Steady-state and dynamic models are developed to study the physical mechanisms that determine the pushing or engulfment of a solid particle at a moving solid-liquid interface. The mathematical model formulation rigorously accounts for energy and momentum conservation, while faithfully representing the interfacial phenomena affecting solidification phase change and particle motion. A numerical solution approach is developed using the Galerkin finite element method and elliptic mesh generation in an arbitrary Lagrangian-Eulerian implementation, thus allowing for a rigorous representation of forces and dynamics previously inaccessible by approaches using analytical approximations. We demonstrate that this model accurately computes the solidification interface shape while simultaneously resolving thin fluid layers around the particle that arise from premelting during particle engulfment. We reinterpret the significance of premelting via the definition an unambiguous critical velocity for engulfment from steady-state analysis and bifurcation theory. We also explore the complicated transient behaviors that underlie the steady states of this system and posit the significance of dynamical behavior on engulfment events for many systems. We critically examine the onset of engulfment by comparing our computational predictions to those obtained using the analytical model of Rempel and Worster . We assert that, while the accurate calculation of van der Waals repulsive forces remains an open issue, the computational model developed here provides a clear benefit over prior models for computing particle drag forces and other phenomena needed for the faithful simulation of particle engulfment.
Bibliographical noteFunding Information:
This work, conducted at the University of Minnesota, was supported in part by the U.S. National Aeronautics and Space Administration , NNX10AR70G , the content of which does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred. We are thankful for significant interaction with the research groups led by A. Cröll (University of Freiburg) and J. Friedrich (Fraunhofer IISB) on SiC particle engulfment studies carried out under the PARSIWAL project.
© 2016 Elsevier Inc.
- Arbitrary Lagrangian-Eulerian
- Finite-element method
- Moving boundary problem