Hydrodynamics of Brownian particles

Pierre-Henri Chavanis

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 3, 375-396

Abstract: When considering the hydrodynamics of Brownian particles, one is confronted to a difficult closure problem. One possibility to close the hierarchy of hydrodynamic equations is to consider a strong friction limit. This leads to the Smoluchowski equation that reduces to the ordinary diffusion equation in the absence of external forces. Unfortunately, this equation has infinite propagation speed leading to some difficulties. Another possibility is to make a Local Thermodynamic Equilibrium (L.T.E) assumption. This leads to the damped Euler equation with an isothermal equation of state. However, this approach is purely phenomenological. In this paper, we provide a preliminary discussion of the validity of the L.T.E assumption. To that purpose, we consider the case of free Brownian particles and harmonically bound Brownian particles for which exact analytical results can be obtained [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943)]. For these systems, we find that the L.T.E. assumption is not unreasonable and that it can be improved by introducing a time dependent kinetic temperature Tkin(t)=γ(t)T instead of the bath temperature T. We also compare hydrodynamic equations and generalized diffusion equations with time dependent diffusion coefficients.

Keywords: Brownian motion; Fokker–Planck equations; Hydrodynamics (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437109008279
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:3:p:375-396

DOI: 10.1016/j.physa.2009.09.050

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().