Multiscale modeling of particle–solidification front dynamics, Part I: Methodology

The interaction between an advancing solidification front and a micron-size particle is an inherently multiscale heat and mass transport problem. Transport at the micro-scale (i.e. the scale of the particle dimension) couples with intermolecular interactions and lubrication forces in a thin layer of melt between the particle and the front to determine the overall dynamics of the interaction. A multiscale model is developed to simulate such front–particle interactions. The solution to the lubrication equations in the melt layer is coupled to the solution of the Navier–Stokes equations for the overall particle–front system. Techniques are developed for coupling the dynamics at the two disparate scales at a common “matching plane”. All interfaces are represented and tracked using the level-set approach. A sharp-interface technique is employed for solution of the governing equations in the resulting moving boundary problem. Validation of the coupling strategy and results for the particle–front interaction phenomenon with the multiscale approach are presented.