Integral formulation to simulate the viscous sintering of a two-dimensional lattice of periodic unit cells

In this paper a mathematical formulation is presented which is used to calculate the flow field of a two-dimensional Stokes fluid that is represented by a lattice of unit cells with pores inside. The formulation is described in terms of an integral equation based on Lorentz's formulation, whereby the fundamental solution is used that represents the flow due to a periodic lattice of point forces. The derived integral equation is applied to model the viscous sintering phenomenon, viz, the process that occurs (for example) during the densification of a porous glass heated to such a high temperature that it becomes a viscous fluid. The numerical simulation is carried out by solving the governing Stokes flow equations for a fixed domain through a Boundary Element Method (BEM). The resulting velocity field then determines an approximate geometry at a next time point which is obtained by an implicit integration method. From this formulation quite a few theoretical insights can be obtained of the viscous sintering process with respect to both pore size and pore distribution of the porous glass. In particular, this model is able to examine the consequences of microstructure on the evolution of pore-size distribution, as will be demonstrated for several example problems.