Drops coalescence

The volume fraction of drops in commercial suspension polymerization reactors is usually high and drop coalescence cannot be ignored. In liquid-liquid dispersions the drop size distributions (DSDs) depend on the breakage and on coalescence processes. 

From experiments in which both drop breakage and coalescence occurred, Kuri-yama et al. [34] found that drop sizes reached a steady value within an hour, when the initial drop viscosity was low. But with a high drop viscosity, the drop size reduction continued for longer periods of time and the final drop size was higher. Although model, nonreacting, fluids were used for those experiments, the results are relevant to suspension polymerization. In their study of drop coalescence in the suspension polymerization of styrene, Konno et al. [47] found that the Sauter mean diameter increased as the polymer viscosity increased. They also concluded that the stabilizer does not effectively prevent the coalescence of drops with diameters larger than d x- 

The overall rate of drop coalescence is related to the collision frequency of the drops and to the coalescence efficiency. By comparing drop collisions in agitated 

If drops adhere for sufficient time to allow them to deform, and to permit drainage of the continuous phase that is trapped between them, then coalescence may occur [26], By taking account of these events, expressions can be obtained for the coalescence efficiency [50], Expressions, for coalescence and for collision rates are not easy to use because they often contain parameters that are difficult to quantify. Alvarez et al. [50] constructed a model for drop breakage and coalescence, in the suspension polymerization of styrene, which takes account of viscosity effects. 

That model assumes that breakage of a drop, exposed to a turbulent flow field, is a result of fluctuations with a wavelength equal to the drop diameter. Fluctuations with wavelengths that are smaller or larger than the drop diameter do not lead to drop breakage. 

For impellers other than the RDT, the estimation of d was discussed above. The dimensionless DSD for the radial impeller studied by Narsimhan et al. (1980) is also fit by X = 1.07 and Oy = 0.27, so it is reasonable to apply these values to approximate the DSD for other impellers. The weak link is prediction of d32(t), since it is directly dependent on circulation time. If the circulation time is known relative to the RDT work of Chang (1990), it may be possible to guess the decay rate by reference to eq. (12-32) and (12-33), since it is the number of impeller passes that determine the time to achieve equilibrium. The reader is reminded that these methods apply only to dilute dispersions and will significantly overestimate the dispersion time in the presence of coalescence. 

Most of the stndies discnssed above were carried out at a bench scale. If scale-np is involved, further comphcations can arise. These are discussed in Section 12-8. 

From an industrial viewpoint, coalescence is undesirable for some processes and desirable for others. For example, coalescence during suspension polymerization is undesirable and leads to reactor setup, or buildup of polymer on vessel walls and agitation equipment. On the other hand, mass transfer processes, such as extraction, centrifugation, and decantation, depend on coalescence to achieve desirable rates of operation. Coalescence between drops leads to intunate mixing in the newly formed larger drop. 

For fine aerosol particles, X 1.0 and the agglomeration rate is the collision rate. However, for hqnid-hqnid systems, the coalescence efficiency is often small and rate limiting. Therefore, classical agglomeration theory (e.g., Smolnchowski eqnation) cannot be directly applied to liquid-liquid dispersions. Coalescence is known as a second-order process ( n ) since the coalescence rate is proportional to F(d, d0n(d)n(d0, where n(d) and n(d ) represent an appropriate measure of the number of drops of size d and d, respectively. 

1 -h b cj), the data should be correlated by an equation of the form of eq. (12-30). Early investigators treated coalescence as an addendum to dispersion theory, where b ranged from 3 to 9, depending on the system and the investigator. As discussed previously, Table 12-2 summarizes much of the work done using this approach. 

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Drops coalesce because of coUisions and drainage of Hquid trapped between colliding drops. Therefore, coalescence frequency can be defined as the product of coUision frequency and efficiency per coUision. The coUision frequency depends on number of drops and flow parameters such as shear rate and fluid forces. The coUision efficiency is a function of Hquid drainage rate, surface forces, and attractive forces such as van der Waal s. Because dispersed phase drop size depends on physical properties which are sometimes difficult to measure, it becomes necessary to carry out laboratory experiments to define the process mixing requirements. A suitable mixing system can then be designed based on satisfying these requirements. 

Liquid diops, suspended in a continuous liquid medium, separate according to the same laws as solid paiticles. Aftei reaching a boundary, these drops coalesce to form a second continuous phase separated from the medium by an interface that may be well- or ill-defined. The discharge of these separated layers is controlled by the presence of dams in the flow paths of the phases. The relative radii of these dams can be shown by simple hydrostatic considerations to determine the radius of the interface between the two separated layers. The radius is defined by... 

Stainless steel flat six-blade turbine. Tank had four baffles. Correlation recommended for ( ) < 0.06 [Ref. 156] a = 6( )/<, where d p is Sauter mean diameter when 33% mass transfer has occurred. dp = particle or drop diameter <3 = iuterfacial tension, N/m ( )= volume fraction dispersed phase a = iuterfacial volume, 1/m and k OiDf implies rigid drops. Negligible drop coalescence. Average absolute deviation—19.71%. Graphical comparison given by Ref. 153. ... 

Uo Overall heat-transfer W/(m -K) Btri/(h-tP- F) fraction of drops coalescing ... 

Information on the coefficients is relatively undeveloped. They are evidently strongly influenced by rate of drop coalescence and breakup, presence of surface-active agents, interfacial turbulence (Marangoni effect), drop-size distribution, and the like, none of which can be effectively evaluated at this time. 

The moving-drop method [2] employs a column of one liquid phase through which drops of a second liquid either rise or fall. The drops are produced at a nozzle situated at one end of the column and collected at the other end. The contact time and size of the drop are measurable. Three regimes of mass transport need to be considered drop formation, free rise (or fall) and drop coalescence. The solution in the liquid column phase or drop phase (after contact) may be analyzed to determine the total mass transferred, which may be related to the interfacial reaction only after mass transfer rates have been determined. 

If a critical film thickness is not reached during film drainage, the drops separate from each other. Conversely, if the critical film thickness is reached, the film ruptures—as a result of van der Waals forces—and the drops coalesce. This generally occurs at thin spots, because van der Waals forces are inversely proportional to h (Verwey and Overbeek, 1948). The value of bent can be determined by setting the van der Waals forces equal to the driving force for film drainage, giving (Verwey and Overbeek, 1948)... 

A solution was placed in the vessel, CDE, and drops of mercury from A and B allowed to fall through the solution for some hours, the head of mercury being maintained nearly constant. The mercury collected in E and, as the drops coalesced, the surface was reduced and the adsorbed substancejliberated. The constriction at F was provided to prevent diffusion of this released substance backwards into C. It was found that the equilibrium was attained, i.e., that the drops had adsorbed the maximum amount of solute, if they took about six seconds... 

Fig. 9.24 Basic phenomena of drop coalescence at a horizontal interface. The drop has to reach the interface. A thin layer of the continuous phase remains between the drop and the interface. The thin layer has to drain until it breaks up. Then the drop can flow into its homophase. Mostly, the drainage process is the time-determining step of this process. 

G. Narsimham and P. Goel Drop Coalescence During Emulsion Eormation in a High-Pressure Homogenizer for Tetradecane-in-Water Emulsion Stahihzed hy Sodium Dodecyl Sulfate. J. Colloid Interface Sci. 238, 420 (2001). 

As with gas—liquid systems, chemical engineering theorists have almost exclusively concerned themselves with the creation of surface area (drop formation), usually relating surface area creation to the expenditure of power raised to an index of around . These expressions are entirely empirical and of only guidance value in the absence of essential experimentation data. Drop coalescence remains a black art. 

Rcp = observed oil drop removal rate due to drop coalescence (Ra - Rgp) - calculated oil drop remova> rate due to flotation by bubbles K = first order rate constants Ro-flfol/Cey,... 

In the latter case, however, there is also a contribution of the fraction Go of drops with zero concentration. When these drops coalesce with drops in the interval (2a 2a + 2 Aa), drops of the desired concentration are also produced ... 

The theory of Groothuis and Zuiderweg is confirmed for drops coalescing on a flat interface by MacKay and Mason (Mia) and for pairs of drops rising in an extraction column by Smith et al. (S3). Dora Thiessen (T3)... 

The stabilising action of the adsorption layers from high molecular substances (protective colloids) is related to the decrease in the forces of molecular attraction. Hence, films from aqueous solution of polyvinyl alcohol obtained between drops of cyclohexane have thickness of 80 nm and respectively, a very low attraction force, in contrast to black films [513]. Along with that the adsorption layers from such compounds possess visco-elasticity properties with modulus of elasticity 104 N m"2, impeding the film thinning and drop coalescence [503]. 

V Coalescence frequency, fraction of drops coalescing per time L/s L/h... 

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