A boundary element solution for two-dimensional viscous sintering

By viscous sintering is meant the process in which a granular compact is heated to a temperature at which the viscosity of the material under consideration becomes low enough for surface tension to cause the powder particles to deform and coalesce. For the sake of simplicity this process is modeled in a two-dimensional space. The governing (Stokes) equations describe the deformation of a two-dimensional viscous liquid region under the influence of the curvature of the outer boundary. However, some extra conditions are needed to ensure that these equations can be solved uniquely. A boundary element method is applied to solve the equations for an arbitrarily initial-shaped fluid region. The numerical problems that can arise in computing the curvature, in particular when this is varying rapidly, are discussed. A number of numerical examples are shown for simply connected regions which transform themselves into circles as time increases.