A continuous time random walk (CTRW) integro-differential equation with chemical interaction

Autor: Alon Nissan, Harvey Scher, Brian Berkowitz, Rami Ben-Zvi
Rok vydání: 2018
Předmět:
Zdroj: The European Physical Journal B. 91
ISSN: 1434-6036
1434-6028
DOI: 10.1140/epjb/e2017-80417-8
Popis: A nonlocal-in-time integro-differential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M (t), which includes the source of non-Fickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is non-linear and second-order, relevant for a bimolecular reaction A + B → C. The interaction term ΓP A (s, t) P B (s, t) is symmetric in the concentrations of A and B (i.e. P A and P B ); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M (t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRW-PT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media.
Databáze: OpenAIRE
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