Sharp interface motion of a binary fluid mixture

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

doi:10.1007/s10955-006-9040-z

Sharp interface motion of a binary fluid mixture

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

Research output: Contribution to journal › Article › peer-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, 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)
Pages (from-to)	445-483
Number of pages	39
Journal	Journal of Statistical Physics
Volume	124
Issue number	2-4
DOIs	https://doi.org/10.1007/s10955-006-9040-z
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

Access to Document

10.1007/s10955-006-9040-z

Fingerprint Dive into the research topics of 'Sharp interface motion of a binary fluid mixture'. Together they form a unique fingerprint.

Cite this

@article{7fe5af4d6e964117bf48bf902f57929c,

title = "Sharp interface motion of a binary fluid mixture",

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.",

keywords = "Binary fluids, Interface evolution, Navier-Stokes equations, Phase segregation",

author = "Sorin Bastea and Raffaele Esposito and Lebowitz, {Joel L.} and Rossana Marra",

note = "Funding Information: Three of the authors (R. E., J. L. L and R. M.) thank Professor J.P. Bourguignon for kind hospitality at the I.H.{\'E}.S.; R.M. and R. E. were partially supported by MIUR, INDAM-GNFM; J.L.L. was supported by AFORS grant AF 49620-01-1-0154. This work has also been supported by the European Commission through its 6th Framework Program “Structuring the European Research Area” and the contract Nr. RITA-CT-2004-505493 for the provision of Transnational Access implemented as Specific Support Action.",

year = "2006",

month = aug,

doi = "10.1007/s10955-006-9040-z",

language = "English (US)",

volume = "124",

pages = "445--483",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "2-4",

}

TY - JOUR

T1 - Sharp interface motion of a binary fluid mixture

AU - Bastea, Sorin

AU - Esposito, Raffaele

AU - Lebowitz, Joel L.

AU - Marra, Rossana

N1 - Funding Information: Three of the authors (R. E., J. L. L and R. M.) thank Professor J.P. Bourguignon for kind hospitality at the I.H.É.S.; R.M. and R. E. were partially supported by MIUR, INDAM-GNFM; J.L.L. was supported by AFORS grant AF 49620-01-1-0154. This work has also been supported by the European Commission through its 6th Framework Program “Structuring the European Research Area” and the contract Nr. RITA-CT-2004-505493 for the provision of Transnational Access implemented as Specific Support Action.

PY - 2006/8

Y1 - 2006/8

N2 - 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.

AB - 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.

KW - Binary fluids

KW - Interface evolution

KW - Navier-Stokes equations

KW - Phase segregation

UR - http://www.scopus.com/inward/record.url?scp=33751049066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751049066&partnerID=8YFLogxK

U2 - 10.1007/s10955-006-9040-z

DO - 10.1007/s10955-006-9040-z

M3 - Article

AN - SCOPUS:33751049066

VL - 124

SP - 445

EP - 483

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2-4

ER -