Communications in Mathematical Sciences
Volume 18 (2020)
Analysis of the energy dissipation laws in multi-component phase field models
Pages: 875 – 885
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.
diffusive interface method, phase field, complex fluids, mixtures
2010 Mathematics Subject Classification
35G50, 35Q35, 35R35
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