Mechanics of shape evolution of particle aggregates in viscous sintering

Sintering of glass/amorphous particles takes place by viscous flow driven by surface tension. While the viscous sintering of two particles is described by the growth of contact area, the shape evolution of aggregates of particles is very complicated and requires analytical methods for the characterization. Here, we analyzed the viscous sintering of linear chains of particles by finite element simulation. Consider a plane which cuts the chain perpendicular to its axis. We show that the growth rate of cross-sectional area is driven by the difference between the integral of pressure on the cross-section and the surface tension acting along its circumference, i.e., the sintering force. The cross-sectional area increases when the sintering force is positive, and decreases when it is negative. This relationship is generalized to particles aggregate of any shape, so that its shape evolution is characterized by the distribution function of growth rate of cross-sectional area.