Thermophoresis of Brownian particles driven by coloured noise

Abstract

The Brownian motion of microscopic particles is driven by the collisions with the molecules of the surrounding fluid. The noise associated with these collisions is not white, but coloured due, e.g., to the presence of hydrodynamic memory. The noise characteristic time scale is typically of the same order as the time over which the particle's kinetic energy is lost due to friction (inertial time scale). We demonstrate theoretically that, in the presence of a temperature gradient, the interplay between these two characteristic time scales can have measurable consequences on the particle long-time behaviour. Using homogenization theory, we analyse the infinitesimal generator of the stochastic differential equation describing the system in the limit where the two characteristic times are taken to zero; from this generator, we derive the thermophoretic transport coefficient, which, we find, can vary in both magnitude and sign, as observed in experiments. Furthermore, studying the long-term stationary particle distribution, we show that particles can accumulate towards the colder (positive thermophoresis) or the warmer (negative thermophoresis) regions depending on the dependence of their physical parameters and, in particular, their mobility on the temperature.

arXiv comment9 pages, 4 figures

References in corpus (4)

• Influence of Noise on Force Measurements
• Drift without flux: Brownian walker with a space dependent diffusion coefficient
• Force measurement in the presence of Brownian noise: Equilibrium distribution method vs. Drift method
• Noise-induced drift in stochastic differential equations with arbitrary friction and diffusion in the Smoluchowski-Kramers limit

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• The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
• Thermophoresis of an Antiferromagnetic Soliton
• Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Localization-delocalization transitions in turbophoresis of inertial particles
• The small-mass limit and white-noise limit of an infinite dimensional Generalized Langevin Equation
• On phoretic clustering of particles in turbulence
• Power-law statistics in the velocity fluctuations of Brownian particle in inhomogeneous media and driven by colored noise
• Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis
• Anisotropic active Brownian particle with a fluctuating propulsion force
• A small delay and correlation time limit of stochastic differential delay equations with state-dependent colored noise