Tuning Cross-stream Lift in Viscoelastic Shear: Distinct Hydrodynamic Signatures of Force-bearing and Force-free Mechanisms

TL;DR

This study analytically compares how force-bearing and force-free mechanisms influence lift forces on particles in viscoelastic shear flows, revealing opposite lift directions due to different hydrodynamic disturbances.

Contribution

It provides a detailed analytical framework showing how different propulsion mechanisms produce distinct hydrodynamic signatures in viscoelastic shear flows.

Findings

Force-bearing and force-free mechanisms generate lift forces of opposite signs.

Hydrodynamic disturbances differ qualitatively between the mechanisms.

Streamwise drag correction has the same sign for both mechanisms.

Abstract

We investigate the lift and drag corrections acting on a particle suspended in a planar viscoelastic shear flow when the particle is tuned to translate relative to the flow by an external mechanism. A cross-stream lift force arises when particle is driven in streamwise direction; we find that the nature of the driving mechanism dictates the lift direction: force-bearing mechanisms (such as gravity acting on non-neutrally buoyant particles) and force-free mechanisms (such as electrophoresis) generate lift forces of opposite sign. By explicitly deriving the first-order fields and stresses, we demonstrate that this reversal originates from distinct hydrodynamic disturbances induced by each mechanism, which produce qualitatively different polymeric stress distributions. This analytical result is further verified through an independent derivation using the reciprocal theorem. Further, we find that driving the particle in the gradient direction gives rise to a streamwise drag correction that is of the same sign for both mechanisms. Beyond microfluidic particle manipulation, these results have broader implications for understanding the locomotion of microswimmers in viscoelastic shear flows, where distinct force-free propulsion mechanisms are expected to generate unique force and torque modifications.