Numerical study of A+A→ and A+B→ reactions with inertia

Romero, Aldo H.; Palacio, Ana María Lacasta; Sancho, J. M.; Lindenberg, Katja

doi:10.1063/1.2779327

Cited by 12 publications

(16 citation statements)

References 37 publications

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“…These observations have motivated intense research toward alternative modeling schemes. Among these, particle tracking (PT) methodologies are considered to be effective techniques to provide appropriate depictions of some of the salient features of reactive transport scenarios [ Gillespie , 1977; Fabriol et al , 1993; Cao et al , 2005; Romero et al , 2007; Palanichamy et al , 2009; Edery et al , 2009].…”

Section: Introductionmentioning

confidence: 99%

Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation

Sánchez-Vila

Fernàndez-García

Guadagnini

2010

Water Resources Research

121

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[1] We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The experiment involves advection-dominated transport in porous media of three dissolved species, i.e., two reactants undergoing a fast irreversible reaction and the resulting product. The authors found that their observations could not be properly fitted with a model based on an advection-dispersion-reaction equation (ADRE) assuming the reaction was instantaneous, the actual measured total reaction product being lower than predictions for all times. The data have been recently well reproduced by Edery et al. (2009Edery et al. ( , 2010) by means of a particle tracking approach in a continuous time random walk framework. These and other authors have questioned the use of partial differential equation (PDE)-based approaches to quantify reactive transport because of the difficulty in capturing local-scale mixing and reaction. We take precisely this approach and interpret the experiments mentioned by means of a continuum-scale model based on the ADRE. Our approach differs from previous modeling attempts in that we imbue effects of incomplete mixing at the pore scale in a time-dependent kinetic reaction term and show that this model allows quantitative interpretation of the experiments in terms of both reaction product profiles and time-dependent global production rate. The time dependence of the kinetic term presented accounts for the progressive effects of incomplete mixing due to pore-scale rate-limited mass transfer, and follows a power law, which is consistent with the compilation of existing experiments reported by Haggerty et al. (2004). Our interpretation can form the basis for further research to assess the potential use of PDE approaches for the interpretation of reactive transport problems in moderately heterogeneous media.Citation: Sanchez-Vila, X., D. Fernàndez-Garcia, and A. Guadagnini (2010), Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation, Water Resour.

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Section: Introductionmentioning

confidence: 99%

Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation

Sánchez-Vila

Fernàndez-García

Guadagnini

2010

Water Resources Research

121

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“…[6] Since it was described by Smoluchowski about a century ago the particle tracking (PT) approach has been implemented widely in various fields of study [e.g., Fabriol et al, 1993;Sun, 1999;Cao et al, 2005;Lindenberg and Romero, 2007;Palanichamy et al, 2007;Srinivasan et al, 2007;Yuste et al, 2008;Benson and Meerschaert, 2008]. These studies suggest different ways to follow a particle while specifying, probabilistically, reaction rules among particles.…”

Section: Introductionmentioning

confidence: 99%

Particle tracking model of bimolecular reactive transport in porous media

Edery

Scher

Berkowitz

2010

Water Resources Research

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[1] We use a particle tracking approach to analyze the dynamics that control bimolecular reactive transport (A + B → C) in porous media. Particle transitions are governed by spatial and temporal distributions to account for the transport within a continuous time random walk framework. Particle tracking simulations are compared to measurements from a laboratory experiment of bimolecular reactive transport in a constant flow field. The simulations capture the experimental sequence of evolving C particle profiles using a marginally Fickian temporal distribution to quantify the particle transitions. The first profile is a fit with the model parameters, and subsequent ones are predictions. The rate of production of reaction product C over time is found to follow a power law. At early times after the injection of A particles into a uniform distribution of B particles, the strong contact and reaction between A and B particles induces the formation of a spatial void between the reactants. At longer times, the production of C is nearly constant and depends on the fluctuations of velocities of reactant particles that can surmount the void. We probe the behavioral dependence of the A, B, and C spatial profiles on the spectra of velocity fluctuations of the reactants. The latter are generated by different temporal distributions, namely, a decaying exponential distribution, which is equivalent to advective-dispersive (Fickian) transport, and the truncated power law with degrees of non-Fickian behavior, which is characteristic of transport in heterogeneous media. We demonstrate that the C profile exhibits subtle dynamics because of competition between the dispersion (spreading of the plumes) of A and B and the (power law) production rate.

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“…An exponent smaller than that predicted by the classical mass law, α < 1, is generally attributed to the formation of persistent spatio-temporal structures in the reactant distributions. 22,23 Following this interpretation, one may expect that introducing some…”

Section: Introductionmentioning

confidence: 97%

Active diffusion limited reactions

Debnath

Ghosh

et al. 2019

The Journal of Chemical Physics

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We investigate the one-and two-dimensional diffusion limited reactions A + A → 0 and A + B → 0 with A active Janus particles and B passive particles in thermal equilibrium. We show that by increasing the self-propulsion time of the A particles, the reactant densities decay faster, at least for time transients of potential interest for chemical applications, e.g., to develop smart drug delivery protocols. Asymptotic and transient density decays obey power laws with exponents that depend on the actual annihilation reaction and its dimensionality.

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Numerical study of A+A→ and A+B→ reactions with inertia

Cited by 12 publications

References 37 publications

Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation

Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation

Particle tracking model of bimolecular reactive transport in porous media

Active diffusion limited reactions

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