Rate of coalescence

Since film drainage and rupture is a kinetic process, coalescence is also a kinetic process. If the number of particles n (flocculated or not) is measured at time t, 

For studying emulsion coalescence, it is important to consider the rate constant of flocculation and coalescence. If coalescence is the dominant factor, then the rate K follows a first-order kinetics. 

Lower part presence of liquid crystalline phases 

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Coalescence The coalescence of droplets can occur whenever two or more droplets collide and remain in contact long enough for the continuous-phase film to become so thin that a hole develops and allows the liquid to become one body. A clean system with a high interfacial tension will generally coalesce quite rapidly. Particulates and polymeric films tend to accumulate at droplet surfaces and reduce the rate of coalescence. This can lead to the ouildup of a rag layer at the liquid-hquid interface in an extractor. Rapid drop breakup and rapid coalescence can significantly enhance the rate of mass transfer between phases. 

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... 

The bubble size at formation varied with particle characteristics. It was further observed that the bubble size decreased with increasing fluidization intensity (i.e., with increasing liquid velocity). The rate of coalescence likewise decreased with increasing fluidization intensity the net rate of coalescence had a positive value at distances from 1 to 2 ft above the orifice, whereas at larger distances from the orifice the rate approached zero. The bubble rise-velocity increased steadily with bubble size in a manner similar to that observed for viscous fluids, but different to that observed for water. An attempt was made to explain the dependence of the rate of coalescence on fluidization intensity in terms of a relatively high viscosity of the liquid fluidized bed. 

Notably, the higher the mass flux, the earlier annular flow is reached. Bubbly flow is more or less non-existent for mass fluxes exceeding 1,000 kg/m s. The most important observation about the flow patterns is that their transitions are controlled primarily by the rate of coalescence, which is not recognized as a contributing factor by any of the micro-scale or macro-scale flow pattern maps. 

An effective hquid-liquid reactor may be designed to obtain drops that continuously break up and coalesce, or it may be designed to obtain very small drops that have very efficient mass transfer and follow the continuous phase with a low rate of coalescence. The former will require a much larger reactor, but the separation of the phases after reaction is simpler. 

Coalescence is important for dispersed phase volumes fraction () greater than about 0.005 the rate of coalescence increases with . 

Relative importance of coalescence and rectified diffusion in the bubble growth is still under debate. After acoustic cavitation is fully started, coalescence of bubbles may be the main mechanism of the bubble growth [16, 34], On the other hand, at the initial development of acoustic cavitation, rectified diffusion may be the main mechanism as the rate of coalescence is proportional to the square of the number density of bubbles which should be small at the initial stage of acoustic cavitation. Further studies are required on this subject. 

Figure 5.8. Rate of coalescence as a function of the number density of internal droplets in the globules. Globule diameter =11.5 pm droplet diameter = 0.36 pm initial droplet volume fraction in the globules = 25% globule volume fraction = 10% SDS concentration = 2.4 10 mol/1 SMO concentration in the oil phase = 2 wt% 0.1% of silicone oil with a gyration radius of 12 nm was added to dodecane. (Reproduced from [44], with permission.)...

Rates of coalescence in pipelines and other turbulent field apparatus should be studied. 

The Apollo technology uses a patented separation media, which is designed to force a rapid rate of coalescence, speeding the separation of oil and water dramatically without using heat. 

In the composition range showing the nodular morphology, the increase in the PEI concentration increased the viscosity of the system and the PEI phase volume, thus reducing the rate of coalescence of the epoxy nodules in the late stage of spinodal phase separation. Smaller epoxy nodules, therefore, were formed at higher PEI concentration. 

Increasing temperature has the effect of decreasing emulsion stability this has been demonstrated by Kunieda et al. [11,14], among others, and is due to the increase of the rate of coalescence of the dispersed phase droplets with increasing thermal energy. Pons et al. [100] also noted that a temperature increase caused an increase in average droplet size due to increasing interfacial tension. 

When the drop size distribution is constant, the rate of coalescing must be equal to the rate of redispersion, and, in that case, the rate of interaction can be expressed as the rate of coalescing. When two drops of volumes Vi and i>2, respectively, coalesce, the total volume of the dispersed phase which is concerned with this coalescence is equal to Vi + v2. The rate of coalescing is now defined as the fraction of the total volume of dispersed phase which... 

Separation of gases and liquids always involves coalescence, but enhancement of the rate of coalescence may be required only in difficult separations. 

The model of viscous sintering was developed by Frenkel (24), who derived the following expression for the rate of coalescence of spherical adjacent particles ... 

Sintering of PS Pearls Calculate the rate of coalescence of PS pearls made from suspension polymerization, which are 0.2 cm in diameter. The temperature of the sintering process is 180°C. Use the Power Uaw constants of the unmodified PS in Appendix A. The surface tension of the melt can be taken to be 32.4 dyne/cm.6... 

The time needed for phase separation depends on polymer type and concentration, the volume ratio, the rate of coalescence of droplets, and the presence of particles. Typical times required for PEG-dextran-water systems are 5 to 30 min. Low-speed centrifugation cuts the time down to 1 min.65 In... 

When a dry film is prepared, the forces that stabilize the dispersion of TP particles must be overcome and the particles must coalesce into a continuous film. The rate of coalescence is controlled by the free volume available, that in turn depends mainly on Tg (Chapter 1). 

A more important fact is the change in the mechanism of foam column destruction with the increase in the applied pressure drop. For example, at small pressure drops a slow diffusion bubble expansion along with the corresponding slow rate of structural rearrangement (either zero or very slow rates of coalescence) occurs in a NaDoS foam with CBF or NBF. This is expressed in the layer-by-layer reduction of foam column height ending with the disappearance of the last bubble layer. In such a foam the critical pressure of the foam column destruction is not reached at any dispersity, and only the foam column height and the rate of internal foam collapse determine the foam lifetime. 

It should be noted that the droplet sizes in Hallworth s emulsions are considerably greater than those investigated by Davis and Smith. The importance of the two possible routes of degradation of the emulsions, coalescence or molecular diffusion, may be dependent upon the droplet size and size distribution. Also an interfacial coherent film may reduce the demulsification by either mechanism, i.e. by reducing the rate of coalescence or by presenting an interfacial barrier to... 

As long as the possible problems are known, microscopy can be regarded as the single most important emulsion characterization tool. In the appropriate circumstances it can give information about the relative amounts of oil, water, and solids in an emulsion system their interactions or associations the size distribution of the dispersed phase and the rate of coalescence of the dispersed droplets. Various microscopic techniques can be used to define not only the physical nature of the sample, but also the chemical composition, both mineral and organic. 

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