Numerical simulation of viscoelastic effects in peristaltic transport of drops

Abstract

• Under creeping-flow conditions, elasticity of a drop slightly hinders its peristaltic transport. • Elasticity of the liquid surrounding the drop has a significant but non-monotonic effect on the drop's peristaltic transport. • Viscosity of the bulk liquid can have an accelerating or decelerating effect on the drop's velocity. • Peristalsis can be regarded as a viable option for the transport of elastic drops in microfluidic systems. Peristalsis is known to be a viable option for the transport of Newtonian drops suspended in another Newtonian liquid. In certain applications, the drop or the bulk liquid is known to be, more or less, viscoelastic. In the present work the effect of a liquid's elasticity is investigated on the peristaltic transport of a single, circular drop. Having assumed that the liquid obeys the Oldroyd-B model, numerical results have been obtained at Deborah numbers up to 15 for two different cases: (1) the drop is viscoelastic, and (2) the liquid surrounding the drop is viscoelastic. Based on the results obtained in this work, it is predicted that under creeping-flow conditions, a drop's elasticity has a negligible effect on its transport velocity provided it is placed on the centerline. But for off-center viscoelastic drops the effect of elasticity is significant and delay their migration to the centerline. For the case in which only the liquid surrounding the drop is viscoelastic, elastic stresses are predicted to have a significant but non-monotonic effect on the drop velocity. In both cases, the response of a drop is predicted to strongly depend on its size and also on the cross-viscosity ratio.