A Thermodynamically-Consistent Phase Field Crystal Model of Solidification with Heat Flux

A Thermodynamically-Consistent Phase Field Crystal Model of Solidification with Heat Flux

Year:    2022

Author:    Cheng Wang, Steven M. Wise

Journal of Mathematical Study, Vol. 55 (2022), Iss. 4 : pp. 337–357

Abstract

In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent in the sense that the time rate of change of the entropy density is positive in the bulk and at the boundaries of the domain of interest. The resulting model consists of two equations, a heat-like equation and a mass-conservation equation that describes how the atom density changes in time and space. The model is simple, yet it can properly capture the variation in the free energy landscape as the temperature is changed. We describe the procedure for constructing a temperature-atom-density phase diagram using this energy landscape, and we give a simple demonstration of solidification using the model.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v55n4.22.01

Journal of Mathematical Study, Vol. 55 (2022), Iss. 4 : pp. 337–357

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Phase field crystal classical density functional theory entropy production heat transfer solidification melting.

Author Details

Cheng Wang

Steven M. Wise

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