Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion
Nonlinear interactions between chemical reactions and buoyancy-driven Rayleigh-Taylor instability of reaction-diffusion acidity fronts of the chlorite-tetrathionate (CT) reaction are studied theoretically in a vertical Hele-Shaw cell or a porous medium. To do so, we perform a numerical integration o...
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2006
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v124_n1_p_Lima http://hdl.handle.net/20.500.12110/paper_00219606_v124_n1_p_Lima |
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paper:paper_00219606_v124_n1_p_Lima2023-06-08T14:44:11Z Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion Acidity Dynamics Fluid dynamics Optimization Porosity Reaction kinetics Asymptotic dynamics Chlorite-tetrathionate (CT) reaction Reaction-diffusion model Diffusion Nonlinear interactions between chemical reactions and buoyancy-driven Rayleigh-Taylor instability of reaction-diffusion acidity fronts of the chlorite-tetrathionate (CT) reaction are studied theoretically in a vertical Hele-Shaw cell or a porous medium. To do so, we perform a numerical integration of a two-variable reaction-diffusion model of the CT system coupled through an advection term to Darcy's law ruling the evolution of the velocity field of the fluid. The fingering dynamics of these chemical fronts is characterized by the appearance of several fingers at onset. These fingers then undergo coarsening and eventually merge to form one single symmetric finger. We study this asymptotic dynamics as a function of the three dimensionless parameters of the problem, i.e., the Damköhler number Da, the diffusivity ratio δ of the two chemical species, and the Rayleigh number Ra constructed here on the basis of the width Ly of the system. For moderate values of Ra, the asymptotic single finger is shown to have self-similar scaling properties while above a given value of Ra, which depends on the other values of the parameters, tip splitting comes into play. Increasing the difference of diffusivities of the two chemical species (i.e., increasing δ) leads to more efficient coarsening and smaller asymptotic fingers. Experimental procedures to verify our predictions are proposed. © 2006 American Institute of Physics. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v124_n1_p_Lima http://hdl.handle.net/20.500.12110/paper_00219606_v124_n1_p_Lima |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Acidity Dynamics Fluid dynamics Optimization Porosity Reaction kinetics Asymptotic dynamics Chlorite-tetrathionate (CT) reaction Reaction-diffusion model Diffusion |
| spellingShingle |
Acidity Dynamics Fluid dynamics Optimization Porosity Reaction kinetics Asymptotic dynamics Chlorite-tetrathionate (CT) reaction Reaction-diffusion model Diffusion Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion |
| topic_facet |
Acidity Dynamics Fluid dynamics Optimization Porosity Reaction kinetics Asymptotic dynamics Chlorite-tetrathionate (CT) reaction Reaction-diffusion model Diffusion |
| description |
Nonlinear interactions between chemical reactions and buoyancy-driven Rayleigh-Taylor instability of reaction-diffusion acidity fronts of the chlorite-tetrathionate (CT) reaction are studied theoretically in a vertical Hele-Shaw cell or a porous medium. To do so, we perform a numerical integration of a two-variable reaction-diffusion model of the CT system coupled through an advection term to Darcy's law ruling the evolution of the velocity field of the fluid. The fingering dynamics of these chemical fronts is characterized by the appearance of several fingers at onset. These fingers then undergo coarsening and eventually merge to form one single symmetric finger. We study this asymptotic dynamics as a function of the three dimensionless parameters of the problem, i.e., the Damköhler number Da, the diffusivity ratio δ of the two chemical species, and the Rayleigh number Ra constructed here on the basis of the width Ly of the system. For moderate values of Ra, the asymptotic single finger is shown to have self-similar scaling properties while above a given value of Ra, which depends on the other values of the parameters, tip splitting comes into play. Increasing the difference of diffusivities of the two chemical species (i.e., increasing δ) leads to more efficient coarsening and smaller asymptotic fingers. Experimental procedures to verify our predictions are proposed. © 2006 American Institute of Physics. |
| title |
Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion |
| title_short |
Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion |
| title_full |
Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion |
| title_fullStr |
Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion |
| title_full_unstemmed |
Nonlinear fingering dynamics of reaction-diffusion acidity fronts: Self-similar scaling and influence of differential diffusion |
| title_sort |
nonlinear fingering dynamics of reaction-diffusion acidity fronts: self-similar scaling and influence of differential diffusion |
| publishDate |
2006 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v124_n1_p_Lima http://hdl.handle.net/20.500.12110/paper_00219606_v124_n1_p_Lima |
| _version_ |
1768546661394546688 |