Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 25: Brownian Motion and Transport
DY 25.3: Talk
Thursday, March 29, 2012, 10:15–10:30, MA 004
Biased and flow driven Brownian motion in periodic channels — •Steffen Martens1, Arthur Straube1, Gerhard Schmid2, Lutz Schimansky-Geier1, and Peter Hänggi2 — 1Humboldt-University Berlin, Department of Physics, Newtonstr. 15, 12489 Berlin, Germany — 2University Augsburg, Department of Physics, Universitaetsstr. 1, 86135 Augsburg, Germany
We investigate the role of the hydrodynamic flow field on the transport of a Brownian particle in a two-dimensional channel structure exhibiting smoothly varying periodic channel width. In particular, we will present an extension of the so-called Fick-Jacobs approximation [Zwanzig 1992] in order to describe the transport of point-size Brownian particles under the influence of an external force field V(q) as well as an applied flow field u(q,t). This is achieved by means of an asymptotic analysis [Martens et al., Phys. Rev. E 2011, Martens et al., Chaos 2011] to the components of the flow field and to stationary probability density for the particle’s position within the channel. We demonstrate how the problem of biased Brownian dynamics in a confined 2D geometry can be reduced to the case of Brownian motion in an effective periodic one-dimensional potential Ψ(x) which takes the external bias, the change of the local channel width, and the flow velocity component in longitudinal direction into account. The influence of the external bias and the pressure drop on the transport quantities like the averaged velocity and the effective diffusion coefficient are studied in detail. The analytic findings are confirmed by numerical simulations of the particle dynamics in a reflection symmetric sinusoidal channel.