A Theoretical Description of a Dilute Emulsion of Very Viscous Drops Undergoing Unsteady Simple Shear

Abstract

This theoretical work shows how the knowledge of the emulsion microscale, including drop stretching and orientation leads to a continuum description of emulsion flows. A first order small deformation theory is explored for describing the rheology of an emulsion of high viscosity drops undergoing unsteady shear flows. The stationary shape and the interfacial velocity of a drop are used in order to obtain the contribution of the drop to the effective stress tensor of the emulsion. A complex rheology including the nonlinear frequency response of the emulsion under oscillatory shear at arbitrary frequency forcing and strain amplitude is identified.