Communications in Mathematical Sciences

Volume 18 (2020)

Number 3

Analysis of the energy dissipation laws in multi-component phase field models

Pages: 875 – 885

(Fast Communication)

DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n3.a13

Authors

Arkadz Kirshtein (Department of Mathematics, Pennsylvania State University, University Park, Pa., U.S.A.)

James Brannick (Department of Mathematics, Pennsylvania State University, University Park, Pa., U.S.A.)

Chun Liu (Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Il., U.S.A.)

Abstract

In this paper, two approaches for modeling three-component fluid flows using diffuse interface method are discussed. Thermodynamic consistency of the proposed models is preserved when using an energetic variational framework to derive the coupled systems of partial differential equations that comprise the resulting models. The issue of algebraic and dynamic consistency is investigated. In addition, the two approaches that are presented are compared analytically and numerically.

Keywords

diffusive interface method, phase field, complex fluids, mixtures

2010 Mathematics Subject Classification

35G50, 35Q35, 35R35

Full Text (PDF format)

The work of Arkadz Kirshtein and Chun Liu is partially supported by NSF grant DMS-1759536. The work of Arkadz Kirshtein and James Brannick is partially supported by NSF grant DMS-1620346.

Received 22 May 2018

Accepted 19 December 2019

Published 30 June 2020