Hydrodynamics of binary fluid phase segregation

TL;DR

This paper derives and supports a hydrodynamic model for binary fluid phase segregation starting from kinetic equations, showing the velocity field obeys incompressible Navier-Stokes with interface conditions, supported by numerical simulations.

Contribution

It provides a derivation of hydrodynamic equations for phase-segregated binary fluids from the Vlasov-Boltzmann framework, including interface conditions and numerical validation.

Findings

Velocity field satisfies incompressible Navier-Stokes equations.

Interface moves with the normal component of the velocity.

Numerical simulations support the theoretical analysis.

Abstract

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field $\bm{u}$ when the system is segregated into two phases (at low temperatures) with a sharp interface between them. $\bm{u}$ satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of $\bm{u} $. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.