On Brinkman flows with curvature-induced phase separation in binary mixtures
Authors
- Colli, Pierluigi
ORCID: 0000-0002-7921-5041 - Gilardi, Gianni
ORCID: 0000-0002-0651-4307 - Signori, Andrea
ORCID: 0000-0001-7025-977X - Sprekels, Jürgen
ORCID: 0009-0000-0618-8604
2020 Mathematics Subject Classification
- 35K35 35Q35 76D07 76T99
Keywords
- Membrane-fluid interaction, Brinkman-type flow, sixth-order Cahn--Hilliard equation, incompressible flow, weak solutions,, vanishing Darcy limit
DOI
Abstract
The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically consistent framework. In this work, we study a novel Brinkman--Cahn--Hilliard system, coupling a sixth-order phase-field evolution with a Brinkman-type momentum equation featuring variable shear viscosity. The Cahn--Hilliard equation includes a nonconservative source term accounting for mass exchange, and the velocity equation contains a non divergence-free forcing term. We establish the existence of weak solutions in a divergence-free variational framework, and, in the case of constant mobility and shear viscosity, prove uniqueness and continuous dependence on the forcing. Additionally, we analyze the Darcy limit, providing existence results for the corresponding reduced system.
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