Thermal expansion of a gel layer on a rigid substrate

It was previously shown that the hydrodynamic relaxation time, τ, of a gel can be found from a measurement of the kinetics of thermal expansion of a rod of gel [J. Non-Cryst. Solids, 130 (1991) 157], Given an independent measure of the elastic modulus of the gel, the permeability of the network can be calculated from τ. For soft gels, it can be difficult to use this geometry, because the rod bends when stood on end. In addition, the result of the analysis in that case is an implicit expression that must be evaluated numerically, even for the simplest thermal history. In this paper, an analysis is presented for the thermal expansion kinetics of a layer of gel on a rigid substrate (e.g., a shallow dish full of gel). A relatively simple explicit solution is obtained in this case. The disadvantage of the method is that the absolute displacement is proportional to the thickness of the body, so sensitive equipment is required to measure the expansion of a thin layer of gel.