Population balance model for solid state sintering I. Pore shrinkage and densification

A general population balance model incorporating the rate of shrinkage of individual pores during solid state sintering of ceramics is described. The kinetics of pore shrinkage is assumed to follow a simple power law with floating value of the exponent. The resulting equation of continuity is solved for the evolution of pore size distribution in time by a transformation technique. The simulated pore size distributions for a number of ceramic oxide systems are in good agreement with experimental data generated in-house as well as from published sources. The model can be embedded in a coupled phenomenon of densification and grain growth, as shown in Part II.