Exact solutions for the viscous sintering of multiply-connected fluid domains

Exact solutions for the viscous sintering of multiply-connected fluid domains are found. The approach is based on a recent observation by the author connecting viscous sintering and quadrature identities. The solutions are exact in that the evolution can be described in terms of a finite set of time-dependent parameters; it is shown that the evolution of certain initial fluid domains under the equations of Stokes flow driven by surface tension can be calculated by following the evolution of the coefficients of an algebraic curve. These coefficients satisfy a finite system of first-order nonlinear ordinary differential equations. Practical methods for solving this system are described. By way of example, explicit calculations of the sintering of unit cells deriving from square packings involving both unimodal and bimodal distributions of particles are given.