PORE MIGRATION IN CERAMIC FUEL ELEMENTS

An analysis is presented on the behavior of an initially spherical pore when placed in a thermal gradient. When the dominant mechanism of material transport is evaporation-condensation, the problem is solved from first principles to give: ∂n ∂t = -[ D ̄vΩC0ΔHV▽T (kT02)] · · [cos θ + 2 3α · 1 2(3 cos2θ-1)], where ∂n ∂t = outward normal velocity at pore surface, D ̄V = diffusion coefficient in vapor evaluated at T0, Ω = molecular volume, C0 = equilibrium concentration in vapor at average temperature To, α = (▽TR 0 T0)(Δ HV kT0) < 1, ΔHV = heat of vaporization, k = Boltzmann constant, ▽T = thermal gradient, R0 = pore radius and θ = normal polar angle. The first-order term of the equation predicts, if D ̄V (which is inversely proportional to the pressure in the pore) is not a function of R0, a motion of the pore up the thermal gradient at a velocity independent of pore size. If the pressure is assumed to be dictated by surface tension effects (and therefore inversely proportional to R0) then the equation predicts a velocity which increases linearly with r0. These results are in substantial agreement with previous approximate treatments for the migration velocity. The second-order term in the equation predicts a deviation from the spherical shape assumed as the starting point. The deviation is such that a spherical pore should, as it migrates, transform itself into an elongated or cigar-shaped form. Some speculations concerning the origin and stability of the lenticular voids sometimes observed are also presented. © 1968.