Sharp interface motion of a binary fluid mixture

Sorin Bastea, Raffaele Esposito, Joel L. Lebowitz, Rossana Marra

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)445-483
Number of pages39
JournalJournal of Statistical Physics
Volume124
Issue number2-4
DOIs
StatePublished - Aug 2006

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Binary fluids
  • Interface evolution
  • Navier-Stokes equations
  • Phase segregation

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