Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field [Formula presented] when the system is segregated into two phases (at low temperatures) with a sharp interface between them. [Formula presented] 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 [Formula presented]. 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.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)