Linear poroelastic response of thin permeable gel films

TL;DR

This paper derives the mechanical response of thin, permeable, poroelastic gel layers, revealing localized surface deformation and providing a Green's function useful for various applications like indentation and microfluidics.

Contribution

It presents a novel analytical model for the point-force response of thin poroelastic gels, accounting for their unique surface deformation characteristics.

Findings

Surface deformation is localized around the indentation point within a radius comparable to the layer thickness.

The Green's function enables prediction of space- and time-dependent surface deformations.

The model applies to indentation, thin membranes, and lubrication involving soft porous walls.

Abstract

When a hydrophilic and deformable porous material is immersed in a bath, it may absorb the solvent and expand by several times its volume, thus forming a highly soft and porous hydrogel. A stress applied on the soft hydrogel surface deforms it and forces the absorbed solvent to move by flowing through the network of pores. This coupled phenomenon sets the framework of poroelasticity. Moreover, polymeric gels are often used in ultra-thin coatings to tune surface properties. Together with the characteristic poroelastic coupling, this thinness challenges the modelling of their response. In this article, we derive the point-force mechanical response of a thin, permeable and poroelastic layer bounded to a rigid substrate. We show that the gel surface is only deformed around the indentation point, within a radius on the order of the layer thickness. The obtained Green's function can be directly used to predict the space- and time-dependent surface deformation of the gel. Our findings are relevant for a broad range of applications, such as indentation experiments on swollen gels, thin membranes or soft and living systems, as well as lubrication problems involving a soft and porous wall, for instance in microfluidics.