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

Abstract 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.

[1]  J. W. Garvin,et al.  Sharp interface simulation of interaction of a growing dendrite with a stationary solid particle , 2005 .

[2]  M. Worster,et al.  The interaction between a particle and an advancing solidification front , 1999 .

[3]  J. Israelachvili.  Intermolecular and surface forces , 1985 .

[4]  Doru M. Stefanescu,et al.  A dynamic model for the interaction between a solid particle and an advancing solid/liquid interface , 1992 .

[5]  J. Sethian,et al.  LEVEL SET METHODS FOR FLUID INTERFACES , 2003 .

[6]  G. Bolling,et al.  A theory for the interaction of particles with a solidifying front , 1971 .

[7]  H. Udaykumar,et al.  Sharp interface Cartesian grid method I: An easily implemented technique for 3D moving boundary computations , 2005 .

[8]  D. Stefanescu,et al.  Particle engulfment and pushing by solidifying interfaces: Part II. Microgravity experiments and theoretical analysis , 1998 .

[9]  J. W. Garvin,et al.  Drag on a particle being pushed by a solidification front and its dependence on thermal conductivities , 2004 .

[10]  G. Kaptay,et al.  A Dynamic Model of Ceramic Particle-Solidification Front Interaction , 2002 .

[11]  S. Omenyi,et al.  Thermodynamic aspects of particle engulfment by solidifying melts , 1976 .

[12]  J. Sethian,et al.  Ordered upwind methods for static Hamilton–Jacobi equations , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[13]  L. Hadji.  Thermal force induced by the presence of a particle near a solidifying interface. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  D. Uhlmann,et al.  Interaction Between Particles and a Solid‐Liquid Interface , 1964 .

[15]  H. Udaykumar,et al.  Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions , 2005 .

[16]  H. Udaykumar,et al.  Sharp interface Cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape , 2005 .

[17]  G. Son,et al.  A Level Set Formulation for Incompressible Two-Phase Flows on Nonorthogonal Grids , 2005 .

[18]  D. Stefanescu,et al.  Particle engulfment and pushing by solidifying interfaces: Part 1. Ground experiments , 1998 .

[19]  J. Sethian.  Evolution, implementation, and application of level set and fast marching methods for advancing fronts , 2001 .

[20]  J. W. Garvin,et al.  Particle–solidification front dynamics using a fully coupled approach, Part I: methodology , 2003 .

[21]  D. Shangguan,et al.  Particle Engulfment and Pushing by Solidifying Interfaces (PEPSI) , 1991 .

[22]  J. W. Garvin,et al.  Effect of a premelted film on the dynamics of particle–solidification front interactions , 2006 .

[23]  Joe F. Thompson,et al.  Numerical grid generation: Foundations and applications , 1985 .

[24]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[25]  John S. Wettlaufer,et al.  The premelting of ice and its environmental consequences , 1995 .

[26]  R. Asthana,et al.  The engulfment of foreign particles by a freezing interface , 1993, Journal of Materials Science.

[27]  H. Zhang,et al.  AN ADAPTIVE LEVEL SET METHOD FOR MOVING-BOUNDARY PROBLEMS: APPLICATION TO DROPLET SPREADING AND SOLIDIFICATION , 2000 .

[28]  J. W. Garvin,et al.  Particle-solidification front dynamics using a fully coupled approach, part II: comparison of drag expressions , 2003 .

[29]  L. Leal,et al.  Laminar flow and convective transport processes : scaling principles and asymptotic analysis , 1992 .

[30]  S. Bankoff,et al.  Long-scale evolution of thin liquid films , 1997 .

[31]  R. Sasikumar,et al.  Distortion of the temperature and solute concentration fields due to the presence of particles at the solidification front—effects on particle pushing , 1991 .

[32]  Wei Shyy,et al.  Computational Fluid Dynamics with Moving Boundaries , 1995 .