduced at the interface. The microscope rested on the working platform. A lamp was used to illuminate the interfacial region under observation through the microscope. Ind. Eng. Chem., Fundam., Vol. 13, No. 1, 1974
27
I
Figure 2. Cross section of the viscous traction interfacial viscometer
A typical experimental run commenced with a thorough cleaning of the dish and the canal assembly with hot chromic acid, distilled water, and acetone. The dish was placed in position on the turntable and fastened to it by means of the four bolts provided for the purpose. The canal assembly was then placed on the sleeves, centered with the help of the pin, and locked into position by tightening the four nuts on the support posts. A calculated amount of liquid was introduced into the dish to yield the desired depth in the channel. The motor was switched on and its speed increased to the desired value. One of several procedures was followed to determine the interfacial centerline velocity. For relatively large velocities, a single Teflon particle (diameter = 0.01 cm) was deposited at the interfacial centerline and the time taken to complete one revolution was measured with a stopwatch. Relatively low velocities were determined by following a Teflon particle in the field of view of the microscope and noting the time taken to traverse a predetermined distance on the microscope scale. Often several particles were deposited at various place2 on the interface and timed as they came into view under the microscope. In several instances, not only was more than one particle introduced and “followed” in the field of view of the microscope, but also the microscope was moved “downstream’’ to bring a particle back into view after it had disappeared. The time taken by the dish to complete one revolution was also recorded. The depth of the liquid in the channel was determined from the difference in the micrometer readings taken for two positions of the probe, one when the tip of the probe just penetrated the surface and the other when it made contact with the floor of the dish. The procedure outlined above required a slight modification for insoluble films. After fastening the dish in position, the substrate was introduced. Next, a calculated amount of the insoluble substance dissolved in a 1:1:3 mixture of chloroform, methanol, and hexane was introduced via a Hamilton CR700 syringe having a range of 0.20 p and graduated in 0.1 pl. The canal assembly was then placed in position. Measurement of Other Properties. Surface tension was determined by the well-known Wilhelmy plate method (Davies and Rideal, 1963), using a Cahn electrobalance in conjunction with a recorder. The commonly used ionizing electrode method, aided by a Keithley electrometer and a recorder, was employed to measure surface potential. The ratio of light scattered by a solution at right angles to a monochromatic incident beam to the light transmitted unscattered was. determined with the aid of a 28
Ind. Eng. Chem., Fundam., Vol. 13,No. 1, 1974
Brice-Phoenix Universal 2000 series light-scattering photometer. Experimental Results and Discussion Criteria for Selection of Surfactants. The surfactants chosen for study were all pure or active with definite known compositions, as far as possible. Secondly, they were all nonbiodegradable so that their characteristics would remain unchanged over a period of time. Thirdly, they were in such a physical state (powder or liquid) that a desired weight or volume of the surfactant could be easily measured. Anionic, cationic, and nonionic surfactants of various types were studied. McCutcheon’s book (1971) proved extremely useful in the screening of surfactants. Systems Exhibiting Low Surface Shear Viscosity. It is well known (Mukerjee and Mysels, 1971) that the activity of a surfactant rises very slowly, if at all, above the critical micelle concentration. Furthermore, the critical micelle concentration of ionic surfactants is of the order of 0.1%; that of nonionic surfactants is 0.001% (Mukerjee and Mysels, 1971; Schick, 1967). The activity of surfactants is, therefore, close to maximum at a concentration of 0.1%. Consequently, it was decided to determine the surface shear viscosity of surfactant solutions at a concentration of 0.1% (by weight for solids and by volume for liquids). Surface viscometric measurements were made with the deep-channel viscous traction viscometer according to the procedure outlined earlier. The surfactants investigated are listed in Table I. Interfacial velocities for all the surfactant solutions studied were found to be within ten per cent of the velocity for distilled water under comparable conditions of liquid depth and dish speed. In accordance with eq 6, it was, therefore, concluded that the surface shear viscosity of these solutions was exceedingly small ( - 10- 4 S.p.1. Motivation for Mixed Surfactant Systems. Surface shear viscosities of the order of and higher are commonly found for insoluble monolayers on aqueous substrates (Joly, 1956, 1964, 1972b). Recently, in a study of surface tension and electric potential at the surface of aqueous solutions of 0-, m-, and p-cyanophenols, Siwek (1971) found the influence of the meta isomer to be the strongest and its solubility to be the lowest. According to Stevens (1969), “efficient” surfactants are those that are usually relatively insoluble as individual ions or molecules in the bulk of a solution. Consequently, it was felt that films of relatively insoluble surfactants adsorbed at ayueous interfaces would tend to exhibit significant surface shear viscosities. Lauric acid and lauryl alcohol were chosen to test this hypothesis. Both are insoluble in water (Perry, 1963) and have simple molecular structures. Saturated solutions of lauric acid and lauryl alcohol were prepared by separately adding excess amounts of each to water. Surface viscometric measurements were made for these saturated solutions. The data obtained were extremely erratic, possibly due to nonuniform distribution of the surfactants in the bulk, nonhomogeneous film formation, or temperature effects on solubility. Nevertheless, the data indicated significant surface shear viscosity to lo-* s.P.) for these solutions. However, monolayers (25 A2/molecule) of these substances on pure aqueous substrates exhibited negligible surface shear viscosity, possibly because of the solvation of the small deposited amounts. It has been established that strong interactions occur in the soluble films given by certain aqueous solutions of mixtures of ionic surface-active compounds and water-insoluble or sparingly soluble polar additives (Mukerjee and Mysels, 1971). Brown, et al. (1953), report high surface
Table I. Soluble Surfactant Systems Yielding Negligible Surface Shear Viscosity Surfactant
,
Ionic type
Antara LM-600
Anionic
Atlasene 500 C Cellopal 100
Nonionic Anionic
Dodecyl sodium sulfate Emulphogene BC ,720
Anionic Nonionic
E thylhexadecyldimethylammonium bromide Fosterege LFD Fosterege W acid Fosterege W D Hexadecyltrimethylammonium bromide Hexanamide Hexyl alcohol Hexylamine Igepal CO-730
Neutronyx 600
Nonionic
Pluronic L64
Nonionic
Formulaa
Source General Aniline and Film Corporation Atlas Refinery, Inc. Tanatex Chemical Co.
Cationic
Free acid of complex organic phosphate ester Fatty alkylol amide condensate Polyethoxyalkylphenolsulfonate triethanolamine salt C H ~ ( C H llSOaNa Z) (288) Tridecyloxypoly (ethylenoxy) ethanol CzHj.C1JT13.( C H I ) ~ N B (379) ~
Eastman Organic Chemicals
Anionic Anionic Anionic Cationic
Amine organophosphate salt Organophosphate acid Organophosphate salt C1~H33. (CHdaNBr (365)
Textilana Corp. Textilana Corp. Textilana Corp. Fisher Scientific Co.
Anionic Anionic Anionic Nonionic
CHs(CH2)aCONH2 (115) CHa(CHs)(CH*OH(102) CHa(CHz)aCHzNH* (101) Nonylphenoxypoly (ethylenoxy) ethanol Alkylphenol polyglycol ether containing 9.5 moles of ethylene oxide Condensate of ethylene oxide with hydrophobic bases formed by condensing propylene oxide with propylene glycol (2900) Polypeptide
Fisher Scientific Co. Fisher Scientific Co. Fisher Scientific Co. General Aniline and Film Corp.
Stepan Chemical Co.
Fisher Scientific Co. General Aniline and Film Corp.
Onyx Chemical Co. Wyandotte Chemicals Corp.
Polypeptide #37, anhydrous Siponic SK Sodium alkylarylsulfonate Surfonic LF-7 Surfynol 485
Nonionic Anionic
Polyoxyethylene thioether Sodium alkylarylsulfonate
Alcolac Chemical Corp. Fisher Scientific Co.
Nonionic Nonionic
Jefferson Chemical Co. AIRCO Chemicals and Plastics
Tanemul B Tergitol 12-M-10 Tergitol NP-33
Nonionic Nonionic Nonionic
Tetronic 304
Nonionic
Tex-Wet 1131 Triton N-111
Anionic Nonionic
Tween 60
Nonionic
Alkyl polyoxyalkylene ether Ethoxylated acetylenic glycol 2,4,7,9-tetramethyl-5-decyne4,7-diol Fatty amide Alkyl thioether ethoxylate Nonylphenyl polyethylene glycol ether Formed by addition of propylene oxide t o ethylenediamine followed by addition of ethylene oxide Amine condensate Nonylphenoxypolyethoxyethanol Polyoxyethylene sorbitan monostearate
Zonyl A
Nonionic
Tanatex Chemical Co. Union Carbide Corp. Union Carbide Corp. Wyandotte Chemicals Corp.
Texize Chemicals, Inc. Rohm and Haas Co. Atlas Chemical Industries E. I. Du Pont de Nemours and Co.
Numbers in parentheses a t the end of formulas indicate known molecular weights.
viscosities for a few solutions of sodium lauryl sulfate and lauryl al'cohol in the vicinity of the micellar range. These data, taken with the rotational torsional method, suffer from several shortcomings (Pintar, et al., 1971). Ross (1958) used the torsion-pendulum method, again subject to several limitations, to relate inferred changes in rela, tive surface viscosity of some mixed solutions of sodium lauryl sulfate and lauryl a!cohol to transitions in foam and film drainage. Recently, Trapeenikov and Dokukina investigated the same system for sodium lauryl sulfate concentrations in the micellar range (Dokukina and Trapeznikov, 1971; Trapeznikov and Dokukina, 1970) using the torsional pendulum method. Solutions of sodium lauryl sulfate alone indicated negligible surface shear viscosity. Also, sodium lauryl sulfate acts as a solubilizing agent for lauric acid in addition to lauryl alcohol. Based on these and other considerations mentioned above, it was decided to study mixed solutions
of sodium lauryl sulfate and lauric acid, and sodium lauryl sulfate and lauryl alcohol. Surface Viscometric D a t a for Mixed Solutions. Surface viscometric data for mixed solutions were taken over a concentration range of 0.001-1.0% by weight of sodium lauryl sulfate. Data were taken a t three different values for the system sodium lauryl sulfate-lauric acid and a t two different values of K for the system sodium lauryl sulfate-lauryl alcohol. ( K is the ratio of the weight of the solubilizer (sodium lauryl sulfate) to the weight of the substance solubilized (lauric acid or lauryl alcohol) .) The chosen values of K were 4, 10, and 40 for sodium lauryl sulfate-lauric acid, and 40 and 60 for sodium lauryl sulfate-lauryl alcohol. In addition, data were taken for solutions of sodium lauryl- sulfate alone ( K = m ) over the concentration range 0.001-1.0% by weight. Reproducibility, as ascertained from several duplicate runs, was found to be within 10%. Ind. Eng. Chem., Fundam., Vol. 13, No. 1 , 1974
29
I
0001
K
0002
om
001
002
005
01
a5
02
I
WEIGHT PERCENT SODIUM LAURYL SULFATE
Figure 4. Dependence of surface viscosity on concentration for mixed solutions of sodium lauryl sulfate and lauric acid DISH REVOLUTION TIME (io)
,SEC
Figure 3. Surface viscometric data for 1.0% sodium lauryl sulfate solution ( K = a).
Data for seven concentrated mixed solutions, one for each of the values investigated, were taken for several values of dish speed ranging from 0.5 to 1.5 rpm. The data plotted as particle revolution time ( t c )us. dish revolution time ( t o ) were found to lie on a straight line passing through, the origin. See Figure 3 for typical behavior. Solid symbols in this figure indicate the results of duplicate runs. The solid line representing the data for distilled water is included to facilitate comparison between pure and impure interfaces. In accordance with eq 3 it can therefore be concluded that the systems investigated exhibit Newtonian surface shear viscosity. Subsequent data were, consequently, taken at only one dish speed. The straight-line behavior described above also indicates that we were operating in the region of primary flow (Pintar, et al., 1971) where the x and y components of velocity are negligible. Surface shear viscosity was determined from the velocit y data on the basis of eq 6. The results are shown in Figures 4 and 5 as a function of the per cent of sodium lauryl sulfate in solution with K as a parameter. The surface shear viscosity is seen to be extremely low s.P.) over the entire concentration range for solutions of sodium lauryl sulfate alone ( K = m ) . For mixed solutions of sodium lauryl sulfate with both lauric acid and lauryl alcohol, the surface shear viscosity is seen to be negligible for very dilute solutions ( 0.1% sodium lauryl sulfate). Note that for intermediate concentrations, the surface-shear viscosity is greater for higher K values, that is, for systems containing relatively lower amounts of the substance solubilized, lauric acid or lauryl alcohol. For the most concentrated solutions, however, the surface-shear viscosity increases with increasing amounts of the substance solubilized. Note that extrapolation of the data in Figures 4 and 5 to K = 0 is not possible because the substance solubilized is practically insoluble by itself and also because in the absence of the solubilizer data cannot be represented in the above manner. Limited surface viscosity data have been reported (Brown, et al., 1953; Dokukina and Trapeznikov, 1971; Trapeznikov and Dokukina, 1970) for the system sodium lauryl sulfate-lauryl alcohol using techniques suffering 30
Ind. Eng. Chern., Fundarn., Vol. 13, No. 1, 1974
0.75
a
-I
v)
a
050
H 5
V Y
$
025
0 00 0001
0002 I l
l l 0005 l l l l l001 l
002 I
I
I 005 1 l l l l01 l
0I2
I
1 0.5 1 1 1 1 1 1 11.0
WEIGHT PERCENT SODIUM L U R K SULFATE
Figure 5. Dependence of surface viscosity on concentration for mixed solutions of sodium lauryl sulfate and lauryl alcohol
from various shortcomings. Data by Brown, et al. (1953), indicate a surface shear viscosity of 2.0 X and 4.0 X 10-3 s.p. for solutions containing 0.1 and 0.5% sodium lauryl sulfate, respectively. Our work reveals that such solutions exhibit extremely low surface shear viscosity, of the order of s.p. However, their data depict a trend similar to the one obtained in this work: for mixed solutions containing 0.1 and 0.5% sodium lauryl sulfate, the surface shear viscosity increases with increasing amounts of the substance solubilized. Data recently reported by Trapeznikov and Dokukina (1970, 1971j for concentrations of sodium lauryl sulfate greater than 0.1% are more in agreement with those obtained in this work. For concentrations below the critical micelle concentration of sodium lauryl sulfate (0.2370)~ they found high surface viscosity even for small amounts of lauryl alcohol in the mixed solutions. For concentrations above the critical micelle concentration of sodium lauryl sulfate, surface shear viscosity may be high or low depending on the amount of lauryl alcohol present in solution. Furthermore, they too found it difficult to obtain “intermediate” values of surface shear viscosity. Related Properties of the Mixed Solutions. The dependence of surface shear viscosity on the concentrations and relative amounts of sodium lauryl sulfate and lauric acid or lauryl alcohol described above is complex. In what follows, we attempt to explain this complex behavior on the basis of the surface tension, surface potential, and
“0001
0002
0.001) 001
0.02
0.05
0.1
4
0.2
-1
I
K 0
05
0
:
I I 0.001 a002
1.0
I
I
light-scattering data taken in accordance with the procedures outlined earlier. Surface Tension. Figure 6 depicts the dependence on concentration of surface tension of mixed solutions of sodium lauryl sulfate and lauric acid. The surface tension decreases greatly with an increase in concentration up to about 0.1% sodium lauryl sulfate and then increases slightly. Furthermore, the surface tension decreases as the relative amount of lauric acid increases at a given concentration of sodium lauryl sulfate. This leads to the conclusion that lauric acid is adsorbed at the surface from the bulk of the mixed solutions. Also, the presence of lauric acid at the interface results in additional lowering of the surface tension. The extent of lowering increases with increasing amounts of lauric acid in solution. The existence of minima in the graphs of surface tension us. concentration suggests that the substance solubilized (lauric acid) is desorbed partially or completely from the surface and is solubilized in the micelles of the surfactant (sodium lauryl sulfate) at concentrations greater than the critical micelle concentration (Mukerjee and Mysels, 1971). It is generally accepted (Elworthy, et al., 1968) that, for aqueous solutions, semipolar or polar substances solubilized like lauric acid are taken up in the “palisade” layer of the micelles and oriented with their hydrophobic moieties toward the center of the micelle and their polar groups at the surface of micelle. Furthermore, the minimum implies that the substance solubilized-lauric acid -has a surface activity at least comparable with that of the surfactant-sodium lauryl sulfate (Mukerjee and Mysels, 1971). Surface Potential. The dependence of surface potential on concentration depicted in Figure 7 is consistent with the picture presented above. Whereas the surface tensionconcentration curve (Figure 6) exhibited a minimum in the vicinity of a concentration of 0.1%, the surface potential is seen to increase continually with concentration, until it levels off above approximately 0.3% sodium lauryl sulfate. Micelle formation, known to remove some adsorbed lauric acid from the surface, apparently still leaves enough at the surface to lead to this kind of behavior. Figure 7 also reveals that decreasing K or increasing amount of lauric acid leads to increasing surface potential, suggesting additional contributions to surface potential by lauric acid molecules adsorbed at the surface. Light-Scattering Ratio. Figures 8 and 9 display light scattering data for the mixed solutions of sodium lauryl sulfate and lauric acid. The concentration of sodium lauryl sulfate is plotted on the abscissa. The ordinate shows the ratio of the intensity of light scattered by the solutions
I , , /
I 0.02
I
I
I
I
/ I / /
0.05 0.1
1
,
I
1
, I l l
0.5
0.2
I
0
WEIGHT PERCENT SWIUM LAURYL SULFATE
WEIGHT PERCENT SODIUM LAURYL SULFATE
Figure 6. Dependence of surface tension on concentration for mixed solutions of sodium lauryl sulfate and lauric acid
I
0.005 0.01
Figure 7. Dependence of surface potential on concentration for mixed solutions of sodium lauryl sulfate and lauric acid 400
0
K
X
0 4
300c1
>
A d )
-
9200-
g 0
g
100-
k *546p
W
c
2 y
1
I
, I,,,,/
J
1
,
,
1,,,,1
I
0.0010.002 0.001)On 0.02 0.05 0.1 0.2 0.5 WEIGHT PERCENT SODIW LAURYL SULFATE
, ,
I , ,J
1.0
Figure 9. Dependence of light scattering ratio on concentration for mixed solutions of sodium lauryl sulfate and lauric acid
(at right angles to the incident primary beam) to the intensity of the unscattered light transmitted through the solution. The ratio is seen to be extremely low over the entire concentration range for solutions of sodium lauryl sulfate alone ( K = m ) despite the expected sharp increase i n slope in the micellar region (Mukerjee and Mysels, 1971). For mixed solutions, however, the behavior is in contrast to the rather precipitous increase of scattering and solubilization in the vicinity of the critical micellar concentration (Jacobs, e t al., 1972). The light-scattering ratio is seen to be extremely low for dilute solutions and to increase sharply over intermediate concentrations. For concentrated solutions, the ratio decreases and then increases. Thib behavior can be explained if it is assumed Ind. Eng. Chem.,
Fundam.,
Vol. 13, No. 1, 1974
31
that lauric acid possesses greater light-scattering power than sodium lauryl sulfate. The light-scattering ratio is low for dilute solutions because lauric acid is present in small amounts. As the concentration increases, increasing amounts of lauric acid in solution lead to increasing lightscattering ratios, until the critical micelle concentration is reached. Then the ratio decreases because lauric acid is taken up in the micelles. Finally, the light-scattering ratio increases as expected because the concentration of the micelles increases. The preceding discussion pertained to the system sodium lauryl sulfate-lauric acid. However, it applies equally well to mixed solutions of sodium lauryl sulfate and lauryl alcohol since the dependence of their surface tension, surface potential, and light-scattering ratio on concentration is similar to that for mixed solutions of sodium lauryl sulfate and lauric- acid. These details are given elsewhere (Gupta, 1972). Possible Explanation of Surface Viscosity Trends. Consider one K value corresponding to a fixed proportion of the solubilizer (sodium lauryl sulfate) and the substance solubilized (lauric acid) in solution. First of all, any significant surface shear viscosities are due to the presence of the substance solubilized. The surface shear viscosity is negligibly low for dilute solutions because the substance solubilized is present in extremely low amounts. As the amount of available substance solubilized increases, the surface shear viscosity increases because of the strong surface adsorption characteristics due to saturated adsorption of the substance solubilized. As the concentration increases still further, micelles of the solubilizer begin to form. These micelles take up the substance solubilized from the bulk as well as the surface. The surface shear viscosity consequently decreases. The extent of decrease depends upon the relative amounts of the solubilizer and the substance solubilized. For relatively low amounts of the substance solubilized, the surface shear viscosity becomes negligible. For relatively high amounts of the substance solubilized the surface shear viscosity decreases but still remains high because enough of the substance solubilized is left behind a t the surface. Let us now consider the effects of varying the ratio of solubilizer to the substance solubilized ( K ) at a given concentration of the solubilizer. The fraction of.the substance solubilized present in the adsorbed film depends not only upon its surface activity relative to that of the solubilizer but also on the relative amounts of the two in solution. This fraction determines the packing a t the interface which in turx. influences the resistance of the interface to shear flow and thus surface shear viscosity. Now, the apparently anomalous dependence of surface shear viscosity on K at intermediate concentrations is manifested in the form of a decrease in surface viscosity for increasing amounts of the substance solubilized in solution. The' picture presented above is offered as a possible explanation of this behavior. Conclusions
A study was conducted of surface shear viscosities of soluble surfactant systems. None of the 100% active, nonbiodegradable, single-component, soluble surfactants investigated yielded significant surface shear viscosities. However, lauric acid and lauryl alcohol, insoluble in water by themselves but solubilized by sodium lauryl sulfate, yielded at certain concentrations and proportions significant surface shear viscosities which were three orders of magnitude greater than the negligible surface viscosity s.p.1 of sodium lauryl sulfate solutions. The surface shear viscosities of mixed solutions of sodium lauryl sulfate and lauric acid, and sodium lauryl sulfate and lau32
Ind. Eng. Chem., Fundam., Vol. 13,No. 1, 1974
ryl alcohol, investigated a t various concentrations and proportions, exhibited complex behavior. The complex behavior is explained in accordance with a molecular picture evolving from the data taken on the surface tension, surface potential, and light-scattering ratios of such solutions. Both lauric acid and lauryl alcohol, which display considerably greater surface activity relative to sodium lauryl sulfate, tend to be adsorbed preferentially a t the surfaces of their mixed solutions and also tend to be taken up in the micelles of sodium lauryl sulfate. Also, the relative amounts of sodium lauryl sulfate and lauric acid or lauryl alcohol adsorbed and packed at the surface depend on their bulk concentrations. It is suggested that trace amounts of relatively insoluble substances or relatively insoluble substances solubilized by other substances are likely to yield significant surface shear viscosity in liquid-gas systems.
Acknowledgments This work was supported by the National Science Foundation under Grants GK-30028X and GK-30028x1 and in part by the American Petroleum Institute under Research Project 133.
Nomenclature c = total concentration, moles/cm3 D = ratio of depth of liquid in contact with gas phase to channel width ( x o / y o ) , dimensionless E = dimensionless surface shear viscosity G = galvanometer reading/product of transmittances of neutral filters (subscripts denoting angle a t which light scattered or transmitted) K = ratio of weight of solubilizer to weight of the substance solubilized, dimensionless ri = radius of inner stationary cylinder, cm Ri = ratio of radius of inner cylinder to channel width (ri/yo), dimensionless t o = time required fer one revolution of the dish, sec tc = particle time required for one revolution, sec V = ratio of fluid velocity to velocity at centerline of channel floor ( u / f ) b ) , dimensionless u = fluid velocity in the z direction, cm/sec O b = velocity at the c e n t e r h e of the channel floor, cm/ sec X = ratio of x coordinate to channel width ( x l y o ) , dimensionless x,y = space coordinates in Cartesian system xo = depth of liquid in contact with gas phase, cm Y = ratio of y coordinate to channel width ( y l y o ) , dimensionless yo = width of channel, cm Greek Letters e = surface shear viscosity, surface poise X = wavelength of light, microns p = microns 7 = bulk viscosity of liquid, poise A = 3.142 u = surface tension, dyn/cm wo = angular velocity of floor, radianslsec Subscripts c = interfacial centerline Superscripts * = pureinterface Literature Cited Brown, A . G..Thuman, W. C., McBain, J. W., J. Colloid Sci. 8 , 491 (1953). Bupara. S. S., Ph.D. Thesis, University of Minnesota, Minneapolis. Minn., 1966. Burton, R . A., Mannheimer. R. J.. Advan. Chem. Ser. No. 3,315 (1967). Cadenhead, D. A., lnd. Eng. Chem. 61(4). 22 (1969). Davies, J. T., Rideal, E. K., "Interfacial Phenomena," 2nd ed, Academic Press, New York, N. Y., 1963.
Dokukina, E. S..Trapeznikov, A. A., Colloid J. USSR 33(5), 562 (1971). Eirich, F. R., Ed., "Rheology: Theory and Applications," Vol. 3, Academic Press, New York. N. Y., 1967. Elworthy, P. H., Florence, A. T., Macfarlane, C. B.. "Solubilization by Surface-Active Agents," Chapman and Hall, London, 1968. Gaines, G. L., "Insoluble Monolayers at Liquid-Gas Interfaces," Interscience, New York. N. Y., 1966. Gupta, L., M.S. Thesis, Illinois Institute of Technology, Chicago, Ill., 1970. Gupta, L., Ph.D. Thesis, Illinois Institute of Technology, Chicago, Ill., 1972. Israel. A., M.S. Thesis, Illinois Institute of Technology, Chicago, Ill., 1968. Jacobs, P. T.. Geer, R. D., Anacker, E. W., J. Colloid lnterface Sci. 39(3), 611 (1972). Joly. M., J. Colloid Sci. 11, 51 9 (1 956). Joly. M., "Surface Viscosity," in "Recent Progress in Surface Science," Vol. 1 , Academic Press, New York, N. Y., 1964. Joly. M., "Rheological Properties of Monomolecular Films-Part I: Basic Concepts and Experimental Methods," in "Surface and Colloid Science." Wiley-lnterscience, New York, N. Y., 1972a. Joly. M.. "Rheological Properties of Monomolecular Films, Part I I: Experimental Results, Theoretical Interpretation-Applications," in "Surface and Colloid Science," Wiley-lnterscience, New York, N. Y., 1972b. Kanner, B., paper presented at Industrial Engineering Chemistry Summer Symposium on Chemistry and Physics of Interfaces, Washington, D.C., June 1968. Kanner, B., Glass, J. E., lnd. Eng. Chem. 61(5), 31 (1969). Karam, H. J., Bellinger. J. C., Balwinski, R . Z.,paper presented at the 60th Annual Meeting of A.I.Ch.E., New York, N. Y., Nov 1967. Leonard, R. A,, Lemlich, R., A.l.Ch.E. J. 11.18 (1965). Lewis, J. 8..Chem. Eng. Sci. 3, 248 (1954a). Lewis, J. B., Chem. Eng. Sci. 3,260 (1954b). Lorinc, A., Kolor. Ert. l l ( l 1 - 1 2 ) , 291 (1969). Mannheimer, R. J..A.l.Ch.E. J. 1 5 ( 1 ) ,88 (1969). Mannheimer, R. J., Schechter, R. S.,J. Colloid lnterface Sci. 32(2), 195 (1970). McCutcheon. C. W., "Detergents and Emulsifiers-1971 Annual," Allured Publishing Corp., Ridgewood, N. J., 1971. Miles, G. D., Ross, J., Shelovsky, L.. J. Amer. Oil Chem. SOC. 27, 268 (1950).
Mukerjee, P., Mysels, K. J., "Critical Micelle Concentrations of Aqueous Surfactant Systems," NSRDS-NBS 36, Secretary of Commerce, U. S. Government, Washington, D.C., 1971. Oldroyd, J. G., Proc. Roy. SOC., Ser. A 232,567 (1955). Perry, J. H., Ed., "Chemical Engineers' Handbook," McGraw-Hill. New Ybrk, N. Y., 1963. Pintar, A. J., Ph.D. Thesis, Illinois Institute of Technology, Chicago, Ill., 1968. Pintar, A. J., Israel, A. B., Wasan, D: T., J. Colloid lnterface Sci. 3 7 ( 1 ) , 52 (1971). Plateau, J.. Phil. Mag., Ser. 4 38,445 (1869). Ross, J., J. Phys. Chem. 62,531 (1958). Ross, J., Epstein, M. B., J. Phys. Chem. 62,533 (1958). Scarpelli, E. M.. "The Surfactant System of the Lung," Lea and Febigher. Philadelphia, Pa., 1968. Schick, M. J.. "Nonionic Surfactants," Surfactant Science Series, Vol. 1, Dekker. New York, N. Y., 1967. Scriven, L. E., Sternlipg, C. V., J. Fluid Mech. 19, 321 (1964). Shah, D. O., paper presented at A.1.Ch.E. National Meeting, St. Louis, Mo., May 1972. Sherman, P.J. Colloid lnterface Sci. 8 , 3 5 (1953). Shih, F. S..Lemlich. R., A.l.Ch.E. J. 13,751 (1967). Siwek, B.. Zesz. Nauk Univ. Jagiellon., Pr. Chem. 16, 79 (1971) Sternling,C. V., Scriven, L. E., A.l.Ch.E. J. 5,514 (1959). Stevens, C. E.. "Surfactants," Kirk-Othmer Encyclopedia of Chemical Technology, 2nd ed, Vol. 19. p 507, 1969. Trapeznikov.-A. A., Dokuk'i'na, E. S..Kolloid. Zh. 33(2), 272 (1970). Vocel. J.. Rvan. J. T.. Can. J. Chem. Ena. 4914). .~ ,. 425 ~- (19711 Vora, .M.' K:, M.S. Thesis, Illinois I n s t h e of Technolog;, Chicago, 111.. 1970. Wasan, D. T.. Annual Report-API Research Project No. 133, Illinois Institute of Technology, Chicago, Ill., 1971. Wasan, D.T., Gupta, L.,Vora, M. K., A./.Ch.E. J. 1 7 ( 6 ) ,1287 (1971) Whitaker, S..lnd. Eng. Chem., Fundam. 3, 132 (1964). Whitaker, S..lnd. Eng. Chem., Fundam. 5,379 (1966). Whitaker, S..Jones, L. O., A.l.Ch.E. J. 12,421 (1966). I
Received for reuiew November 13, 1972 Accepted October 1, 1973
Turbulent Flow in an Annulus with Injection. An Experimental Study Ali M. El-Nashar' Nuclear Engineering Laboratory, Queen Mary College, University of London, London, England
Flow and heat transfer measurements were made in an annulus having a diameter ratio of 0.5 with injection at the inner tube. The Reynolds number of the main flow upstream of the test section ranged from 5.9 X lo4 to 2.1 X lo5 and the ratio of the injected mass flow rate to the main flow rate upstream varied from zero to 0.5. Heat was generated at the outer tube at a maximum rate of 2000 Btu/ft2 hr. Injection was found to increase the local heat transfer coefficient by 20% corresponding to the maximum injection mass ratio of 0.5 and for N R = 2.0 X lo5. This was accompanied by a substantial increase in the axial pressure drop along the test section. Injection caused a pronounced decrease in the mean axial velocities near the porous tube and a shift of the position of maximum velocity toward the outer tube. This was accompanied by an increase in both the turbulence intensity and Reynolds shear stress near the porous wall.
Introduction Turbulent fluid flow in annuli has many practical applications as, for example, in heat exchangers and in nuclear reactor fuel elements. The evaluation of the friction factor and the heat transfer coefficient for different diameter ratios and for different flow conditions has been the subject of many investigations (Brighton and Jones, 1964; Knudsen and Katz, 1950; Rothfus, et al., 1955). To increase the heat transfer coefficient from the heated sur-
'
Research Fellow. Department of Mechanical Engineering, Clemson University, Clemson, S. C. 29631.
face of an annulus, which could be either or both of the inner or outer tubes making the annulus, surface roughening was investigated (Brandon and Kidd, 1968). An alternative means which is the subject of the present experimental study, is to inject a part of the coolant normal to the heated surface. In an annular arrangement, the injection could be achieved by making the unheated tube of a porous material. In the present investigation, an annulus having a diameter ratio of 0.5 was tested. Heat transfer took place at the outer tube and the injection was made through the inner tube. The Reynolds number range used was 5.9 x lo4 to Ind. Eng. Chem.,
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