Numerical investigation of the role of surface viscosity on droplet deformation and breakup in extensional flow

In this work, we perform boundary-integral simulations to explore the role of surface viscosity on droplet deformation and breakup in an axisymmetric extensional flow. The problem is solved under the Stokes flow regime, and the surface rheology of the droplet is modeled using the Boussinesq-Scriven constitutive relationship for a Newtonian interface. We compare the results from our boundary element simulations to the small deformation perturbation theories for surface viscosity. 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 explore the coupled influence of surface viscosity, Marangoni stresses, and the effects of pressure thickening/thinning surfactants on droplet dynamics and present the underlying mechanisms behind the different observations in this talk. We conclude by discussing the relative importance of surface shear and dilational viscosity on droplet stability based on their measured values observed in various experimental studies on surfactants, lipid bilayers, and proteins.