Morphological changes of a surface of revolution due to capillarity-induced surface diffusion

Abstract

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. © 1965 The American Institute of Physics.