Inertial forces and elastohydrodynamic interaction of spherical particles in wall-bounded sedimentation experiments at low \(\textit{Re}_\textrm{P}\)

Abstract

Unsteady, wall-bounded sedimentation of spheres at low particle Reynolds numbers, Re\(_\textrm{P}\lesssim 0.1\), under the influence of small elastic deformation was investigated experimentally. The complete kinematics of elastic and rigid spheres sedimenting from rest at various initial distances from a rigid plane wall in a rectangular duct were measured. Several previously unrecognized phenomena arising from fluid inertia and superimposed elastohydrodynamic effects were identified and analyzed. Among these is an inertial wall attraction, whereby particles migrate toward the wall during the initial acceleration phase. After this initial phase, rigid spheres sedimenting at Re\(_\textrm{P}\approx O(10^{-1})\) followed behavior consistent with classic wall-lift models, including approximately linear migration away from the wall. In contrast, at smaller Reynolds numbers, Re\(_\textrm{P}\approx O(10^{-2})\), both rigid and elastic spheres exhibited persistently unsteady sedimentation, characterized by deceleration despite increasing wall distance. These results enable the formulation of a conceptual framework that classifies near-wall sedimentation regimes according to particle Reynolds number and the position of boundaries relative to the Stokes length scale. For increasing deformability, the unsteady behavior was further modulated by nonlinearities. The observations suggest the presence of an elastohydrodynamic memory effect arising from the coupling of fluid inertial forces with particle deformability. The experimental findings are supported by computational fluid dynamics simulations that provide qualitative insight into the evolving flow field. Overall, the results demonstrate that classic assumptions commonly applied to particle sedimentation in creeping flows break down in the presence of nearby boundaries and reveal a counterintuitive trend: as the particle Reynolds number decreases, fluid inertia can play an increasingly important role in governing particle motion near walls. The proposed conceptual framework may therefore aid the interpretation of the near-wall dynamics of deformable microplastic particles, for which comparable material properties and flow regimes are encountered in environmental and wastewater flows.