Surface pattern formation in a swelling gel

Abstract

We study the time evolution of surface pattern formation in a swelling spherical gel using proton nuclear magnetic resonance microimaging of water molecules migrating into the gel. Relaxation-weighted images permit mapping of the local evolution of the swelling ratio which, within the framework of a nonlinear poroelastic theory, can be identified with the determinant of the deformation gradient tensor. The wavelength of the surface pattern is examined and some analogies with the extensively studied problem of the wavelength at threshold for swelling rings are pointed out. By controlling the degree of cross-linking within a surface layer of the gel it is possible to monitor the transition from an undulating folding pattern to the formation of singular creases.