Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field $\mathit{u}$ when the system is segregated into two phases (at low temperatures) with a sharp interface between them. $\mathit{u}$ 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 $\mathit{u}$. 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.

• Received 20 August 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.235701