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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Humberto Híjar

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 t...Continue Reading

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Dec 24, 2013·The Journal of Chemical Physics·Humberto Híjar

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Citations

Jan 20, 2018·Physical Review. E·Yunyun LiPulak K Ghosh

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