The drop coalescence process

Several mathematical models have also been presented in the open literature to describe the drop coalescence rate [31, 49, 50, 56-62]. As in the case of the drop breakage rate, the drop coalescence rate can be expressed in terms of a collision frequency, u), and a Maxwellian efficiency term  

Detailed expressions for the calculation of the drop breakage (Equation 5.7) and coalescence (Equation 5.11) rate kernels can be found in the original publication of Kotoulas and Kiparissides [36]. 

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Emulsion drop size is the result of competing effects that take place during emulsification the drop breakup and the drop coalescence processes. Many properties and phenomena are likely to influence one or the other effect, sometimes in a complex way. As the formulation approaches HLD = 0 the interfacial tension decreases, thus facilitating the drop breakup and the formation of smaller drops. In a concomitant way, the emulsion stability becomes extremely low, allowing rapid coalescence, which favors the occurrence of larger drops. As a consequence of these opposite effects, the drop size exhibits a minimum for each type of emulsion, i.e., on each side of HLD = 0. For each system, the location of the minimmn depends not only on the formulation (HLD value) but also on the stirring energy and efficiency [40]. 

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