Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow

Abstract The steady and transient deformation of a drop that is immersed in an ambient simple shear flow is studied in the limit of Stokes flow. The flow is examined as a function of the viscosity ratio λ between the drop and the suspending fluid, and the capillary number Ca. The motion of the drop is considered in an unbounded fluid and in proximity to a bounding plane wall. The problem is formulated in terms of the boundary integral method and is solved using a boundary element numerical procedure. The results provide information on the shape of stationary and transient deformed drops for a wide range of λ and Ca. The streamlines inside and outside deformed drops are analyzed and are shown to exhibit different patterns depending on λ and to a lesser degree on Ca. The kinematics of the flow on the surface of the drop is studied including the travel time of interfacial markers and the straining motion of interfacial patches. The stationary drop shapes are used to compute the effective stress tensor of a dilute emulsion of drops in shearing motion. It is found that a dilute emulsion behaves like an elastic, shear-thinning medium, for all values of λ. The effect of a plane wall is examined with reference to the time-scales of drop deforamation and migration away from the wall. The computed migration velocities are compared with those predicted by available asymptotic theories and experimental data and some differences are identified and discussed.