A contact mechanics method for characterizing the elastic properties and permeability of gels

When a saturated gel immersed in the same liquid is suddenly brought into contact with a smooth rigid indenter, the liquid cannot immediately flow out of the pores, and so the gel initially behaves as an incompressible material. This gives rise to a pressure gradient in the liquid phase and the liquid flows until the pressure in it goes to zero everywhere, and all the stresses are transferred to the elastic network. As a result of the flow, the force needed to maintain a constant contact area relaxes with time. In this work, we study the feasibility of using an indentation test to measure this time-dependent force and to determine the elastic modulus, the Poisson's ratio, and the permeability, D _p, of the network. Specifically, we consider a two-dimensional Hertz contact problem of a rigid circular cylinder indenting on a half space consisting of an elastic gel. The network of the gel is assumed to be linearly elastic and isotropic, and liquid flow within the gel is assumed to obey Darcy's law, which states that the flux is proportional to the pressure gradient. Exact expressions are obtained for the initial and final force required to maintain a given contact length. These expressions allow us to determine the elastic constants of the network. The permeability of the network can be obtained from the time-dependent relaxation of the load, which is obtained by solving the exact continuum equations.