A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness

Boschman, Anne; Espath, Luis; van der Zee, Kristoffer G.

Abstract

In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surface materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a bulk-surface dynamics, which is postulated on a material body P where the boundary ∂P may lose smoothness, that is, the normal field may be discontinuous on an edge ∂ 2P. The final set of equations somewhat resemble the Navier–Stokes–Cahn–Hilliard equation for the bulk and the surface. Aside from the systematical treatment based on a specialized version of the virtual power principle and free-energy imbalances for bulk-surface theories, we consider two additional ingredients: an explicit dependency of the apparent surface density on the surface thickness and mixed boundary conditions for the velocity, chemical potential, and microstructure.

Citation

Boschman, A., Espath, L., & van der Zee, K. G. (2024). A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness. Physica D: Nonlinear Phenomena, 460, Article 134055. https://doi.org/10.1016/j.physd.2024.134055

• Journal Article Type: Article
• Acceptance Date: Jan 10, 2024
• Online Publication Date: Jan 13, 2024
• Publication Date: 2024-04
• Deposit Date: Jan 14, 2024
• Publicly Available Date: Jan 17, 2024
• Journal: Physica D: Nonlinear Phenomena
• Print ISSN: 0167-2789
• Electronic ISSN: 1872-8022
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 460
• Article Number: 134055
• DOI: https://doi.org/10.1016/j.physd.2024.134055
• Keywords: Bulk-surface partial differential equations; Continuum mechanics; Fluid Mechanics
• Public URL: https://nottingham-repository.worktribe.com/output/29743217
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S016727892400006X?via%3Dihub