Flattening of a Nearly Plane Solid Surface due to Capillarity

Abstract

The relaxation of a nearly plane surface to flatness is discussed under the assumption that all surface properties are independent of orientation. A general solution is obtained for the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion. Green's function solutions are developed for each of the transport processes separately, and criteria are obtained to decide which process dominates. The initial forms of these solutions represent point concentrations (particles), or line concentrations (wires) of material set upon an infinite plane. The progressive topographical developments described by the formulas are idealized representations of the latter stages of the sintering of small wires and particles to a plane.