Volume 99, Number 6, September 2012
|Number of page(s)||6|
|Published online||02 October 2012|
Thermophoresis of Brownian particles driven by coloured noise
1 Department of Mathematics, University of Arizona - Tucson, AZ 85721 USA
2 Department of Physics, Bilkent University - Cankaya, Ankara 06800, Turkey
Received: 11 June 2012
Accepted: 27 August 2012
Brownian motion of microscopic particles is driven by collisions with surrounding fluid molecules. The resulting noise 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 of magnitude as the inertial time-scale over which the particle's kinetic energy is lost due to friction. 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's 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 time-scales are taken to zero keeping their ratio constant and derive the thermophoretic transport coefficient, which, we find, can vary in both magnitude and sign, as observed in experiments. Studying the long-term stationary particle distribution, we show that particles accumulate towards the colder (positive thermophoresis) or the hotter (negative thermophoresis) regions depending on their physical parameters.
PACS: 05.60.-k – Transport processes / 05.40.Jc – Brownian motion / 47.61.-k – Micro- and nano- scale flow phenomena
© EPLA, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.