Elastic instabilities and phase coexistence of gels

TLDR: In this article, a macroscopic static theory of gels upon swelling or volume phase transition was developed, and the stability criteria for uniaxially strained bulk gels were derived for spherically symmetric geometry with the outer boundary of the gel having a finite radius.

Abstract: We develop a macroscopic static theory of gels upon swelling or volume phase transition. After deriving the linear elasticity theory of strained systems from the general nonlinear formalism of deformation, we show that the surface modulational instability of a gel plate occurs as the result of softening of (generalized) Rayleigh surface waves. We also derive the stability criteria for uniaxially strained bulk gels. In addition to these linear analyses we developed, for the first time to our knowledge, a theory of three-dimensional phase coexistence of gels exhibiting a volume phase transition. Our study is limited mostly to the case of spherically symmetric geometry with the outer boundary of the gel having a finite radius. Various features of the two phase coexistence are found, some of which have no counterparts in the usual phase separation in binary fluids or gas-liquid systems.