Abstract
We derive hydrodynamic equations describing the evolution of a binary fluid segregated into two regions, each rich in one species,which are separated (on the macroscopic scale) by a sharp interface. Our starting point is a Vlasov-Boltzmann (VB) equation describing the evolution of the one particle position and velocity distributions, fi (x, v, t), i = 1, 2. The solution of the VB equation is developed in a Hilbert expansion appropriate for this system. This yields incompressible Navier-Stokes equations for the velocity field u and a jump boundary condition for the pressure across the interface. The interface, in turn, moves with a velocity given by the normal component of u.
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Bastea1, S., Esposito, R., Lebowitz, J.L. et al. 10.1007/s10955-006-9040-z. J Stat Phys 124, 445–483 (2006). https://doi.org/10.1007/s10955-006-9040-z
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DOI: https://doi.org/10.1007/s10955-006-9040-z