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JAMES M. CHURCH and REUEL SHlNNARl Department of Chemical Engineering, Columbia University, New York, N. Y.
Stabilizing Liquid-Liquid Dispersions by Agitation Many industrial processes, such as suspension polymerizations involving dispersion of liquids, are stabilized by trial and error methods. Now the range of conditions necessary for maximum stability can be predicted
IN
MANY CHEMICAL and allied industries processes using dispersion of two immiscible liquids play an important role. Three categories may be distinguished :
0 Stable dispersions or emulsions, which remain unchanged for a considerable time after preparation, under favorable conditions of storage. 0 Unstable dispersions, which break down readily and separate. This type of dispersion is prepared by mechanical agitation, in the course of which there will be continuous coalescence and breakup of the particles. 0 Turbulence-Stabilized Dispersions. This name is proposed for dispersions in which coalescence is considerably reduced by the combined action of a protective colloid and of turbulent agitation. I n this case, the individual droplets remain stable as long as agitation at the same rate continues.
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One important process using this type of dispersion is suspension polymerization (6, 7). Essentially, this is bulk polymerization carried out in individual droplets. Without the presence of a stabilizer, the dispersion would agglomerate after a certain degree of polymerization. By the combined action of protective colloids and turbulent agitation, agglomeration can be prevented until individual droplets are transformed into solid spherical particles. A similar process is the preparation of ball powder (9). Though turbulence-stabilized dispersions have gained considerable industrial importance, their behavior is not well understood. The object of this work is to investigate their properties and attempt to predict behavior from considerations of fluid dynamics.
Review of Previous Work The properties of dispersions employed in suspension polymerization have been discussed by several authors (74-76). A good review of existing information is also available (6,7), and therefore only a brief summary will be included here. 1 Present address, Department of Chemical Engineering, Technion, Israel Institute of Technology, Haifa, Israel
In general, when a monomer is agitated in water an unstable dispersion is formed and continuous breakup and coalescence occur. When polymerization starts, the monomer will remain in dispersion until it is about 20 to 30y0 polymerized. At this stage, the droplets tend to become sticky and they agglomerate, and further agitation will only intensify their agglomeration. The addition of a protective colloid will help to prevent the agglomeration of the individual droplets until solidification has proceeded further and there is less tendency for the droplets to adhere to each other. Many inorganic water-insoluble salts also act in a manner similar to protective colloids. The stability of individual droplets has been studied by a tracer method where part of the monomer was colored (7). In some dispersions, the individual droplets remain fairly stable throughout the process, while in others the droplets tend to coalesce and break up from the very beginning. In the latter case, the dispersion did not become stable until after the monomer had partially polymerized. Also high surface tensions and high viscosities of the continuous phase usually increase the stability of the dispersion. To produce large droplets, it is apparently essential to reduce the differences in the density of both phases as much as possible. Particle size of the final product was found to be strongly dependent on agitation (76). Where agitation is stopped before complete hardening of the droplet occurs, coalescence takes place.
Mechanism of Droplet Sfabilization in a n Agitated Dispersion To carry out any of the processes mentioned and to prevent both its breakup and its coalescence with other droplets, an individual droplet must be kept suspended in the liquid for a considerable time. This could be accomplished by using a stable dispersion of the first kind and agitating it slightly just to keep the droplets in dispersion and assist transfer processes. Though stable emulsions with droplet sizes above 1 mm.
are known, it appears that these have not found widespread use in the above applications. I n most cases, the stability of the droplets for the duration of the process is achieved by the combined action of a protective colloid and agitation. The mechanism of such a stabilization could be postulated as follows : In an agitated liquid-liquid dispersion
of concentration of practical significance
(above 5’%) the individual droplets collide continuously with each other. The average time between collisions is very short for each droplet-probably less than 1 second. However, only part of these collisions result in immediate coalescence. Generally, the droplets rebound owing to the elastic properties of the liquid film entrapped between them and of the droplets. By adding a protective colloid, it is possible to increase the strength of this film which prevents immediate coalescence, and by a suitable choice of colloid and concentration immediate coalescence can be prevented entirely. However, some of the collisions will not result in an elastic rebound and the colliding drops will adhere to each other. Then the attraction between them will tend to decrease film thickness; finally the film will collapse permitting coalescence between the droplets. The particular case of an oil droplet coalescing at an oil-water interface has been studied experimentally, and, in the presence of a protective colloid, the change of coalescence is negligible during a certain period of time &(critical). With longer time of contact, the probability of coalescence increases with time owing to thinning-$lown of the absorbed film ( 2 , 5 ) . The mechanism of stabilization proposed here is somewhat analogous to the theory of stabilization which has been advanced for aerosols. I n an agitated dispersion, adhering droplets are exposed to turbulent velocity and pressure fluctuations, which tend to separate them. A dispersion may therefore be postulated in which agitation is sufficiently strong to separate all adhering droplet clusters during the initial time span where the chance for coalescence is practically nill. I n such a dispersion, individual droplets would remain separated and stable for very long time intervals-as long as agitation is continued. Interruption of the agitation, however, would result in rapid coalescence. Stabilization of a liquid-liquid VOL. 53, NO. 6
JUNE 1961
479
dispersion is dependent upon several conditions :
e A protective film must b e present, to prevent immediate coalescence as well as to slow u p coalescence sufficiently to allow the adhering droplets to be broken u p by agitation. Agitation must b e sufficiently intense to separate all zdhering droplet pairs a n d clusters. The forces which tend to separate adhering dropjets are caused by both local pressure and velocity fluctuations in the fluid and by shear forces in the vicinity of the impellor and the wall. As the time between collisions is very short, the turbulent velocity fluctuations in the fluid throughout the mixing-tank should be of predominant importance. Both the force of adhesion between droplets and the force caused by agitation depend on the diameter of the droplet. However, the force and the energy of adhesion between two droplets are approximately linear functions of the diameter (7, 3, 4, 70), whereas the forces caused by the agitation depend on a much higher power of the diameter. The chances of separation are therefore greater the larger the droplets. Thus in each system of two fluids in a fixed level of agitation: there exists a minimum dropletsize above which stabilization by agitation becomes possible. If the average size is much smaller than this, the droplets will coalesce as in an unstabilized dispersion, until they reach this minimum value. 0 In t h e stable state, no notable breakup of droplets should occur owing to agitation. Breakup of droplets may be caused both by local velocity fluctuations and by shear forces near the impellor. It is impossible to make any a priori predictions which of the two mechanisms is more important. However, for a fixed geometry of the vessel and agitator, the maximum stable droplet size must? per force, depend on agitator speed and the properties of the fluids only. This maximum stable droplet diameter must be larger than the minimum diameter for prevention of coalescence as defined above. Otherwise the dispersion will behave as if no protective colloid were present. 0 As t h e forces affecting t h e droplets vary with time, t h e time scale of these fluctuations should b e considerably less t h a n t h e critical time of coalescence. There are two time scales which may affect the scability of individual droplets. I n a uniformly agitated dispersion, only the time scale of the local velocity fluctuations of the microscale of time of the turbulence should be of importance. On the other hand, if the agitation is very nonuniform the macroscale of time of the gross flow must be taken into consideration. If separation of adhering droplet clusters 480
occurs only in the regions of high shear stress, each cluster must pass the region in the vicinity of the impellor a t least once before the critical time has elapsed. S o w , the macroscale of time is approximately proportional to the ratio flow through the agitator to the volume of fluid in the vessel. And, for dimensionally similar vessels, it is inversely proportional to agitator speed. The macroscale will then increase rapidly with vessel size, whereas the microscale will not change much. Uniform agitation should therefore render scale-up a less risky procedure in processes involving the agitation of stabilized dispersions. e T h e agitation must b e sufficiently strong to prevent separation of the dispersion d u e to t h e difference in specific gravity between t h e two phases.
Analysis of Effect of Agitafion The condition in Equation 1 depends on the properties of the colloid film only-the properties of which can be measured experimentally. However. this is outside the scope of this investigation. Thin films can behave like elastic bodies and have a definite yield value (3. 4 ) . The following quantitative analysis of the effect of agitation on turbulencestabilized dispersions is based on previous work by the authors (10, 77), in which the influence of a locally isotropic flow field on breakup and coalescence of liquid-liquid dispersions was investigated. The conditions for existence of locally isotropic flow in a stirred vessel were also discussed. However, the existence of locally isotropic flow is in no way a condition for the formation of "agitation-stabilized dispersions," and similar results could be obtained by using a different flow model. In an earlier work ( 7 I ) , the following equation was derived for the minimum diameter, below which coalescence occurs : &in
=
Cip-3/8~-1/4A(/1)-3/8
diameter increases owing to damping of the turbulent oscillations in the dispersed phase. The stability of the droplets against breakup is thus increased a t large values of pd,t'p, (72, 13). If the droplets are large, they may separate because of specific gravity differences. The maximum droplet size that can be kept in suspension increases with agitator speed. For the case involving solid particles, a relation has been proposed as follows ( 8 ):
where f($) is an empirical function, and $ is the volume ratio of the dispersed and continuous phases. Although sufficient data are not available to prove this relation, the exact form of the equation is not too important for the formulation of the proposed theory. Equations 1, 2, and 3 are correct only if the diameter, d, of the droplets is small, compared to the macroscaie of the turbulence L, and large compared to the microscale of the turbulence p (70, 77). The equations for coalescence, breakup and suspension are shown graphically in Figure 1. Log d is plotted as a funciion of 1 / 3 log B which in a fully baffled tank is proportional to log N . For the generalized plot, arbitrary constants were chosen. The stabilization by turbulence is possible only if the minimum diameter, &,, that can be stabilized by the turbulent pressure fluctuations is smaller than the maximum stable diameter in Equation 2 for breakup and Equation 3 for suspension. Any droplet of a turbulence-stabilized dispersion must be larger than dmsn (coalescence) and smaller than both d,, (breakup) and d,, (suspension). Figure 1 shows that this condition is fulfilled only in the shaded area of the graph. If i: is less than &an (coalescence) is larger than d,, (suspension), and the dispersion separates into two
(1)
In a baffled vessel and a t high Reynolds numbers 2 is equal to K.V3D2. A(h) is the energy necessary to separate two adhering droplets. Equation 1 applies to any liquid-liquid dispersion, with or without the presence of a protective colloid; however, the value of A(h) depends strongly on the thickness and the properties of the film of colloid absorbed on the droplet. The breakup of droplets in an agitated tank was also previously analyzed (9) and the following equations apply: I L O G IN1 5 : ouero*c snsrgy
Equation 2 is correct only if p d / p C is not very large. Otherwise the stable
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STIRRER dl5llPOtlO"
SPEED PO,
RPM
"",I mOIB
Figure 1. Theoretical relations for breakup, coalescence, and suspension of droplets in a stirred tank
LIQUID-LIQUID D I S P E R S I O N S phases. If a is larger than z,, dmi, (coalescence) is larger than d,, (breakup), and the dispersion will behave like an unstabilized dispersion. The stabilizer is unable to prevent coalescence in the case of small droplets, because the energy needed to separate two droplets will cause instability in a single droplet. If z is less than amas, all droplets will coalesce until they reach a diameter at which they can be stabilized. At specific energy input higher than amas, the droplets will coalesce. But, before a stable equilibrium can be reestablished, these must be broken up again. The functional relationships, when plotted in Figure 1, set off a triangular region of stability. These relationships were obtained when the existence of locally isotropic flow was stipulated. However, qualitatively, the existence of such a region of stable conditions is not dependent on the assumption of local isotropy. I t may be derived, for instance, from a concept of breakup by high shear only. By solving simultaneously Equations 1 and 2, the limits of the stable region may be defined quantitatively. The that can be minimum diameter, d,
