Virginia Polytechnic Institute and State University

Abstract:

Flows composed of two immiscible liquids and undergoing shearing motions can form fingers as a result of an interfacial instability due primarily to the viscosity jump. The jump in the viscosity from one fluid to the other results in the jump in the tangential velocity gradient across the interface, and can be thought of as a viscous counterpart of the Kelvin-Helmholtz instability. Density stratification enters in the jump in the normal-stress condition as a type of Rayleight-Taylor mechanism. We are interested more generally in co-extrusion flow of very viscous liquids, where the interface between the two fluids is often rippled. There are five dimensionless parameters: a low Reynolds number, interfacial tension parameter which may be low volume ratio, viscosity ratio, and less importantly the density ratio. A semi-implicit VOF/CSF scheme is developed for tracking the motion of two viscous liquids sheared at low speeds. Examples of linear stability theory, weakly nonlinear dynamics, wave saturation, and large amplitude fingering motions are presented in two- and three- dimensions, as initial-value problems. Finally, simulations of drop breakup in simple shear flow will be presented.