A fixed-grid numerical modelling of transient liquid phase bonding and other diffusion-controlled phase changes

A transient liquid phase (TLP), in which a liquid layer is formed and subsequently solidifies, and other diffusion-controlled phase changes are generally associated with moving phase-change interfaces. Both fixed and variable grid discretization models have been formulated to investigate these diffusion-controlled problems. However, all numerical efforts to date have employed one of the approaches explicitly to track the moving interfaces across which there exist step changes in concentrations. In this article, the fixed-grid source-based method originally developed to simulate the temperature fields for melting-solidification phase change processes has been adopted to simulate diffusion-controlled dissolution and solidification. This method solves a unique diffusion equation for the different phases and the moving interfaces using implicit time integration. Compared with previously developed models, it is not only simpler in numerical formulation and procedure, but also more convenient to extend to many phases and high-dimensional problems. We report here the detailed formulation of the relevant equations, and compare and validate the model using experimental data and previous modelling predictions for several systems available from the existing literature.