Evaluation and linking of effective parameters in particle-based models and continuum models for mixing-limited bimolecular reactions

Abstract

Particle-based models and continuum models have been developed to quantify mixing-limited bimolecular reactions for decades. Effective model parameters control reaction kinetics, but the relationship between the particle-based model parameter (such as the interaction radius R) and the continuum model parameter (i.e., the effective rate coefficient Kf) remains obscure. This study attempts to evaluate and link R and Kf for the second-order bimolecular reaction in both the bulk and the sharp-concentration-gradient (SCG) systems. First, in the bulk system, the agent-based method reveals that R remains constant for irreversible reactions and decreases nonlinearly in time for a reversible reaction, while mathematical analysis shows that Kf transitions from an exponential to a power-law function. Qualitative link between R and Kf can then be built for the irreversible reaction with equal initial reactant concentrations. Second, in the SCG system with a reaction interface, numerical experiments show that when R and Kf decline as t-1/2 (for example, to account for the reactant front expansion), the two models capture the transient power-law growth of product mass, and their effective parameters have the same functional form. Finally, revisiting of laboratory experiments further shows that the best fit factor in R and Kf is on the same order, and both models can efficiently describe chemical kinetics observed in the SCG system. Effective model parameters used to describe reaction kinetics therefore may be linked directly, where the exact linkage may depend on the chemical and physical properties of the system. ©2013. American Geophysical Union. All Rights Reserved.