Particle motion in viscosity gradients near a plane wall
Phys. Rev. Fluids 10, 094204 – Published 22 September, 2025
DOI: https://doi.org/10.1103/kf46-19nw
Abstract
In this study, we investigate the Stokesian hydrodynamics of rigid circular and spherical particles near a plane wall within a heterogeneous viscous environment. We focus on the resistance problem to evaluate the hydrodynamic forces and torques acting on the particle. The viscosity field is assumed to vary spatially, comprising a background linear profile and a disturbance field. We derive analytical expressions for the circular particle using reciprocal theorem in the limit of small viscosity gradient, and later validate them against finite-element-based numerical simulations. For the spherical particle, only numerical results are shown. We consider two typical background viscosity variations: with transverse (wall-perpendicular) and longitudinal (wall-parallel) gradients. The findings reveal that viscosity gradient induces novel hydrodynamic couplings in near-wall particle motion. Specifically, within transverse gradient, force-rotation and torque-translation cross-couplings are evident in both wall-parallel translating and near-wall rotating circular and spherical particles. In two dimensions, the leading-order dynamics are uncoupled, and these terms solely dictate the hydrodynamics, whereas in three dimensions they oppose the existing leading-order couplings. Wall-perpendicular particle translation, however, remains uncoupled. In longitudinal gradient, wall-parallel translation and near-wall rotation of a circular particle develops force-force and force-torque couplings, respectively, while wall-normal translation acquires both; for a spherical particle, all translation and rotation modes exhibit couplings. We qualitatively attribute these to the viscosity gradient-induced asymmetries in near-wall traction distributions around the particle, resulting from associated pressure and shear-rate profile modifications. Overall, this study provides fundamental insights into the combined influence of wall and viscosity gradient on particle hydrodynamics. These couplings are also directly manifested in particle trajectories, so the results may have potential implications for particle transport, sorting, and separation in microfluidic devices.
