10.1007/s10955-006-9040-z |
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| Authors: | Sorin Bastea Raffaele Esposito Joel L Lebowitz Rossana Marra |
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| Institution: | (1) Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550, USA;(2) Dipartimento di Matematica, Universit degli Studi di L'Aquila, Coppito, 67100, L'Aquila, Italy;(3) Departments of Mathematics and Physics, Rutgers University, New Brunswick, NJ 08903, USA;(4) Dipartimento di Fisica, Università di Roma Tor Vergata e INFN, 00133 Roma, Italy |
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| 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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| Keywords: | Interface evolution Navier-Stokes equations Binary fluids Phase segregation |
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