Inertial forces and elastohydrodynamic interaction of spherical particles in wall-bounded sedimentation experiments at low particle Reynolds number

Abstract

Wall-bounded sedimentation of spherical particles at low particle Reynolds numbers $Re_\text{P}\lessapprox 0.1$ under the influence of elastic deformation was investigated experimentally. The complete kinematics of both elastic and rigid spheres sedimenting from rest near a rigid or an elastic plane wall in a rectangular duct were recorded. Several specific phenomena related to both inertial and elastohydrodynamic effects were identified and discussed. Among these phenomena is an inertial wall attraction, i.e., particles approach the wall while being accelerated from rest. It was found, that this initial attraction was a universal, purely hydrodynamic phenomenon which occurred in all experiments at $Re_\text{P}\lessapprox 0.1$. After the initial stage, rigid spheres sedimenting at $Re_\text{P}\approx O(10^{-1}$) near the wall behaved in the classical way, showing linear migration due to hydrodynamic lift forces. Non-classic evolution of the particle velocity with respect to the wall distance was observed for both rigid and elastic spheres sedimenting at $Re_\text{P}\approx O(10^{-2}$). Sedimentation was persistently unsteady and the spheres decelerated although the wall distance was increased. Another phenomenon is that very soft spheres showed instationarities superimposed by nonlinearities. These peculiarities in the kinematics are attributed to the non-trivial coupling between particle-fluid inertial forces and elastic effects, i.e., to the existence of elastohydrodynamic memory. Instationarities were also observed during the sedimentation of rigid spheres along an elastic wall. For example, in the near-wall region, elastohydrodynamic interactions damped the dynamics during mass acceleration. Meanwhile, persistent undulating motion towards the wall was observed, i.e., elastohydrodynamic particle trapping instead of hydrodynamic lift was observed.