Mesoscopic simulation of Brownian particles confined in harmonic traps and sheared fluids

We consider the motion of a Brownian particle bound by a harmonic force in a thermal bath driven from equilibrium by a uniform shear imposed externally. We extend the classical theory of Brownian motion to calculate the probability distribution function for finding the Brownian particle in a phase-space volume element when it is in the presence of the external shear. We find the explicit form of the reduced distribution for velocities in the stationary limit and show that it becomes anisotropic by extending itself over the direction of the imposed shear. We also consider the effects of the imposed shear on the time correlation functions of the Brownian particle and show that these quantities acquire contributions depending exclusively on the nonequilibrium state of the solvent, which render them non symmetric and time-irreversible. In order to verify these conclusions we develop a hybrid mesoscopic simulation technique based on Molecular Dynamics and Multi-particle Collision Dynamics. We observe a very good agreement between the predictions of the model and the results obtained independently from the simulation method, thus suggesting that the latter could be used as a complement to current experimental procedures.