The computational analysis of materials processing systems involving three dimensional heat and/or mass transport phenomena, coupled with fluid flow and non-trivial moving boundaries, poses a significant challenge despite recent advances in available hardware and software. Relevant processes include welding, crystal growth, electro-chemical processing, and more. We are particularly interested in meniscus-defined oxide single crystal growth systems in which it is specifically important to model phenomena such as radiative heat transport, significant liquid phase flows, and interfacial dynamics involving anisotropic kinetic as well as anisotropic capillary phenomena.
In this presentation we provide details of our progress in the development of an efficient combination of the Lattice Boltzmann Method (LBM) and more conventional techniques for the analysis of a class of materials processing systems, using the specific example of Czochralski (CZ) single crystal growth of an oxide material. We will discuss the status of our algorithms for the analysis of mutually evolving liquid/solid and liquid/gas interfaces as well as convective and radiative heat transport in a non-trivial three dimensional system (compatible with a CZ growth set-up).
A particular focus will be placed on the application of appropriate boundary conditions at the partially faceted liquid/solid interface, at the liquid/gas interface and along the Triple-Phase-Line (TPL) where the liquid, crystalline and gas phases meet. The liquid/solid interface is advanced using an explicit formulation consistent with step-flow and step-source kinetics, which depend on surface topography as well as on local deviation from equilibrium. Motion of the liquid/gas interface is also obtained using an explicit approach where a quasi-kinetic formulation is used involving local values of interfacial curvature as well as stress-tensor components. Finally, at the TPL a special effort is made to account for growth angle anisotropy.
Preliminary results accounting for a dependence of the growth angle on the orientation of relevant interfaces will be presented where our ideas for further refinement of our model for growth angle anisotropy, with respect to details of the morphology of these interfaces, will also be discussed.