### Abstract

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.

Original language | English (US) |
---|---|

Article number | 60002 |

Journal | EPL |

Volume | 99 |

Issue number | 6 |

DOIs | |

State | Published - Sep 2012 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*EPL*,

*99*(6), [60002]. https://doi.org/10.1209/0295-5075/99/60002

**Thermophoresis of Brownian particles driven by coloured noise.** / Hottovy, Scott; Volpe, Giovanni; Wehr, Jan.

Research output: Contribution to journal › Article

*EPL*, vol. 99, no. 6, 60002. https://doi.org/10.1209/0295-5075/99/60002

}

TY - JOUR

T1 - Thermophoresis of Brownian particles driven by coloured noise

AU - Hottovy, Scott

AU - Volpe, Giovanni

AU - Wehr, Jan

PY - 2012/9

Y1 - 2012/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84867539526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867539526&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/99/60002

DO - 10.1209/0295-5075/99/60002

M3 - Article

VL - 99

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 6

M1 - 60002

ER -