On the description of Brownian particles in confinement on a non-Cartesian coordinates basis

We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the...

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Veröffentlicht in:The Journal of chemical physics 2016-08, Vol.145 (7), p.074105-074105
Hauptverfasser: Dagdug, Leonardo, García-Chung, Angel A., Chacón-Acosta, Guillermo
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Sprache:eng
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Zusammenfassung:We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4960652