Diffusio-Mechanical Theory of Gel Bending Induced by Liquid Penetration

A thin gel sheet bends as liquid penetrates from one side of the surface. We develop a diffusio-mechanical theory for the phenomena and calculate the time dependence of the bending behaviors for two types of gels, (a) a free gel that can swell in all directions freely and (b) a bound gel with its bottom surface adhered to a plastic film that can bend but cannot stretch. The theory shows that the bending behaviors of the two gels are distinctively different. The free gel bends as the liquid penetrates, takes a maximum curvature, and then slowly bends back to take the original flat shape. On the other hand, the bound gel keeps bending and gets an equilibrium state in a bent configuration. Analytical expressions are given for the maximum curvature, the equilibrium curvature, and the time at which the gel takes its maximum curvature.