(381c) Deformation and Burst of a Liquid Droplet with Viscous Surface Moduli in a Linear Flow Field

Suspensions of fluid particles with complex interfacial architecture (for instance, capsules, vesicles, polymersomes, lipid bilayers, emulsions and foams embedded with certain surface-active agents and surfactants) find an immense number of applications in the field of engineering and bioscience. Interfacial rheology plays an important role in the dynamics of many of these systems, yet little is understood on how these effects alter droplet deformation and breakup. In this study, we present conditions for the breakup of a single droplet with viscous surface moduli, under the assumption of weak flow and negligible Marangoni forces. The viscous interface is modeled as a two-dimensional surface having a surface shear viscosity, surface compression/dilational viscosity, and a constant surface tension over the interface, using a Boussinesq-Scriven constitutive relationship. We present the drop breakup analysis in Stokes flow in the limit of small droplet deformation using the perturbation theory approach. In particular, we examine how the critical capillary number for breakup depends on the interfacial viscosity for different viscosity contrasts between the inner and outer fluid and different flow types. For all the flows considered (uniaxial extensional, planar hyperbolic, and simple shear flow), we observe that surface shear viscosity increases the critical capillary number at a given viscosity ratio (i.e., stabilizes the droplet), while surface dilational viscosity lowers the critical capillary number at a given viscosity ratio (i.e., destabilizes the droplet). The destabilizing effect of surface dilational viscosity appears similar to surfactant convection effects, while the stabilizing impact of surface shear viscosity appears similar to surfactant dilution. We explore the physical picture behind these observations in this work.