Hydrodynamic Interaction Model for Two Droplets under Large Step Shear Strains

Abstract

A hydrodynamic interaction model is presented to predict the behaviors of two droplets in a medium after application of large step shear strains. The model expresses the droplets by arrays of rigid spheres. Because of retraction rate e in time differentials for the rigid spheres, they move toward the center of mass of them in each array and this motion of the rigid spheres generates flow field in the medium similar to the field caused by recovery of droplets owing to the interfacial tension. The interaction between the rigid spheres is calculated using the hydrodynamic interaction tensor. The model predicts that the distance between the droplets in deformation direction decreases with increasing time and that the shape of the droplets becomes sigmoidal. In addition, the model calculation shows change in the distance in the deformation direction is independent of initial distance between the droplets providing that the initial distance is less than a certain value. These three predictions agree with the experimental results and strongly indicate that the origin of the interaction between the droplets is the hydrodynamic interaction.