Single-file diffusion of interacting particles in a finite-sized channel

Abstract : We study the dynamics of charged macroscopic particles millimetric steel balls confined in a linear channel of finite length, sufficiently narrow to avoid particles crossing. We show that their individual response to thermal fluctuations strongly depends either on their position in the channel or the local potential they experience. Three different dynamical regimes are identified. At small times, a " free regime " takes place, with the outermost particles exhibiting the highest diffusion coefficient. This effect results from an " echo " of the thermal fluctuations reflected by the channel wall. Then, forbidden crossing induces a correlated regime similar to single file diffusion. Surprisingly, the corresponding mobility increases with the local potential. Lastly, the finite length of the channel induces the saturation of fluctuations. We show that those behaviors may be described heuristically with the help of models for N hard-core interacting particles diffusing in a finite channel of length L, provided that we replace the uniform interparticle distance L / N by a characteristic distance k B T / K 1/2 built upon the temperature T and the stiffness K of the local potential. It provides a very satisfactory estimate for the fluctuations sizes, whereas they are greatly overestimated assuming hard-core interactions.
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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2010, 82, 〈10.1103/PhysRevE.82.031201〉
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Jean-Baptiste Delfau, Christophe Coste, Catherine Even, Michel Saint Jean. Single-file diffusion of interacting particles in a finite-sized channel. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2010, 82, 〈10.1103/PhysRevE.82.031201〉. 〈hal-01404851〉

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