Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonian fluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distance from the wall. The drop migration velocity and the deformation scale inversely with the square and the cube of the distance from the wall, respectively. The migration velocity varies non-monotonically with increasing viscoelasticity (increasing Deborah number); initially increasing and then decreasing. An analytical explanation has been given of the effects by computing the migration velocity as arising from an image stresslet field due to the drop. The semi-analytical expression matches well with the simulated migration velocity away from the wall. It contains a viscoelastic stresslet component apart from those arising from interfacial tension and viscosity ratio. The migration dynamics is a result of the competition between the viscous (interfacial tension and viscosity ratio) and the viscoelastic effects. The viscoelastic stresslet contribution towards the migration velocity steadily increases. But the interfacial stresslet-arising purely from the drop shape-first increases and then decreases with rising Deborah number causing the migration velocity to be non-monotonic. The geometric effect of the interfacial stresslet is caused by a corresponding nonmonotonic variation of the drop inclination. High viscosity ratio is briefly considered to show that the drop viscoelasticity could stabilize a drop against breakup, and the increase in migration velocity due to viscoelasticity is larger compared to the viscosity-matched case.