Authors: Sorin Bastea, Raffaele Esposito, Joel L. Lebowitz, and Rossana Marra
ABSTRACT
Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we
derive an equation for the velocity field u when the system is segregated
into two phases (at low temperatures) with a sharp interface between
them. 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 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.
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