(310c) Numerical Investigation of the Role of Surface Viscosity on Droplet Breakup and Relaxation in Extensional Flow

In this work, we perform boundary-integral simulations to explore the impact of surface viscosity on droplet breakup and relaxation in an axisymmetric extensional flow under the Stokes flow regime. We model the surface rheology of the droplet using Boussinesq–Scriven constitutive relationship for a Newtonian interface. We compare the results from our boundary element simulations to the second-order perturbation theories for surface viscosity in the limit of small capillary number. We observe that the surface shear/dilational viscosity increases/decreases the critical capillary number beyond which the droplet becomes unstable and breaks apart by reducing/increasing the droplet deformation at a given capillary number compared to a clean droplet. We also discuss the relative importance of surface shear and dilational viscosity on droplet stability based on their measured values reported in experimental studies on surfactants, lipid bilayers, and proteins. In the second half of the talk, we explore the coupled influence of surface viscosity, Marangoni stresses, and the effects of pressure thickening/thinning surfactants on droplet deformation and breakup. We conclude by discussing the combined impact of surface viscosity and surfactant transport on the relaxation of an initially extended droplet in a quiescent external fluid.