arXiv subjects

Kin Shing Chan

Publications and source records attributed to Kin Shing Chan.

3 recordsLinked to original sources

arXiv2025

Two phase micropolar fluid flow with nonlocal energies: Existence theory, nonpolar limits and nonlocal-to-local convergence

We study a nonlocal variant of a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. The model is described by a Navier--Stokes--Cahn--Hilliard system that extends the earlier nonlocal variants of the model introduced by Abels, Garcke and Gr\"un for binary Newtonian fluid mixtures with unmatched densities. We establish the global 3D weak existence and global 2D strong well-posedness, followed by the weak convergence of the nonlocal model to its local counterpart as the nonlocal interaction kernel approaches the Dirac delta distribution. In the two dimensional setting we provide consistency estimates between strong solutions of the nonlocal micropolar model and strong solutions of nonlocal variants of the Abels--Garcke--Gr\"un model and Model H.

math.AP↗

arXiv2025

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

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.

math.AP↗

arXiv2025

On a phase field model for binary mixtures of micropolar fluids with non-matched densities and moving contact lines

We introduce a new phase field model for binary mixtures of incompressible micropolar fluids, which are among the simplest categories of fluids exhibiting internal rotations. The model fulfils local and global dissipation inequalities so that thermodynamic consistency is guaranteed. Our model consists of a Navier--Stokes--Cahn--Hilliard system for the fluid velocity, pressure, phase field variable and chemical potential, coupled to an additional system of Navier--Stokes type for the micro-rotation. Our model accounts for non-matched densities as well as moving contact line dynamics, and serve as a generalisation to earlier models for binary fluid flows based on a volume averaged velocity formulation. We also establish the existence of global weak solutions in three spatial dimensions for the model equipped with singular logarithmic and double obstacle potentials.

math.AP↗