Modeling of oscillatory shear flow of emulsions under small and large deformation fields

Abstract

A model for a mixture of two Newtonian liquids that undergo oscillatory shear flow is presented. The model expresses qualitatively the relationship between the oscillating stress and the oscillating shape of the drops characterized by a second order symmetric tensor called a morphology tensor. The governing equations of the model are solved analytically in small-amplitude oscillatory shear (SAOS) flow and, to the second order of the capillary number, in large-amplitude oscillatory shear (LAOS) flow. Maxwell-type dynamic moduli under SAOS are found to give quite similar predictions as those of Palierne [J. F. Palierne, Rheol, Acta 29, 204 (1990)] and Bousmina [M. Bousima, Rheol, Acta 38, 73 (1999)] emulsion models. Nonlinear dependence of the shear stress and the difference in first normal stress on strain are predicted for LAOS. The predictions of the model are found to be in agreement with the experimental results of Cavallo et al. [R. Cavallo et al., Rheol. Acta (in press, 2002)].