Effect of interfacial slip on the deformation of a viscoelastic drop in uniaxial extensional flow field

Abstract

The effect of interfacial slip on the deformation of a viscoelastic droplet, suspended in another viscoelastic medium, in the presence of a uniaxial extensional flow, is studied analytically. Using the Oldroyd-B constitutive relation, the Stokes flow problem is solved in the limit of a small capillary number and small Deborah number. Experimentally observed interfacial velocity slip is incorporated using a Navier slip boundary condition. The interfacial slip significantly reduces the magnitude of droplet deformation when the droplet has larger viscosity as compared with the suspending phase. The droplet shape becomes less ellipsoidal in the presence of slip. The effect of slip diminishes for low viscosity droplets. Slip effectively weakens the dependence of the droplet deformation on the droplet to medium viscosity ratio. The viscoelasticity of the suspending phase plays a dominant role on the droplet deformation as compared with the viscoelasticity of the droplet phase when there is velocity slip at the droplet surface. The interfacial slip aids the viscoelasticity of the suspending phase in deforming the droplet, while the effect of viscoelasticity of the droplet phase is suppressed by the interfacial slip.