Transport properties of Brownian particles confined to a narrow channel by a periodic potential

Xinli Wang, German Drazer

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick-Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of Péclet numbers.

Original languageEnglish (US)
Article number102002
JournalPhysics of Fluids
Volume21
Issue number10
DOIs
StatePublished - Jan 1 2009

Fingerprint

transport properties
cross sections
planetary waves
confining
flow distribution
coefficients
approximation
simulation

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

@article{6c9877a62f274e8d95ad0b672f142e2e,
title = "Transport properties of Brownian particles confined to a narrow channel by a periodic potential",
abstract = "We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick-Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of P{\'e}clet numbers.",
author = "Xinli Wang and German Drazer",
year = "2009",
month = "1",
day = "1",
doi = "10.1063/1.3226100",
language = "English (US)",
volume = "21",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics Publising LLC",
number = "10",

}

Transport properties of Brownian particles confined to a narrow channel by a periodic potential. / Wang, Xinli; Drazer, German.

In: Physics of Fluids, Vol. 21, No. 10, 102002, 01.01.2009.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Transport properties of Brownian particles confined to a narrow channel by a periodic potential

AU - Wang, Xinli

AU - Drazer, German

PY - 2009/1/1

Y1 - 2009/1/1

N2 - We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick-Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of Péclet numbers.

AB - We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick-Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of Péclet numbers.

UR - http://www.scopus.com/inward/record.url?scp=71049185507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71049185507&partnerID=8YFLogxK

U2 - 10.1063/1.3226100

DO - 10.1063/1.3226100

M3 - Article

VL - 21

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 10

M1 - 102002

ER -