The mechanical properties of a liquid-filled porous solid with reference to articular cartilage

Abstract

An investigation is made into the flow of fluids through deformable porous materials with the aim of an application to articular cartilage, which depends on interstitial fluid for some of its mechanical properties. The law governing flows due to fluid pressure is shown to be valid in a cylinder of material with the same permeability in all directions, both with axial flow only and with axial and radial flow combined, up to Reynolds numbers of about 1. A literature survey shows that there is a large range of values of Reymolds numbers proposed as the limit of the validity of this law, indicating that there is no universal "critical" Reynolds number inflow through porous media. The variation of permeability with strain is measured, both indirections parallel and perpendicular to the direction of applied strain, inlay porous polymeric material. A model of articular cartilage is proposed which consists of a porous solid matrix, which has a reversible non-linear load/displacement characteristic, with liquid-filled pores. Assuming a simple variation of permeability with strain predicts time-dependent deformations to a good degree of accuracy, agreement being excellent at normal physiological loads. Under oscillating loads, deformations are much larger than those predicted by the model, and it is thought that this is due to the effect of the bulk modulus of the cartilage, which becomes dominant in short term responses.