Deformation of a surfactant-laden viscoelastic droplet in a uniaxial extensional flow

Abstract

The present study deals with the effect of surfactant distribution on the deformation of a viscoelastic droplet suspended in another viscoelastic medium, subjected to a uniaxial extensional flow. Under the assumption of negligible fluid inertia and small shape deformation, an asymptotic approach is adopted to solve the flow field. The Oldroyd-B model is used to represent both the carrier and droplet phases. The dynamics of the droplet is studied for the limiting cases of surface diffusion as well as surface convection mode of surfactant transport. The presence of an imposed flow results in a non-uniform distribution of surfactants which generates a surface tension gradient or Marangoni stress that is significantly found to affect the deformation of a viscoelastic droplet. The present analysis is performed for the general scenario where either of the phases may exhibit Newtonian or viscoelastic behavior. Upon comparison with the special case where both the phases are Newtonian, noteworthy differences in the effect of Marangoni stress on the dynamics of droplets are observed. It is found that increase in the Marangoni stress along the droplet surface reduces the effect of viscoelasticity on the shape deformation of the droplet. It is also found that a critical viscosity ratio can be defined for a viscoelastic droplet at which the effect of Marangoni stress on its shape deformation is the maximum.