Three-dimensional morphology evolution of solid-fluid interfaces by pressure solution

Abstract

This chapter offers an introduction to recent theoretical research on chemo-mechanical phenomena in solid/liquid systems under non-hydrostatic stress. Its purpose is to acquaint the reader with a number of key concepts and results through an analysis of one specific problem. The problem chosen is the surface roughness of a stressed elastic solid that is dissolving in a solution phase, as determined by the state of stress in the solid. This roughness is treated as a surface instability that is governed by a three-dimensional, local criterion derived from a linear stability analysis of a homogeneously stressed half-space. Using a normal mode decomposition, with modes in the shape of a polarized wave, the solution to the linear elasticity problem is constructed by superposition of three Galerkin vectors to account for the three components of the stress vector acting on the surface. It is shown that for isotropic surface properties, the dominant mode determining the instability has its normal parallel to the maximum principal stress. The surface morphology evolution is thus shown to be controlled by the principal stress directions. The three-dimensional, local stability criterion is then applied to experimental results reported by den Brok and Morel for single-crystal K-alum specimens in the shape of a rectangular plate with a cylindrical hole that allowed the creation of a stress gradient. The wavy pattern, which is observed in these experiments only under an applied load, is well predicted when interpreting it theoretically as a surface instability. However, the wavelength of the dominant mode of instability was expected theoretically to vary by several orders of magnitude due to the stress gradient across the specimen. This dependence, and the predicted growth in time of the instability has not been observed in the laboratory, suggesting further complexity in the stress-driven evolution of surface morphologies, which remains to be explored both theoretically and experimentally.