The aim of this paper is to analyze the convection and diffusion of a solute in a porous medium, ... more The aim of this paper is to analyze the convection and diffusion of a solute in a porous medium, under the influence of non‐smooth chemical reactions taking place on the pore surfaces. Our model consists of a system of two coupled convection‐diffusion equations, one in the fluid part and another one on the boundaries of the grains of the porous medium. The coupling is made through a nonlinear reaction term, modeling the mass exchange between the bulk and, respectively, the surface concentration.
An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
The model analyzed in this paper has its origins in the description of composites made by a hosti... more The model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction. In a previous paper (Amar in IFB 21:41–59, 2019), by means of a concentration procedure, the internal layer was replaced by an imperfect interface. The present paper is concerned with the concentration of the external coating layer and the homogenization, via the periodic unfolding method, of the resulting model, which is far from being a standard one. Despite the fact that the limit problem looks like a classical Dirichlet problem for an elliptic equation, in the construction of the homogenized matrix and of the source term, a very delicate analysis is required.
ABSTRACT. This paper deals with the homogenization of a nonlinear problem mod-elllng chemica! rea... more ABSTRACT. This paper deals with the homogenization of a nonlinear problem mod-elllng chemica! reactive flows through periodically perforated domains. The chemical reactions take place on the walls of the porous médium. The effective behavior of these reactive flows is described by a new elliptic boundary-value problem contalning an extra zero-order term which captures the effect of the chemical reactions. 1.
The homogenization of some reaction-diffusion problems in a highly heterogeneous composite medium... more The homogenization of some reaction-diffusion problems in a highly heterogeneous composite medium formed by two connected constituents separated by an imperfect interface is analyzed. The main feature of our setting is represented by the fact that, across this imperfect interface, both the solution and its flux are assumed to exhibit jumps. Several models arise at the limit. In particular, a modified bidomain model is obtained and compared to some existing models in the literature (see [1]-[4]). Our results can serve as a tool for biochemists interested in studying the complex mechanisms involved in the calcium dynamics in living cells.
The aim of this paper is to analyze the convection and diffusion of a solute in a porous medium, ... more The aim of this paper is to analyze the convection and diffusion of a solute in a porous medium, under the influence of non‐smooth chemical reactions taking place on the pore surfaces. Our model consists of a system of two coupled convection‐diffusion equations, one in the fluid part and another one on the boundaries of the grains of the porous medium. The coupling is made through a nonlinear reaction term, modeling the mass exchange between the bulk and, respectively, the surface concentration.
An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
The model analyzed in this paper has its origins in the description of composites made by a hosti... more The model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction. In a previous paper (Amar in IFB 21:41–59, 2019), by means of a concentration procedure, the internal layer was replaced by an imperfect interface. The present paper is concerned with the concentration of the external coating layer and the homogenization, via the periodic unfolding method, of the resulting model, which is far from being a standard one. Despite the fact that the limit problem looks like a classical Dirichlet problem for an elliptic equation, in the construction of the homogenized matrix and of the source term, a very delicate analysis is required.
ABSTRACT. This paper deals with the homogenization of a nonlinear problem mod-elllng chemica! rea... more ABSTRACT. This paper deals with the homogenization of a nonlinear problem mod-elllng chemica! reactive flows through periodically perforated domains. The chemical reactions take place on the walls of the porous médium. The effective behavior of these reactive flows is described by a new elliptic boundary-value problem contalning an extra zero-order term which captures the effect of the chemical reactions. 1.
The homogenization of some reaction-diffusion problems in a highly heterogeneous composite medium... more The homogenization of some reaction-diffusion problems in a highly heterogeneous composite medium formed by two connected constituents separated by an imperfect interface is analyzed. The main feature of our setting is represented by the fact that, across this imperfect interface, both the solution and its flux are assumed to exhibit jumps. Several models arise at the limit. In particular, a modified bidomain model is obtained and compared to some existing models in the literature (see [1]-[4]). Our results can serve as a tool for biochemists interested in studying the complex mechanisms involved in the calcium dynamics in living cells.
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