Experimental trajectories of two drops in planar extensional flow

Abstract

In this paper we map the experimental trajectories of two deformable drops in planar extensional flow and compare the experimental results with theoretical calculations for spherical drops. We examine the effects that deformation, initial position, and viscosity ratio have on the interaction of two drops and the necessity of incorporating deformation into trajectory calculations, which can be used to estimate the collision rates, the collision efficiencies, and the collision interaction times. For drops which do not come into close contact, the existing theoretical calculations for spherical drops accurately predict the symmetric trajectories and capture the increased hydrodynamic interaction for higher viscosity ratios. For drops which come into close contact, the spherical drop theory accurately predicts the approach and exit trajectories and with a slight empirical modification adequately predicts the interaction times for deformable drops with a Taylor deformation parameter up to 0.22. The experimental results show that for drops with close contact, the collision trajectories are asymmetric and irreversible with a minimum separation between the centers of mass that is less than the minimum separation of two spheres. This minimum separation corresponds to the minor axis of the deformed drop and is not captured by the spherical theory. However, overall, the modified trajectory theory based upon the hydrodynamic mobility for spherical drops does provide a reasonable estimate for the trajectories and the interaction times for two deformable drops in planar extensional flow.