The probability distribution of a trapped Brownian particle in plane shear flows

Abstract

We investigate the statistical properties of an over-damped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and they are substantiated by numerical results. There is a good agreement between the two approaches for a wide range of parameters.

arXiv comment5 pages, 4 figure

References in corpus (6)

• Vesicles in a Poiseuille flow
• Direct measurement of shear-induced cross-correlations of Brownian motion
• Dynamics of a trapped Brownian particle in shear flows
• Brownian motion of finite-inertia particles in a simple shear flow
• Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models
• Particles held by springs in a linear shear flow exhibit oscillatory motion

Cited by in corpus (1)

• Time correlations and persistence probability of a Brownian particle in a shear flow