Effects of inertia on the deformation of liquid drops in simple shear flow

Abstract

Simple shear flow past a one-dimensional array of two-dimensional viscous drops with constant surface tension at small and moderate Reynolds numbers up to Re = 100 is considered in a Couette flow device. The deformation of the drops from the initial circular shape is computed using a variation of Peskin's immersed boundary formulation in conjunction with a finite-difference method for solving the equations of two-dimensional incompressible Newtonian flow. The results establish critical capillary and Weber numbers for large elongation and breakup as functions of the Reynolds number. When the physical properties of the drops are fixed, inertial effects tend to promote drop deformation. The kinematic structure of the flow is discussed with reference to eddy formation, distribution of wall shear stress, drag force exerted on the walls, and vorticity production at the interface.