Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers

Abstract

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Effect of material anisotropy on the fingering instability in reverse smoldering combustion

“…Fig. 7 shows the solutions of the local boundary value problems (19) for different values of h. In Fig. 7 consistent with the values of the effective thermal conductivity, k eff Isotropic , and mass diffusivity, D eff Isotropic , constants for the isotropic geometry with the same value volume fraction V s of a circular inclusion.…”

“…This is the main objective of the present paper. Recently, the macroscopic description of the smoldering combustion problem has been derived from a basic pore scale description in an isotropic porous medium [9] by using the homogenization theory based on periodic structures [14][15][16][17][18] and two-scale convergence methods [19,20]. The main assumptions related to the method by homogenization, the physics of the phenomenon of interest at the pore scale and the main results deduced from the upscaling procedure are briefly recalled in Section 2.…”

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

“…Reaction-diffusion equations posed for thin layers endowed with periodic microstructures arise as mathematical models for a large number of real-world applications. Prominent examples refer, for instance, to blood flow through the blood vessels (here one considers the blood vessel walls as thin membranes with periodic microstructures), membrane filtration (see [23]), passage of oxygen particles through paperboard or through some other paper-based packaging materials (see [31]), formation of fingers in smoldering combustion [17], heat and current flow through thin organic light-emitting diodes (OLEDs) mounted on glass substrates [20].…”

“…We mention here but a few of them which we think are closer to our investigations. Linear reaction-diffusion-convection equations coupled with non-linear surface chemical reactions for infinitely thin layers were studied in [17] in the context of smoldering combustion. In [16], the authors studied pressure-driven Stokes flow through a infinitely thin layer.…”

Upscaling of a double porosity problem with jumps in thin porous media

“…For mathematical studies of similar diffusion problems in thin periodic media, we refer, for instance, to [12], [18], [28], [31], [34], [30], [22], [24], [25] and the references therein. For elasticity problems in related thin periodic domains, we refer to [13], [17], [36], [14], [15], [26], [27].…”