Theory and numerical calculation of pattern formation in shrinking gels

Abstract

We discuss pattern formation in three-dimensional gels with cylindrical shapes during their shrinking such as volume phase transition. A Ginzburg–Landau theory is given for the pattern formation in shrinking gels. A characteristic feature in shrinking gels is the dense layer formed around the gel surface in the early stage of phase transition. This layer reduce considerably permeation of solvent and the shrinkage practically stops. We introduce the external osmotic pressure and the external elastic stress acting on the gel surface in order to take account of the effect of the layer. Patterns are classified according to the anisotropy and the incompressibility of gels by the linearized stability analysis of the theory. It appears that the external stress term suppresses the growth of the fluctuation with short wavelength. The results obtained by a numerical calculation for the evolution of patterns are also shown.