Analysis of the effect of breakup frequency on the steady droplet size in flowing polymer blends

Abstract

The effect of various shapes of the breakup frequency vs droplet size curves on the description of the competition between the droplet breakup and coalescence was analyzed. It was shown that very different expressions for the breakup frequency are used in the literature. A comparison of the results of the solutions of an approximate kinetic equation describing dynamic equilibrium between the droplet breakup and coalescence leads to the conclusion that the dependence of the breakup frequency on the droplet radius has a fundamental effect on the steady droplet size. There exists a volume fraction range where the droplet size is constant if the breakup frequency has a step character as a function of droplet radius. The kinetic equation need not have a unique steady solution if the breakup frequency is decreasing or is a nonmonotonic function of droplet radius.