Numerical study assessing the applicability of the reduction to effective one-dimensional description of diffusion in a hemispherical shaped tube

• Published in: Journal of non-Newtonian fluid mechanics 2010-09, Vol.165 (17), p.987-991
• Main Authors: Vázquez, Marco-Vinicio, Dagdug, Leonardo
• Format: Article
• Language: English
• Subjects: Computer simulation; Diffusion; Diffusion coefficient; Mathematical analysis; Mathematical models; Non Newtonian fluids; Reduction; Tubes
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2010.02.011

Computational simulations of a Brownian particle diffusing in a hemispherical shaped tube were run to assess the range of applicability of the reduction of the three-dimensional diffusion to an effective one-dimensional description. On a previous work, for a conical tube, Berezhkovskii et al. [18] found that the one-dimensional description using the Fick–Jacobs' equation with a position dependent diffusion coefficients, D ( x ) (one suggested by Zwanzig [11], and another by Reguera–Rubí [12]), have a restricted range of applicability. Unexpectedly, our results show that applying the Zwanzig’s formula one can predict variation of τ in the whole range of a / R in n → w direction, while the Reguera–Rubí’s formula fits numerical data in the w → n direction. This is a remarkable result since it is known that Reguera–Rubí’s predicts better the mean first-passage time’s behavior without regard of direction in other geometries, and this is the main result of this paper.