Thermodynamics and computation of N-phase diffuse-interface flows

Abstract: Diffuse-interface (phase-field) models provide a versatile framework for interfacial dynamics in multiphase fluids. The prototypical diffuse-interface models for incompressible fluid mixtures are the Navier-Stokes Cahn-Hilliard (NSCH) models. Over the last few decades, many NSCH models with non-matching densities have been proposed. Even though these phase-field models aim to represent the same physical phenomena, they seem to differ at first sight. To explore their connections, I present unifying frameworks for both two-phase and N-phase NSCH models with non-matching densities. I then show that, from the perspective of mixture theory, NSCH models can be understood as reduced diffuse-interface mixture models in which the evolution equations for the diffusive fluxes are replaced by constitutive closures. This perspective naturally leads to diffuse-interface models that are fully compatible with mixture theory and clarifies the relation between classical phase-field formulations and full mixture-theoretic models. I will then turn to constitutive closure and calibration for N-phase NSCH systems. Beyond the standard requirement of reduction consistency when one phase is absent, I consider the stronger condition that physically identical components can be merged without changing the governing PDEs. This leads to a mixture-aware notion of reduction consistency that strongly constrains the admissible constitutive assumptions and, under a small set of structural axioms, uniquely determines the free-energy and mobility structure. To enable practical computations, I will then discuss a thermodynamically consistent calibration procedure for N-phase diffuse-interface free energies that determines a symmetric capillarity matrix matching prescribed pairwise surface tensions. The final part of the talk is concerned with computation. For incompressible mixtures with two or more constituents, structure-preserving computation is challenging because the numerical method should inherit the rich structure of the continuum model, including preservation of the saturation constraint, dissipation of the free energy, and symmetric treatment of all constituents, even for arbitrary density ratios. I will present a symmetric method for incompressible N-phase NSCH mixture models that retains these properties at the fully discrete level. The talk concludes with representative numerical simulations of N-phase flows.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)