Sintering force behind shape evolution by viscous flow

A non-spherical amorphous/glass particle relaxes to its equilibrium shape by viscous flow driven by capillarity at elevated temperatures. The shape evolution of an axisymmetric ellipsoidal particle, which is a model of viscous sintering of two spheres in the later stage, was simulated by the finite-element method. A force inside the particle is defined on a plane which cuts the center and perpendicular to the semi-major axis. It is given by the surface tension along the circumference and the average pressure on the plane. The velocity field near the center of the particle is a pure straining motion. The simulation showed that the radial growth rate was proportional to a stress which is given by the force divided by the cross-sectional area. This result suggests that the force can be regarded as the sintering force. Conversely, the force can be determined from the experimental observation of the length of semi-minor axis.