Thermophoresis of Brownian particles driven by coloured noise

TL;DR

This paper theoretically investigates how coloured noise and temperature gradients influence the long-term behavior of Brownian particles, revealing that thermophoretic transport can vary in magnitude and direction based on particle parameters.

Contribution

It introduces a homogenization approach to derive the thermophoretic coefficient considering coloured noise and temperature effects, explaining experimental observations.

Findings

Thermophoretic coefficient can change sign and magnitude.

Particles can accumulate in colder or warmer regions depending on parameters.

Long-term distribution depends on particle mobility and temperature dependence.

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.