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.
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