Bending of gel beams: method for characterizing elastic properties and permeability

When a saturated gel is deformed, its mechanical response is profoundly influenced by the flow of liquid in its pores. For example, if a gel bar is suddenly deformed in 3-point bending, the liquid cannot immediately flow out of the pores, so the gel initially responds incompressibly; consequently, its deflection provides a measure of its shear modulus, G_p, rather than Young's modulus, E_p. In this paper, the kinetics of deformation of such a rod are analyzed, showing that it is possible to obtain the permeability, D, of the gel from the time-dependence of the load, as well as finding both G_p and E_p. Analyses are presented for the time dependence of the load at constant deflection for a square and cylindrical beam, and for load at constant deflection rate for a square beam. The method is applied to determine G_p, E_p, and D for a silica gel made from tetraethoxysilane.