Effects of dispersed phase viscosity on drop deformation and breakup in inertial shear flow

Abstract

The deformation and breakup of a single liquid drop subjected to simple shear flow is studied numerically using a diffuse interface free energy lattice Boltzmann method. The effect of dispersed phase viscosity on the behavior of the drop at a drop Reynolds number Re=10 is investigated over the range of viscosity ratios λ=0.1−2 (dispersed phase viscosity over continuous phase viscosity) with a focus on λ<1. For every λ the critical capillary number Cac for breakup is determined. For the range of λ considered, Cac decreases as λ increases. Both the extent of deformation and the breakup mechanism depend on the viscosity ratio and the capillary number. At the highest subcritical capillary number, the drop becomes less elongated and more inclined towards the vertical axis as the viscosity ratio increases. The changes in the drop breakup process are examined as the capillary number increases from the lowest supercritical Ca~Cac, to 1.2, 1.5 and 2Cac. Drops break by the end-pinching mechanism, except for λ=2 at Ca=2Cac where the drop undergoes capillary wave breakup.