Influence of interfacial slip on the suspension rheology of a dilute emulsion of surfactant-laden deformable drops in linear flows

The present study deals with the effect of interfacial slip on the deformation and emulsion rheology of a dilute suspension of droplets in a linear flow. The droplets are laden with surfactants that are bulk-insoluble and get transported only along the interface. An asymptotic approach is adopted for the present analysis in order to tackle the nonlinearity present due to deformation of droplets. The analysis is carried out under two different limiting scenarios namely: surface diffusion-dominated-surfactant transport and surface convection-dominated surfactant transport. For either of the limiting cases we look into the droplet dynamics for two commonly encountered bulk flows - uniaxial extensional and simple shear flow. Under the assumption of negligible fluid inertia in either phase, it is shown that slip at the droplet interface significantly affects the surfactant-induced Marangoni stress and hence droplet deformation and emulsion rheology. Presence of interfacial slip not only brings about a decrease in the droplet deformation but also reduces the effective viscosity of the emulsion. The fall in both droplet deformation and effective viscosity is found to be more severe for the limiting case of surface convection-dominated surfactant transport. For the case of an imposed simple shear flow, the normal stress differences generated due to droplet deformation are affected as well due to the presence of interfacial slip.