Dynamics of liquid‐liquid mixing: A 2‐zone model

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Abstract
The development of multiphase liquid‐liquid morphologies during mixing at small Reynolds numbers has been modeled. The mixing process is divided into (i) stretching of dispersed drops. (ii) breakup of the liquid threads formed, and (iii) coalescence of the final droplets upon collision. Rules and criteria of the distinct processes are presented and combined to a general 2‐zone mixing model simplifying the flow field into a sequence of alternating “strong and weak zones.” In a “strong zone,” dispersed drops and threads are stretched unless their radius is too small; meanwhile, the stretching threads might break up into droplets. In the subsequent “weak zone,” the remaining threads may disintegrate while any drops present may coalesce. After passing a number of zones, stretching, breakup, and coalescence lead to a dynamic equilibrium that could be considered as the “final” morphology. Using the 2‐zone mixing model, the influence of material parameters and processing conditions on the morphology has been studied. Interestingly, increasing either viscosity (dispersed or continuous phase) yields a finer morphology due to the delay of thread breakup, allowing for further stretching and suppression of coalescence.

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