Two phase micropolar fluid flow with unmatched densities modeled by Navier--Stokes--Cahn--Hilliard systems: Local strong well-posedness and consistency estimates

TL;DR

This paper establishes the local well-posedness and consistency of a phase field model for binary micropolar fluid mixtures with unmatched densities, extending previous Newtonian fluid models to include internal rotations.

Contribution

It introduces a thermodynamically consistent micropolar fluid model with unmatched densities and proves local strong solution existence and model consistency.

Findings

Proved local-in-time strong solutions exist for the micropolar fluid model.

Established a consistency relation between micropolar and Newtonian fluid models.

Extended the mathematical framework to include internal rotations in binary fluid mixtures.

Abstract

We study a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. Furnishing with classical no-slip, no-spin and no-flux boundary conditions, in a smooth and bounded three-dimensional domain, we establish the well-posedness of local-in-time strong solutions. Since the model studied is a generalization of the earlier model introduced by Abels, Garcke and Gr\"un for binary Newtonian fluids with unmatched densities, we provide a consistency result between the corresponding strong solutions to both models in terms of a parameter associated to the micro-rotation viscosity.