title: On the description of Brownian particles in confinement on a non-Cartesian coordinates basis.
abstract: 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.
authors.affiliation: Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, México D. F. 09340, Mexico.
authors.forename: Leonardo
authors.initials: L
authors.lastname: Dagdug
authors.affiliation: Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, México D. F. 09340, Mexico.
authors.forename: Angel A
authors.initials: AA
authors.lastname: García-Chung
authors.affiliation: Applied Mathematics and Systems Department, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, México D. F. 05348, Mexico.
authors.forename: Guillermo
authors.initials: G
authors.lastname: Chacón-Acosta