Mathematical modeling of liquid phase migration in solid–liquid mixtures: Application to the sintering of functionally graded WC–Co composites

Liquid phase migration (LPM) is an interfacial-energy-driven flow that takes place in a solid–liquid two-phase system. This phenomenon is similar to but different from the well-known capillary-driven flow. Understanding and controlling LPM is crucial for liquid phase sintering of various functionally graded materials, including WC–Co, with composition gradients. To date, there have been few studies that focus on the LPM phenomenon, partially because it is a complex process that involves mass transport with moving boundaries and changing volumes. This paper describes a quantitative study on the kinetics of LPM. The governing equation for LPM that takes into account the changes in volume was derived and a novel “grid-tracking” numerical technique was also developed for solving the governing equation. The methodology and techniques described in this paper can be applied to simulate and predict the kinetics of LPM during liquid phase sintering and the composition gradients as the result of LPM.