Reaction-anomalous diffusion processes for A+B⇌C

Wen-Biao Zhang and Ming Yi

Physica A: Statistical Mechanics and its Applications, 2019, vol. 527, issue C

Abstract: In this paper, we study the bimolecular chemical reaction system A+B⇌C under anomalous diffusion. The master equations for reaction-anomalous diffusion processes are given by the CTRW model, which follows from conservation laws. Moreover, under appropriate assumptions, we derive the fractional reaction-anomalous equations at the macroscopic level from the CTRW model. Based on these equations, the system’s statistical properties are analyzed. It is illustrated that, in addition the integer second-order moment under the normal Brownian motion meeting Einstein’s relation, some fractional order moments are also linearly proportional to time t. These findings are related to the complexity of reversible bimolecular reactions under the circumstances of anomalous diffusion.

Keywords: Anomalous diffusion; CTRW; Fractional reaction-anomalous diffusion equation; Generalized Einstein’s relation (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119307952

DOI: 10.1016/j.physa.2019.121347

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