Shear-induced migration of a viscous drop in a viscoelastic liquid near a wall at high viscosity ratio: Reverse migration

Abstract

• A drop under shear migrates laterally away from a wall in shear. • Medium viscoelasticity and viscosity ratio affects the migration. • High viscosity ratio and high Deborah number leads to migration towards the wall. • The critical viscosity ratio varies inversely with the capillary number. • The critical Deborah number also varies inversely with the capillary number. Wall-induced migration of a viscous drop in a viscoelastic fluid subjected to a plane shear is numerically simulated to investigate the effects of drop/matrix viscosity ratio. In a Newtonian system, drop migration away from the wall is inhibited as the viscosity ratio is increased. Here, we show that the introduction of the matrix viscoelasticity further decreases the migration and can even reverse its direction ‘from away’ to ‘towards the wall’, a phenomenon not seen in Newtonian systems. The migration towards or away from the wall eventually settles in a quasi-steady state that only depends on the instantaneous wall separation independent of the initial position of the drop. Drops migrating towards the wall initially increase their velocity, but as they approach the wall, they decelerate, showing a non-monotonic variation. The migration direction depends on the viscosity ratio, viscoelasticity (Deborah number), and the capillary number. We compute phase diagrams in the parameter space showing boundaries where migration changes direction. The critical Deborah number (at a fixed viscosity ratio) and the critical viscosity ratio (at a fixed Deborah number) for direction reversal approximately scales with the inverse of the capillary number.