Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology

TL;DR

This paper models the mechanical response of a thick, permeable poroelastic gel under contactless colloidal-probe conditions, revealing how poroelasticity influences force interactions in soft-lubrication scenarios.

Contribution

It derives the fundamental point-force response of a permeable poroelastic substrate and applies it to analyze force components in contactless colloidal-probe experiments.

Findings

Derived the response of a semi-infinite permeable poroelastic substrate.

Analyzed conservative and dissipative force components in oscillating sphere experiments.

Results applicable to soft, living, and fragile materials like hydrogels and biological membranes.

Abstract

When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which complexifies further the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamental solution in order to address the specific poroelastic lubrication coupling associated with contactless colloidal-probe methods. In particular, we derive the conservative and dissipative components of the force associated with the oscillating vertical motion of a sphere close to the poroelastic substrate. Our results may be relevant for dynamic surface force apparatus and contactless colloidal-probe atomic force microscopy experiments on soft, living and/or fragile materials, such as swollen hydrogels and biological membranes.