Soft-lubrication interactions between a rigid sphere and an elastic wall

TL;DR

This paper develops a theoretical model to analyze the forces and torques on a rigid sphere moving near an elastic wall in a viscous fluid, accounting for small surface deformations and elastic properties.

Contribution

It introduces a soft-lubrication model that analytically computes elastohydrodynamic forces and torques on a sphere near an elastic boundary, including thin and thick elastic layers.

Findings

Derived analytical expressions for EHD forces using Lorentz reciprocal theorem.

Performed perturbation analysis for small surface deformations.

Analyzed the effects of elastic layer thickness on the forces.

Abstract

The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic (EHD) interactions experienced by the particle. Here, we derive a soft-lubrication model, in order to compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elastic wall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, and perform a perturbation analysis in dimensionless compliance. The response is computed in the framework of linear elasticity, for planar elastic substrates in the limiting cases of thick and thin layers. The EHD forces are also obtained analytically using the Lorentz reciprocal theorem.