An approximate analytical model for the late-stage sintering of an array of rods by viscous flow

Abstract

The late stages of sintering of a linear array of rods by viscous flow have been studied theoretically. An approximate model in which the actual interface profile is assumed to be locally planar has been developed. Within the framework of the model, analytic solutions to the steady-state Navier-Stokes equations have been derived and the course of sintering followed by advancing the profile through a sequence of short-duration time intervals. After each step the profile is mathematically redefined and new values for the velocities and pressure calculated. In the later stages a logarithmic plot of the reduced neck radius versus time displays a distinctly nonlinear character. Thus the kinetics cannot be described by a simple exponential function as can the early stages when Kuczynski’s geometric simplifications remain valid. A comparison between the two models reveals the rate of neck growth in the later stages to be significantly less for the locally planar interface model. It is suggested that this reduction is due to a lower stress gradient for the flow or material into the neck as a result of the dependence of stress in the neck region upon the changing curvature everywhere.