Viscoelastic drop falling through a viscous medium

Abstract

Deformation and sedimentation velocities of a viscoelastic drop falling through a Newtonian medium are numerically investigated using a front-tracking finite difference method. In contrast to a viscous drop, viscoelasticity deforms an initially spherical drop into an oblate shape and decreases its sedimentation velocity. Further increase of elasticity results in a dimple at the rear end, as the viscoelastic stress at the trailing end of the drop pulls the drop interface inward. The dimple becomes more prominent with increasing Deborah number, amount of polymeric viscosity, and capillary number. An approximate analysis is performed to model the stress development along the axis of symmetry, specifically its increase at the rear end that governs the dimple formation. For even higher values of Deborah number, the interfacial tension cannot balance the viscoelastic stresses leading to an unstable situation toward a toroidal shape. We numerically find the critical Deborah number for the transition. It shows an approximate inverse scaling with capillary number. For unstable cases, downward progressing dimple develops a globular end. Development of the globular end results in a sudden increase in the cross-sectional area of the drop and a sharp decrease of the settling velocity.