Two-dimensional analysis of pore drag and drop

Abstract

We consider stationary coupled migration (drag) and conditions for separation (drop) of pores situated on grain boundaries or triple junctions in two-dimensional (2D) geometry. Pore mobility is realized by surface diffusion and boundaries migrate owing to surface tension. A small velocity approximation yields pore mobility and estimates for the velocity at which separation occurs. The estimate is refined by numerical solution. In contrast to previous expectations, separation occurs in 2D and the critical velocity for pores with circular cross section is non-zero. Our numerics are further confirmed by bifurcation analysis. The critical velocities for 2D pores at triple junctions are considerably smaller than for 2D pores on grain boundaries, which in turn are smaller by a factor of two to three compared to critical velocities of three-dimensional lenticular pores on grain boundaries. We also determine the coupled pore-boundary mobility and demonstrate that the boundary mobility is practically always reduced by pores.