Coalescence rates

There appear to be two stages in the collapse of emulsions flocculation, in which some clustering of emulsion droplets takes place, and coalescence, in which the number of distinct droplets decreases (see Refs. 31-33). Coalescence rates very likely depend primarily on the film-film surface chemical repulsion and on the degree of irreversibility of film desorption, as discussed. However, if emulsions are centrifuged, a compressed polyhedral structure similar to that of foams results [32-34]—see Section XIV-8—and coalescence may now take on mechanisms more related to those operative in the thinning of foams. 

Density. The difference in density between the two hquid phases in eqiiilibrium affects the countercurrent flow rates that can be achieved in extrac tion equipment as well as the coalescence rates. The density difference decreases to zero at a plait point, but in some systems it can become zero at an intermediate solute concentration (isopycnic, or twin-density tie line) and can invert the phases at higher concentrations. Differential types of extractors cannot cross such a solute concentration, but mixer-settlers can. 

Inteifacial tension. A high interfacial tension promotes rapid coalescence and generally requires high mechanical agitation to produce small droplets. A low interracial tension allows drop breakup with low agitation intensity but also leads to slow coalescence rates. Interfacial tension usually decreases as solubility and solute concentration increase and falls to zero at the plait point (Fig. 15-10). 

In a countercurrent-type column contactor, stable operation is possible as long as the rate of arrival of droplets in any section does not exceed the coalescence rate at the main interface once this value is exceeded, droplet backup will occur at the interface and slowly build back into the column active area, a condition known as flooding. This is an inoperable condition. 

The latter have obseivations during mass transfer. Coalescence Rates The droplets coalesce and redisperse at rates... 

The first flow pattern zone corresponds to the isolated bubble (IB) regime where the bubble generation rate is much higher than the coalescence rate. It includes both bubbly flow and/or slug flows and is present up to the onset of coalescence process domination. The second zone is the coalescing bubble (CB) regime, which is... 

A reduction in the electrical charge is known to increase the flocculation and coalescence rates. Sufficient high zeta potential (> — 30 mV) ensures a stable emulsion by causing repulsion of adjacent droplets. The selection of suitable surfactants can help to optimize droplet surface charges and thus enhance emulsion stability. Lipid particles with either positive or negative surface charges are more stable and are cleared from the bloodstream more rapidly than those with neutral charge [192, 193]. 

It may turn out that the specific coalescence rate is time invariant, in that case Eq. (71) reduces to... 

Thus far it has not been possible to derive from the first principles the coalescence rate function for preferential combination of pellet species of different sizes. Kapur (K4) has proposed an ad hoc rate function in continuous sample space as follows ... 

Fig. 19. Mean granule volume as a function of the agglomeration time, showing the time dependence of specific random-coalescence rate function. [From Kapur (K2).]...

Ouchiyama and Tanaka (Ol) have presented an interesting derivation of a nonrandom coalescence rate function which is similar to the one in Eq. (73). According to these authors the frequency of loading between two pellets of diameter D and D is ... 

Coalescence process, 10 117, 765 Coalescence rates, 11 775 Coal gas, 6 784-790 Coal gasification, 6 760-765, 771-832 12 332. See also Coal gasification processes... 

Vonnegut, Moffett, Sliney, and Doyle (V3), Berg, Fernish, and Gaukler (B7), and Lindblad (L7) have confirmed Rayleigh s (R2) original reports that coalescence rates of droplets can be radically increased by means of electrostatic charges. Vonnegut et al. worked with the coalescence of a jet of drops from a needle. They concluded that the field necessary to coalesce the drop increased with an increase in the relaxation time (product of resistivity and... 

Probably the first tests that should be carried out to determine the best diluent for the system are those concerned with coalescence rates of the phases. These can be done in several ways, but all comparisons should be made using the same experimental conditions. 

Figure 5.12 represents the evolution in time of the surface-averaged droplet diameter for different amounts of solid particles. The kinetic curves confirm the qualitative evolution previously described. The droplet growth is initially rapid but the coalescence rate progressively decreases until the average diameter reaches an asymptotic value. Figure 5.13 shows the change in the droplet size distribution... 

Let the total number of drops be N and the average volume of each drop be v, so that the total volume of dispersed phase is Nv. Then the volume of dispersed phase involved in coalescence is UiNv and the number of coalescences per unit time is w,A. Here is the coalescing rate or coalescing frequency measured in sec.-1 and the chance of having more than two drops involved in a single coalescence is assumed negligible. 

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