Lateral migration of viscoelastic droplets in a viscoelastic confined flow: role of discrete phase viscoelasticity†
The cross-stream motion of viscoelastic droplets in viscoelastic fluids has received little attention since the classical study of migration of drops in a second order fluid. In this work, going beyond the existing classical theory, we experimentally elucidate the effect of drop-to-medium viscosity ratio k and elasticity ratio ξ on wall and center migration of viscoelastic droplets in a Poiseuille flow of a viscoelastic medium (PVP) at low Reynolds numbers (Re ≪ 1). We observed a contrasting migration behavior of Newtonian and viscoelastic droplets having the same viscosity ratios and propose the presence of a lift force FVD due to the viscoelasticity of the droplet phase. We use analytical scaling and empirical modelling to show that the force FVD scales with a prefactor that depends upon the Weissenberg number WiD and drop-to-medium viscosity ratio k and elasticity ratio ξ. Further, we utilize the proposed force for sorting of viscoelastic and Newtonian droplets.