Droplet breakup mechanisms: Stepwise equilibrium versus transient dispersion

Abstract

In dispersive mixing of immiscible liquids the minimum attainable dropsize is often deduced from the critical value of the Capillary number (the ratio of the shear stress to the interfacial stress) necessary for drop breakup under quasiequilibrium conditions. The critical Capillary number shows a minimum if the viscosity ratio between dispersed and continuous phase is about one. Hence, it is commonly accepted that the finest morphology is obtained if both viscosities match. In practical mixing devices, however, small drops are formed by a transient mechanism of thread breakup during extension rather than by stepwise breakup under equilibrium conditions. For Newtonian liquids, a comparison is made between the dropsizes resulting from a stepwise equilibrium and a transient breakup mechanism. Generally, the transient mechanism yields smaller drops and, more interestingly, a higher viscosity ratio between the dispersed and continuous phases results in a finer morphology, as already indicated by Tjahjadi and Ottino (1991). In the present paper the comparison is elaborated over a broad range of the relevant parameters while a compact illustrative presentation of the results is given to stress the possible consequences for practical blend morphologies.