publication . Article . 2013

Fickian and non-Fickian diffusion with bimolecular reactions

Yotam Berkowitz; Yaniv Edery; Harvey Scher; Brian Berkowitz;
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  • Published: 25 Mar 2013 Journal: Physical Review E, volume 87 (issn: 1539-3755, eissn: 1550-2376, Copyright policy)
  • Publisher: American Physical Society (APS)
Abstract
Mixing zone dynamics of a reaction product $C$ during diffusion of two species ($A$ and $B$) are examined, using a two-dimensional particle tracking model (PT) for the reaction $A+B\ensuremath{\rightarrow}C$, allowing for both Fickian and non-Fickian transitions. The form of PT we use is equivalent to a continuous time random walk, which is a widely used model for anomalous transport and diffusion. It is shown that the basic patterns of the $C$ dynamics---the temporal evolution of the spatial profile and the temporal $C$ production---are similar for both modes of diffusion. However, the distinctive time scale for the non-Fickian case is very much larger even whe...
Subjects
arXiv: Physics::Geophysics
free text keywords: Statistics and Probability, Statistical and Nonlinear Physics, Condensed Matter Physics, Particle, Reaction product, Statistical physics, Diffusion process, Physics, Gaussian, symbols.namesake, symbols, Exponential function, Reaction front, Fick's laws of diffusion, Continuous-time random walk, Classical mechanics
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