Calculated Size Distributions for Gas Bubble Migration and Coalescence in Solids

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Abstract
Bubble coalescence in solids is assumed to result when collisions occur between bubbles as they migrate by surface diffusion through the solid. The migration of an isolated pore is examined in detail and the results are applied in a finite-difference approach, programmed for a digital computer, to predict the variation of the number of bubbles per unit volume as a function both of bubble size and of post-irradiation annealing time. Two idealized models of bubble coalescence have been treated. The first model considers coalescence resulting from random migration of the bubbles, and the second considers coalescence resulting from unidirectional, biased migration, such as would result in the presence of a thermal gradient. Both models are based on surface diffusion migration of randomly distributed bubbles in a perfect, infinite solid. The results give the predicted variation with time of the entire distribution of bubble sizes, so that various parameters, including the mean bubble radius and volume change, can be predicted. Comparison of the predicted values to parameters measured in appropriate experiments could provide a means of measuring fundamental properties of materials. The results can also be applied to the problem of swelling of reactor fuel materials because of trapped fission gases. Although the present analysis is limited by a number of simplifying assumptions, it is clear that the presence of a thermal gradient can greatly enhance the swelling rate.