## 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, f_{i} (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 language | English (US) |
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Pages (from-to) | 445-483 |

Number of pages | 39 |

Journal | Journal of Statistical Physics |

Volume | 124 |

Issue number | 2-4 |

DOIs | |

State | Published - Aug 2006 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

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