Bending a gel rod with an impermeable surface

When a gel rod is bent, a pressure gradient is created in the liquid; the liquid flows until the pressure goes to zero everywhere, and all the stress is transferred to the network. As a result of the flow, the force needed to hold the rod at a fixed deflection decreases with time. It has been shown [J. Non-Cryst. Solids 142 (1992) 18] that measurement of the time-dependent force permits calculation of the elastic modulus, Poisson's ratio, and permeability of the network. The original analysis allows for flow of liquid between the bar and the surrounding bath, as well as flow within the bar. In this paper, the surface of the bar is assumed to be impermeable, so that liquid flows only within the bar. This would be the case (for example) if there were a dense skin on the gel rod. The relaxation function is shown to be quite different in shape from that of a bar with a permeable surface, so that a skin would be detectable from the kinetics of stress relaxation.