Film drainage, coalescence

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)... 

An attempt has been made by Tsouris and Tavlarides[5611 to improve previous models for breakup and coalescence of droplets in turbulent dispersions based on existing frameworks and recent advances. In both the breakup and coalescence models, two-step mecha-nisms were considered. A droplet breakup function was introduced as a product of droplet-eddy collision frequency and breakup efficiency that reflect the energetics of turbulent liquid-liquid dispersions. Similarly, a coalescencefunction was defined as a product of droplet-droplet collision frequency and coalescence efficiency. The existing coalescence efficiency model was modified to account for the effects of film drainage on droplets with partially mobile interfaces. A probability density function for secondary droplets was also proposed on the basis of the energy requirements for the formation of secondary droplets. These models eliminated several inconsistencies in previous studies, and are applicable to dense dispersions. 

A variety of interaction behaviours can be observed between liquid/liquid interfaces based on the types of colloidal forces present. In general, they can be separated into static and dynamic forces. Static forces include electrostatic, steric, van der Waals and hydrophobic forces, relevant to stable shelf life and coalescence of emulsions or dispersions. Dynamic forces arise ftom flow in the system, for instance during shear of an emulsion or dispersion. EHrect force measurements tend to center on static force measurements, and while there is a large body of work on the study of film drainage between both liquid or solid interfaces, there are very few direct force measurements in the dynamic range between liquid interfaces. Below are general descriptions of some of the types of force observed and brief discussions of their origins. 

When two drops first come into contact in the process of coalescing, a film of continuous phase becomes trapped between them. The film is compressed at the point of encounter until it drains away and the two drops can merge. Decreasing the viscosity of the continuous phase, by heating or by addition of a low-viscosity diluent, may promote drop coalescence by increasing the rate of film drainage. Surface-active impurities or surfactants, when present, also can affect the coalescence rate, by accumulating at the surface of the drop. Surfactants tend to stabihze the film and reduce coalescence rates. Fine... 

Coalescence being the secondary process, the number of distinct droplets decreases leading to a stage of irreversibility and finally complete demulsification takes place. Coalescence rate very likely depends primarily on the film-film repulsion, film drainage and on the degree of kinetics of desorption. Kinetically, coalescence is a unimolecular process and the probability of merging of two droplets in an aggregate is assumed not to affect the stability at other point of contact (32). 

Coalescence, not dispersion, dominates as the controlling mechanism in phase inversion. Factors affecting film drainage rates, such as agitation rate. 

The time for film drainage is obtained from the duration of the collision, which is determined by the rotation of the collision doublet It was shown that flattening of the droplet delays the drainage and, above a capillary number of 0.02, considerably reduces the coalescence probability. 

Hagesffither et al [27] derived a model for film drainage in turbulent flows and studied its predictive capabilities. It was concluded that the film drainage models are not sufficiently accurate, and that adequate data on bubbly flows are not available for model validation. For droplet flows it was found that the pure drainage process (without interfacial mass transfer fluxes) was predicted with fair accuracy, whereas no reliable coalescence criterion was found (similar conclusions were made by Klaseboer et al [41, 42]). Furthermore, it was concluded that a head on collisions are not representative for all possible impact parameters. Orme [86] and Havelka et al [32], among others, noticed that the impact parameter is of great importance for the droplet-droplet collision outcome in gas flows. However, no collision outcome maps have been published yet for bubble-bubble collisions. 

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,... 

If the continuous phase is a liquid, the main obstacle to coalescence is the drainage of the film of liquid in the small space in between the two particles. The efficiency is in these cases usually quantitied as a function (generally a negative exponential function) of the ratio of the characteristic time for droplet contact and film drainage. For example, in the case of small bubbles coalescing due to turbulent velocity fluctuations the coalescence kernel assumes the form (Buffo et al, 2012 Laakkonen et al, 2006 Petitti et al, 2010)... 

The presence of solids at the interface usually retards film drainage rates, thereby reducing the probability of coalescence. A few suspension-polymerization processes use solid particles as suspending agents. 

This is the one to be dealt with here and later to be considered as a reference based on which other cases could be discussed. This breaking process comprises several steps (a) long-distance approach between drops or between drop and flat interface, (b) interdrop film drainage and, finally, (c) coalescence (10-13). 

Coming back to Fig. 6, it is seen that the apparent decay occurs in three periods. First, there is a period of time in which no separation takes place. This induction period may be related to the drop approach and film drainage, with no coalescence occurrence, so that no drop big enough to settle quickly is formed. 

The flocculation and coalescence processes of a polydis-persed lamella or film can be divided into two processes film drainage and film rupture. To model the film-mpture process of polydispersed emulsions, film stress-relaxation experiments were carried out. In these experiments, the film was quickly expanded and then the relaxation of the film was measured. To characterize the film-drainage process, dynamic film-tension measurements were conducted in which the film was continuously and slowly expanded while the film tension was monitored. Single interfaces were also studied by forming a drop at the eapillary (7). 

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