The partial differential equation describing morphological changes of a surface of revolution due to capillarity-induced surface diffusion has been derived under the assumption of isotropy of surface tension and surface self-diffusion coefficient. A stable, convergent finite-difference method has been developed for the general case of an arbitrary surface of revolution and solutions have been obtained for the specific problems of the blunting of field-emission tips and the sintering of spheres. Spheroidization of cylindrical rods, as well as field-emission tips with taper below a certain critical value, is predicted; for tapers above the critical value, steady-state shapes are predicted and equations describing the blunting and recession of the tips are presented. If the sintering results for spheres are represented by a plot of log x/a vs log t, it is found that the inverse slope varies from approximately 5.5 to approximately 6.5 for the range 0.05≤x/a≤0.3, in contrast with the constant value of 7 found by Kuczynski from an order-of-magnitude analysis. At higher values of x/a, n increases steadily and without bound.

Alternative solution for diffusion to two spheres with first-order surface reaction Diffusion in concentrated hard sphere dispersions: Effective two particle mobility tensors J. Chem. Phys. 78, 5825 (1983); 10.1063/1.445427 Diffusion in concentrated hard sphere dispersions: Effects of two and three particle mobilities A numerical solution has been obtained which gives the morphological changes and kinetics during the coalescence of two spheres by surface diffusion. The solution may be utilized for determining surface cliffusion coefficients by observing the coalescence of two gas bubbles within a solid or interfacial diffusivities by observing the same phenomenon involving spherical precipitates in a solid matrix. The former parameters are of great interest in the fission-gas swelling of nuclear fuels whereas the latter figure prominently in various transformations in the solid state. The present analysis provides a theoretical framework by which these parameters may be determined under conditions of minimal absorption difficulties, as well as guidelines for applicability of the results.

The governing equation for the capillarity-induced shape changes of a surface of revolution by surface diffusion, ~n B~ (v~K) ~t -y ~s ~s where ~n/~t is the normal velocity of the surface, y is measured normal to the axis of revolution, s is arc length, K is the total surface curvature and B is a kinetic parameter which is constant for a given temperature and material, is presented. A numerical solution to this equation is used to analyse finite cylinders with hemispherical ends. A critical length-to-diameter ratio (L/D) of 7.2 is predicted, below which only one spheroidal particle results and above which two or more are formed, and is shown to have experimental support in several systems.

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