Chemical potential in viscous phases under non-hydrostatic stress

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Abstract
Two phases of the same pure component are considered, coexisting in univariant equilibrium at a planar interface under hydrostatic pressure p. The equilibrium is disturbed by increasing the compressive stress parallel to the interface, while keeping constant the compressive stress normal to the interface. It is assumed that all the ensuing deformation is non-recoverable (elastic effects negligible) and predicted that the phase boundary will migrate, with the phase having higher viscosity being consumed. The three concurrent processes—viscous deformation, self-diffusion and change of phase—can be simply related to a single field of potentials if the postulate is entertained that, under non-hydrostatic stress, the potential takes different values for different directions at a single point within a material. This postulate embodies Prigogine's concept of a material's internal coordinates; it enlarges on the work of Gibbs and does not conflict with it.