Mechanism of coalescence

Adventitious surfactants also have a marked effect on the mechanism of coalescence. In studying the coalescence of curved water surfaces, Lindblad (L8) used aged distilled water that was stored for about 30 h in a polyethylene bottle opened to the air through a narrow polyethylene tube inserted in the water. He found that if fresh distilled water (water exposed not longer than 1 h to the air) was used, the delay time in coalescence was approximately half as long. Consequently, he concluded that this difference is due to some form of contamination which settled into the water or onto the water surface. 

The mechanism of coalescence of solid spheres (Figure 9.6c and Figure 9.6d) differs from that considered above. In this case the viscous coalescence is impossible, but the mass transfer occurs through the surface diffusion or solubility [39], According to Equation 9.11, a motive force for this process is... 

What is necessary for a collision to be followed by a coalescence What is the mechanism of coalescing These are questions that have fascinated many scientists and engineers both in the field of the physical chemistry of emulsions and foams and in the engineering field of agitated dispersions. 

In the case of low interfacial coverage with surfactant, the collision of two emulsion drops (step A—in Fig. 2) usually terminates with their coalescence (step B—>C in Fig. 2). The merging of the two drops occurs when a small critical distance between their surfaces, hj. is reached. Sometimes, depending on the specific conditions (larger drop size, attractive surface forces, smaller surface tension, etc., — see, e.g.. Ref. 2), the approach of the two drops could be accompanied with a deformation in the zone of their contact (step B—>D in Fig. 2) in this way a liquidfilm of almost uniform thickness h is formed in the contact zone. This film could also have a critical thickness h, of rupture in fact, the film rupture is equivalent to drop coalescence (see step D—>C in Fig. 2). The mechanisms of coalescence... 

Figure 10.31 Three possible mechanisms of coalescence between contacting grains, (a) solid-state grain boundary migration (b) bquid-fibn migration (c) solution-precipitation through the liquid.

An alternative approach based on the concept of the dissipation of the kinetic energy of particle collisions via surface viscosity has been studied by Ennis et al. (1991). It is particularly applicable to fluid bed granulation through the introduction of liquid binding agents but does appear to have some relevance for high temperature defluidization. The mechanism of coalescence is considered to be a function of a binder Stokes number SL defined as... 

The behavior of bubbles in fluidized beds has been known to be stochastic in nature and has been studied by several investigators [30-32]. It is possible to exactly predict the sizes and positions of bubbles at each moment in time. Because the bubbles do not occur with exactly the same positions and sizes each time, the prediction would be dependent on the initial conditions. Such a system appears to be stochastic [33]. Although it is possible to understand the mechanism of coalescence and movement for isolated bubbles in a deterministic manner, it is not possible to extend the deterministic model to accurately predict the behavior of a large swarm of bubbles. 

Mechanisms of coalescence in polymer blends are generally not well understood [56, 57]. Flow induced coalescence has been discussed briefly above. Under quiescent conditions such as cooling of a strand or an injection molded part, mechanisms such as Smoluchowski coalescence or Ostwald ripening may be important [58]. However, under manufacturing conditions, relaxation of flow stresses and interfacial tension driven changes in domain shape are probably of more importance. 

Before determining the degree of stabiUty of an emulsion and the reason for this stabiUty, the mechanisms of its destabilization should be considered. When an emulsion starts to separate, an oil layer appears on top, and an aqueous layer appears on the bottom. This separation is the final state of the destabilization of the emulsion the initial two processes are called flocculation and coalescence (Fig. 5). In flocculation, two droplets become attached to each other but are stiU separated by a thin film of the Hquid. When more droplets are added, an aggregate is formed, ia which the iadividual droplets cluster but retain the thin Hquid films between them, as ia Figure 5a. The emulsifier molecules remain at the surface of the iadividual droplets duiing this process, as iadicated ia Figure 6. 

Although the thermodynamic aspects of acylotropy are well documented, there have been few kinetic studies of the process. The activation barrier is much higher than for prototropy and only Castells et al. (72CC709) have succeeded in observing a coalescence phenomenon in H NMR spectra. At 215 °C in 1-chloronaphthalene the methyl groups of N-phenyl-3,5-dimethylpyrazole-l-carboxamide coalesce. The mechanism of dissociation-combination explains the reversible evolution of the spectra (Scheme 9). 

FIG. 20-68 Mechanisms of granule coalescence for low- and high-deformability systems. Rebound occurs for average granule sizes greater than the critical granule size D. K = deformability. 

A shift in controlhng mechanism from coalescence to layering when the ratio of recycled pellets to new feed changes [Sastiy and Fuerstenau, Trans. Soc. Mining Eng., AIME, 258, 335-340 (1975)]. 

Coalescence Coalescence is the most difficult mechanism to model. It is easiest to write the population balance (Eq. 20-71) in terms of number distribution by volume n v) because granule volume is conserved in a coalescence event. The key parameter is the coalescence kernel or rate constant P(ti,i ). The kernel dictates the overall rate of coalescence, as well as the effect of granule size on coalescence... 

In general, analytical solutions are only available for specific initial or inlet size distributions. However, for batch granulation where the only growth mechanism is coalescence, at long times the size distribution may become self-preserving. The size distribution is selfpreserving if the normahzed size distributions

[Pg.1906]

For systems with large density differences, the dominating mechanism for coalescence is accumulation of the low-density fluid in the low-pressure regions. 

Silicones exhibit an apparently low solubility in different oils. In fact, there is actually a slow rate of dissolution that depends on the viscosity of the oil and the concentration of the dispersed drops. The mechanisms of the critical bubble size and the reason a significantly faster coalescence occurs at a lower concentration of silicone can be explained in terms of the higher interfacial mobility, as can be measured by the bubble rise velocities. 

Phase Separation. An approximate estimation of phase separation may be obtained visually. In general, creaming, flocculation, and coalescence have occurred before phase separation is visible, thus sometimes making quantitative evaluations more difficult. Accelerating the separation by centrifugation followed by appropriate analysis of the specimens may be useful to quantitatively determine the phase separation. Details on mechanisms of creaming and phase separation as well as some advances in the monitoring techniques of emulsion stability have been reviewed by Robins [146]. 

Kapur and Fuerstenau (K6) have presented a discrete size model for the growth of the agglomerates by the random coalescence mechanism, which invariably predominates in the nuclei and transition growth regions. The basic postulates of their model are that the granules are well mixed and the collision frequency and the probability of coalescence are independent of size. The concentration of the pellets is more or less fixed by the packing... 

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