Film drainage

For cakes of high permeabihty, the capillary drain height may be an insignificant fraction of cake thickness, and film drainage becomes the controlling factor in a centrifugal field (7). Under unsteady-state conditions, equation 18 represents the drainable Liquid left in the cake as a function of the centrifugal filtration parameters ... 

Once a collision occurs, the liquid between the drops is squeezed, forming a film. As the drops are continually squeezed by the external flow field, the drops rotate as a dumbbell and the film drains. At some distance h0, the drops begin to influence each other and their rate of approach, dh/ dt, decreases and is now governed by the rate of film drainage. 

Fig. 27. Various modes of film drainage and the corresponding equations for the rate of film thinning and drainage time are shown. The criteria for specific modes are also indicated.

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)... 

Variation of the driving force during film drainage is taken into account. 

The shape of the curves for the dilational modulus (Figures 7 and 8) suggests a single relaxation mechanism, probably the unfolding of the demulsifier molecules at the interface. The frequency peak in the e"(f) plot is a measure of the characteristic relaxation time. A shorter relaxation time, by inducing faster film drainage, increases demulsification efficiency. 

Hence, film rupture is much faster than either film transport or film drainage and filling. In this initial analysis we therefore neglect any time lag for the rupture event and assess breakage as... 

Thin-film dewetting, 7 409 Thin film drainage, 12 13 Thin-film evaporators (TFE), 15 259... 

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. 

When two emulsion drops or foam bubbles approach each other, they hydrodynamically interact which generally results in the formation of a dimple [10,11]. After the dimple moves out, a thick lamella with parallel interfaces forms. If the continuous phase (i.e., the film phase) contains only surface active components at relatively low concentrations (not more than a few times their critical micellar concentration), the thick lamella thins on continually (see Fig. 6, left side). During continuous thinning, the film generally reaches a critical thickness where it either ruptures or black spots appear in it and then, by the expansion of these black spots, it transforms into a very thin film, which is either a common black (10-30 nm) or a Newton black film (5-10 nm). The thickness of the common black film depends on the capillary pressure and salt concentration [8]. This film drainage mechanism has been studied by several researchers [8,10-12] and it has been found that the classical DLVO theory of dispersion stability [13,14] can be qualitatively applied to it by taking into account the electrostatic, van der Waals and steric interactions between the film interfaces [8]. 

Tween 20 was considerably more effective at reducing the stability of foams of a-la than was the case with /3-lg. There was a significant decrease in a-la foam stability in the presence of Tween, at R values as low as 0.05. Minimal foam stability was observed at R = 0.15. There was no observed change in film drainage behavior or onset of surface diffusion in the adsorbed protein layer up to this R value. The only observed change was a progressive decrease in film thickness. Therefore, it is likely that disruption of adsorbed multilayers is responsible for a reduction in the structural integrity of the adsorbed protein layer and that this increases the probability of film rupture. 

Tallmadge, J. A. Gutfinger, C. Entrainment of Liquid Films Drainage, Withdrawal, and Removal. Ind. Eng. Chem. 1967, 59, 19-35. 

In addition to film drainage, the stability of a foam depends on the ability of the liquid films to resist excessive local thinning and rupture which may occur as a result of various random disturbances. A number of factors may be involved with varying degrees of importance, depending on the nature of the particular foam in question. 

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