Impact of surface viscosity on the stability of a droplet translating through a stagnant fluid.

This study examines the impact of interfacial viscosity on the stability of an initially deformed droplet translating through an unbounded quiescent fluid. The boundary-integral formulation is employed to investigate the time evolution of the droplet in the Stokes flow limit. The viscous droplet interface is modeled using the Boussinesq-Scriven constitutive relationship. We observe that below a critical value of the capillary number, Ca_C, the initially perturbed droplet reverts to its spherical shape. Above this Ca_C, the translating droplet deforms continuously, resulting in a growing tail at the rear end for initial prolate perturbations and a cavity for initial oblate perturbations. We find that the presence of surface shear viscosity inhibits the tail/cavity growth at the droplet's rear end and increases the Ca_C compared to a clean droplet. In contrast, surface dilational viscosity increases tail/cavity growth and lowers Ca_C compared to a clean droplet. We explore the mechanisms behind each of these observations in our talk and provide phase diagrams for how these interfacial effects alter the critical capillary number for different values of the droplet's viscosity ratio and initial Taylor deformation parameter.