Coalescence fractional extent

We can obviously directly connect the variation of the relative area to the fractional extent of coalescence, using equations [10.67] and [12.70], it becomes ... 

Carbon dioxide bubbles nucleate on the underside of the carbon anodes (and to a lesser extent on the sides), grow through a near spherical shape and start to coalesce to form large bubbles that are more discshaped than spherical. These bubbles, now occupying a significant fraction of the anode area, then sweep across the anode underside to an edge where they escape. As they do so, they accumulate more gas from smaller stationary or slower bubbles in their path and leave behind bubble free regions where fresh nucleation can occur. These dynamics are well described by Fortin et al. [39],... 

In the absence of any flocculation, the coalescence of an emulsion results in a reduction of its viscosity. At any given volume fraction of oil, an increase in droplet size will result in a reduction of viscosity, and this is particularly the case for concentrated emulsions. Thus, by following the decrease in emulsion viscosity with time, information may be obtained on its coalescence. However, care should be exercised when applying simple viscosity measurements, particularly if flocculation occurs simultaneously (as this results in an increased viscosity). It is possible - at least in principle - to predict the extent of viscosity reduction on storage by combining the results of droplet size analysis (or droplet number) as a function of time with the reduction in viscosity during the first few weeks. 

The characteristics of an emulsion depend to a large extent on the physicochemical properties of the fluids involved, and also on the chemical additives used. Emulsifying surfactant products perform two functions. When they reduce surface tension, they help reduce the size of the bubbles and droplets. They also serve to stabilize the emulsion to prevent it from coalescing as soon as the stirring ceases. The first characteristic parameter of an emulsion is the volume fraction of each fluid. When a fluid is gradually incorporated into another which is being stirred, the incorporated fluid constitutes necessarily the dispersed phase and the receiving fluid the continuous phase, since the volume of the dispersed phase is smaller than that of the continuous phase. An inversion phenomenon may occur when the volumes of both phases become comparable. Surfactant additives also act to control phase inversion processes. 

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