Gel mechanics: a comparison of the theories of Biot and Tanaka, Hocker, and Benedek

This article compares the Biot J. Appl. Phys. 12, 155 (1941)] and Tanaka, Hocker, and Benedek (THB) J. Chem. Phys. 59, 5151 (1973)] theories of gel deformation. Biot's theory treats the gel as a continuum with the pore pressure as a state variable whereas the THB theory treats the gel as a mixture of solid and liquid phases. We revisit the problem of gel deswelling and use this example to show that there can be substantial differences between the two theories. The THB theory is not a complete mixture theory since the displacements of the liquid are assumed to be negligibly small in comparison with the displacements of the network. We propose a simple extension of the THB model, which takes into account the momentum transfer of the liquid phase. We show that with this simple addition and some very reasonable assumptions, the extended THB theory is identical to the Biot theory.