Estudo do Coeficiente de Difusão Secundária em Problema de Difusão com Fluxo Bimodal
DOI:
https://doi.org/10.5540/tema.2020.021.02.229Keywords:
Difusão bimodal, Difusão anômala, Método de Diferenças Finitas, Equação diferencial de quarta ordem.Abstract
Uma formulação recentemente desenvolvida para o problema de difusão anômala com termo de quarta ordem apresentou em determinadas situações particulares valores negativos na solução. Neste trabalho é realizado um estudo do efeito coeficiente de difusão secundária visando contribuir para o entendimento do comportamento das soluções nestas situações. Foi implementada uma função para representar a variação na parcela sujeita a difusão primária e secundária, de acordo com a quantidade da propriedade em difusão. Os resultados obtidos são compatíveis com aqueles apresentados em trabalhos anteriores na literatura.
References
R. Metzler, J.-H. Jeon, A. G. Cherstvy, and E. Barkai, “Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking,” Phys. Chem. Chem. Phys., vol. 16, no. 44, pp. 24128–24164, 2014.
J. Wu and K. M. Berland, “Propagators and Time-Dependent Diffusion Coefficients for Anomalous Diffusion,” Biophysical Journal, vol. 95, pp. 2049–2052, 8 2008.
M. J. Saxton, “Anomalous diffusion due to obstacles: a Monte Carlo study,” Biophysical Journal, vol. 66, pp. 394–401, 2 1994.
P. F. Nealey, R. E. Cohen, and A. S. Argon, “Limited-supply non-Fickian diffusion in glassy polymers,” Polymer, vol. 36, pp. 3687–3695, 1 1995.
J. I. Ramos, “On the numerical treatment of an ordinary differential equation arising in one-dimensional non-Fickian diffusion problems,” Computer Physics Communications, vol. 170, pp. 231–238, 8 2005.
P. M. Smith and M. M. Fisher, “Non-Fickian diffusion of water in melamineformaldehyde resins,” Polymer, vol. 25, pp. 84–90, 1 1984.
V. Ganti, M. M. Meerschaert, E. Foufoula-Georgiou, E. Viparelli, and G. Parker, “Normal and anomalous diffusion of gravel tracer particles in rivers,” Journal of Geophysical Research: Earth Surface, vol. 115, 6 2010.
L. Bevilacqua, A. C. N. R. Galeão, and F. P. Costa, “A new analytical formulation of retention effects on particle diffusion processes,” Anais da Academia Brasileira de Ciências, vol. 83, pp. 1443–1464, 2011.
L. Bevilacqua, A. C. N. R. Galeão, and F. P. Costa, “On the significance of higher order differential terms in diffusion processes,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 33, pp. 166–175, 2011.
L. Bevilacqua, A. C. N. R. Galeão, J. G. Simas, and A. P. R. Doce, “A new theory for anomalous diffusion with a bimodal flux distribution,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, pp. 1–10, 2013.
R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-state and Time-dependent Problems. Philadelphia: SIAM, 2007.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.