Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids

ten Eikelder, Marco F.P.; van der Zee, Kristoffer G.; Schillinger, Dominik

Abstract

The prototypical diffuse-interface model for incompressible fluid mixtures is the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model. Despite its foundation in continuum mixture theory, it is not fully compatible with this theory due to the diffusive flux approximation. This paper introduces a class of thermodynamically consistent diffuse-interface incompressible fluid mixture models that is fully compatible with the continuum theory of mixtures. The proposed models can be formulated in either constituent or mixture quantities, enabling a direct comparison with the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model with non-matching densities. This comparison reveals the key modelling simplifications employed in the latter.

Citation

ten Eikelder, M. F., van der Zee, K. G., & Schillinger, D. (2024). Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. Journal of Fluid Mechanics, 990, Article A8. https://doi.org/10.1017/jfm.2024.502

• Journal Article Type: Article
• Acceptance Date: May 13, 2024
• Online Publication Date: Aug 12, 2024
• Publication Date: Jul 10, 2024
• Deposit Date: May 16, 2024
• Publicly Available Date: Jan 11, 2025
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 990
• Article Number: A8
• DOI: https://doi.org/10.1017/jfm.2024.502
• Keywords: Navier–Stokes equations
• Public URL: https://nottingham-repository.worktribe.com/output/34864883
• Additional Information: Copyright: © The Author(s), 2024. Published by Cambridge University Press.; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.; Free to read: This content has been made available to all.