  We present a continuum model describing dissolution and growth of a crystal
contact confined against a substrate. Diffusion and hydrodynamics in the liquid
film separating the crystal and the substrate are modeled within the
lubrication approximation. The model also accounts for the disjoining pressure
and surface tension. Within this framework, we obtain evolution equations which
govern the non-equilibrium dynamics of the crystal interface. Based on this
model, we explore the problem of dissolution under an external load, known as
pressure solution. We find that in steady-state, diverging (power-law)
crystal-surface repulsions lead to flat contacts with a monotonic increase of
the dissolution rate as a function of the load. Forces induced by viscous
dissipation then surpass those due to disjoining pressure at large enough
loads. In contrast, finite repulsions (exponential) lead to sharp pointy
contacts with a dissolution rate independent on the load and on the liquid
viscosity. Ultimately, in steady-state the crystal never touches the substrate
when pressed against it, independently from the nature of the crystal-surface
interaction due to the combined effects of viscosity and surface tension.
