An elliptical-pore model for late-stage planar viscous sintering

Abstract

A simple ‘elliptical-pore model’ of the shrinkage of compressible pores in late-stage planar viscous sintering is proposed. The model is in the spirit of matched asymptotics and relies on splitting the flow into an ‘inner’ and ‘outer’ problem. The inner problem in the vicinity of any given pore involves solving for its free-surface evolution exactly using complex-variable methods. The outer flow due to all other pores is assumed to be given by an assembly of point sinks/sources. As a test of the model, the evolution of a singly infinite periodic row of compressible pores is considered in detail. The effectiveness of the simple model is tested by comparison with a full numerical simulation. A novel boundary integral method based on Cauchy potentials and conformal mapping is used. In the case of pores with constant pressure, it is found that pores shrink faster than if in isolation. Compressible pores obeying the ideal gas law are also studied and are found to tend to a quasi-steady non-circular state. A higher-order model is also presented and compared with numerical simulations of the viscous sintering of a doubly periodic array of pores in Stokes flow.