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
