Lift and drag force on a spherical particle in a viscoelastic shear flow

Abstract

We present a comprehensive 3D numerical study of particles with imposed velocities relative to the local bulk flow (termed “slip velocities”) in a viscoelastic shear flow. We consider the force on a spherical particle sedimenting, a spherical bubble rising, and a spherical neutral squirmer swimming in an imposed viscoelastic shear flow. We demonstrate that any particle moving with a slip velocity in the flow or gradient direction of the shear flow experience a lateral lift force. We calculate and compare the magnitude and direction of the lift force in all situations. At small Deborah (De) and Weissenberg (Wi) numbers, our results show good agreement with an existing perturbation theory for rigid particles (Einarsson and Mehlig, 2017 [1]) and new perturbation theories for drops and for squirmers respectively. Our simulations extend these results to higher De and Wi regimes. Through our simulations, we uncover the physical mechanism of the lateral force on all particles. For rigid particles, we find the lift force arises from an imbalance in polymer stress on either side of the particle, which in turn is due to the imbalance of polymer stretch surrounding the particle. If this lift force is not balanced by an external force, a lateral drift velocity arises. We further consider the implication of this lateral drift for rigid particles hydrodynamically forced in a viscoelastic Poiseuille flow, where particles can migrate either toward the channel center plane or toward the wall, depending on whether the direction of the applied force is in the direction aligned or opposite to the direction of the Poiseuille flow, respectively. We study both the migration of a single particle as well as a suspension of particles in channel flow. Even with the addition of hydrodynamic interactions, we show that particles forced in the direction of the Poiseuille flow migrate towards the channel center.