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A transition in the spatially integrated reaction rate of bimolecular reaction‐diffusion systems
Author(s) -
Arshadi Masoud,
Rajaram Harihar
Publication year - 2015
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr017674
Subject(s) - reaction rate , diffusion , context (archaeology) , perturbation (astronomy) , chemical reaction , mechanics , work (physics) , chemical kinetics , front (military) , thermodynamics , chemistry , chemical physics , kinetics , geology , physics , meteorology , classical mechanics , catalysis , paleontology , quantum mechanics , biochemistry
Numerical simulations of diffusion with bimolecular reaction demonstrate a transition in the spatially integrated reaction rate—increasing with time initially, and transitioning to a decrease with time. In previous work, this reaction‐diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), leading to predictions that front motion scales ast , and correspondingly the spatially integrated reaction rate decreases as the square root of time1 / t. We present a general nondimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the spatially integrated reaction rate scales astrather than1 / t. The duration of this early time regime (where the spatially integrated reaction rate is kinetically rather than diffusion controlled) is shown to depend on the kinetic rate parameters, diffusion coefficients, and initial concentrations of the two species. Numerical simulation results confirm the theoretical estimates of the transition time. We present illustrative calculations in the context of in situ chemical oxidation for remediation of fractured rock systems where contaminants are largely dissolved in the rock matrix. We consider different contaminants of concern (COCs), including TCE, PCE, MTBE, and RDX. While the early time regime is very short lived for TCE, it can persist over months to years for MTBE and RDX, due to slow oxidation kinetics.