Reversible A↔B reaction–diffusion process with initially mixed reactants: Boundary layer function approach

Sinder, M.

doi:10.1016/j.physb.2011.05.003

Cited by 6 publications

(6 citation statements)

References 32 publications

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“…where G 1 ( , ; ) and G 2 ( , ; ) correspond to the Green function for each species and C(0) represents the quantity of particles which may initially be present on the surface. These Green functions are obtained by solving the following equation: by taking into account the suitable boundary conditions for each species related to (17) and (18). Thus, the solutions given by (17) and (18) are obtained from the combination of (15), (16), and (19) by taking into account their boundary conditions, following the procedure employed in [58].…”

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

“…These Green functions are obtained by solving the following equation: by taking into account the suitable boundary conditions for each species related to (17) and (18). Thus, the solutions given by (17) and (18) are obtained from the combination of (15), (16), and (19) by taking into account their boundary conditions, following the procedure employed in [58]. It is also interesting to note that the boundary conditions chosen for the Green function were performed in order to evidence the adsorption-desorption process manifested by the surface on the distribution ( , ).…”

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

“…In (17) and (18), the first term promotes the spreading of the initial condition and the other terms represent the influence of the surface on the diffusive process in the bulk. Thus, we need to quantify these terms, in order to obtain the solution for each species.…”

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

“…By using the previous equations, the inverse of Laplace transform of (17) and (18) Equations (41) and (42) are the solutions for the scenario analyzed here, which is characterized by a diffusion with processes occurring on a surface. By using these results, it is possible to obtain the survival probability, which is defined as 1(2) ( ) = ∫ ∞ 0 1(2) ( , ) and it is related to the quantity of particles each species present in the bulk.…”

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

“…In this sense, it is worth not only studying chemical reactions on substrates, but also analyzing different phenomena occurring in a given surface, for example, the adsorption of proteins [9][10][11][12], which can be controlled by nanoroughness on the surface of the material [13,14] or hybridization of DNA [15][16][17], among others. In these systems, different species may diffuse and react [18][19][20][21], which implies considering suitable changes in the diffusion equation or in the boundary conditions to account for the processes of interest [18,19,22,23]. These contexts usually are analyzed by using the standard approaches related to Markovian processes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Diffusion Process and Reaction on a Surface

Fuziki

Lenzi

Ribeiro

et al. 2018

Advances in Mathematical Physics

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We investigate the influence of the surface effects on a diffusive process by considering that the particles may be sorbed or desorbed or undergo a reaction process on the surface with the production of a different substance. Our analysis considers a semi-infinite medium, where the particles may diffuse in contact with a surface with active sites. For the surface effects, we consider integrodifferential boundary conditions coupled with a kinetic equation which takes non-Debye relation process into account, allowing the analysis of a broad class of processes. We also consider the presence of the fractional derivatives in the bulk equations. In this scenario, we obtain solutions for the particles in the bulk and on the surface.

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Section: Diffusion and Surface Effectsmentioning

confidence: 99%

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Diffusion Process and Reaction on a Surface

Fuziki

Lenzi

Ribeiro

et al. 2018

Advances in Mathematical Physics

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Viscous Fingering of Reversible Reactive Flows in Porous Media

Alhumade

Azaiez

2014

Transactions on Engineering Technologies

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Enhanced reaction kinetics and reactive mixing scale dynamics in mixing fronts under shear flow for arbitrary Damköhler numbers

Bandopadhyay

Borgne

Méheust

et al. 2017

Advances in Water Resources

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Mixing fronts, where fluids of different chemical compositions mix with each other, are known to represent hotspots of chemical reaction in hydrological systems. These fronts are typically subjected to velocity gradients, ranging from the pore scale due to no slip boundary conditions at fluid solid interfaces, to the catchment scale due to permeability variations and flow line geometries. A common trait of these processes is that the mixing interface is strained by shear. Depending on the Péclet number P e, which represents the ratio of the characteristic diffusion time to the characteristic advection time, and the Damköhler number Da, which represents the ratio of the characteristic diffusion time to the characteristic reaction time, the local reaction rates can be strongly impacted by the dynamics of the mixing interface. This impact has been characterized mostly either in kinetics-limited or in mixing-limited conditions, that is, for either very low or very high Da. Here the coupling of shear flow and chemical reactivity is investigated for arbitrary Damköhler numbers, for a bimolecular reaction and an initial interface with separated reactants. Approximate analytical expressions for the global production rate and reactive mixing scale are derived based on a reactive lamella approach that allows for a general coupling between stretching enhanced mixing and chemical reactions. While for P e < Da, reaction kinetics and stretching effects are decoupled, a scenario which we name "weak stretching", for P e > Da, we uncover a "strong stretching" scenario where new scaling laws emerge from the interplay between reaction kinetics, diffusion, and stretching. The analytical results are validated against numerical simulations. These findings shed light on the effect of flow heterogeneity on the enhancement of chemical reaction and the creation of spatially localized hotspots of reactivity for a broad range of systems ranging from kinetic limited to mixing limited situations.

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Reversible A↔B reaction–diffusion process with initially mixed reactants: Boundary layer function approach

Cited by 6 publications

References 32 publications

Diffusion Process and Reaction on a Surface

Diffusion Process and Reaction on a Surface

Viscous Fingering of Reversible Reactive Flows in Porous Media

Enhanced reaction kinetics and reactive mixing scale dynamics in mixing fronts under shear flow for arbitrary Damköhler numbers

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