Drying gels. III. warping plate

An analysis is presented of the warping of a plate of gel as it dries by evaporation from one side. First, an elastic solution is obtained for the stresses and strains in a plate with an arbitrary variation in free strain through its thickness. The solution for a porous viscous material, such as a gel, is obtained by analogy. The free strain rate of the gel is determined by extension of the theory presented in Part I of this series. Two cases are considered: 1) a plate drying by evaporation from one side, with the other side in contact with a reservoir of liquid; 2) a plate with no such reservoir. In both cases, the plate initially becomes concave toward the direction of evaporation. If a reservoir is present, the plate does not dry unless the permeability is very low. If a dry region does form, the curvature of the plate tends to reverse, in keeping with experimental observations. The slower the drying rate, the smaller the residual curvature. The magnitude of the curvature and its dependence on drying rate are sensitive to the assumed properties of the gel, particularly the assumed dependence of the viscosity of the solid phase on the relative density.