Harmonically bound Brownian motion in fluids under shear: Fokker-Planck and generalized Langevin descriptions

Humberto Híjar
Phys. Rev. E 91, 022139 – Published 27 February 2015

Abstract

We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
4 More
  • Received 13 May 2014

DOI:https://doi.org/10.1103/PhysRevE.91.022139

©2015 American Physical Society

Authors & Affiliations

Humberto Híjar*

  • Grupo de Sistemas Inteligentes, Facultad de Ingeniería, Universidad La Salle, Benjamín Franklin 47, 06140, D. F., México

  • *humberto.hijar@lasallistas.org.mx

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 91, Iss. 2 — February 2015

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×