Steady-state and dynamic models for particle engulfment during solidification

Yutao Tao, Andrew Yeckel, Jeffrey J. Derby

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 [29]. 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.

Original languageEnglish (US)
Pages (from-to)238-263
Number of pages26
JournalJournal of Computational Physics
StatePublished - Jun 15 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


  • Arbitrary Lagrangian-Eulerian
  • Engulfment
  • Finite-element method
  • Moving boundary problem
  • Solidification


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