(498d) 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 dilatational viscosity increases tail/cavity growth and lowers Ca_C compared to a clean droplet. Interestingly, we find that both shear and dilatational viscosity delay the time of pinch-off due to different mechanisms. We also provide simulation results to describe how Marangoni effects as well as pressure-thinning or pressure-thickening surfactants alter the behavior discussed above. Lastly, we provide phase diagrams to describe how such interfacial viscosity will alter droplet stability for different classes of surface active materials, different droplet sizes, and different droplet viscosity ratios.