Diffusion–reaction–dissolution–precipitation model in a heterogeneous porous medium with nonidentical diffusion coefficients: Analysis and homogenization

Article type: Research Article

Authors: Ghosh, Nibedita | Mahato, Hari Shankar^{; *}

Affiliations: Department of Mathematics, IIT Kharagpur, WB 721302, India

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We study a pore-scale model where two mobile species with different diffusion coefficients react and precipitate in the form of immobile species (crystal) on the surface of the solid parts in a porous medium. The reverse may also happen, i.e. the crystals may dissolute to give mobile species. The mathematical modeling of these processes will give rise to a coupled system of ordinary and partial differential equations. We first prove the existence of a unique nonnegative global weak solution and then upscale the model from microscale to macroscale.

Keywords: Reactive transport, diffusion–reaction–dissolution–precipitation, Langmuir reaction rates, global existence, homogenization, asymptotic analysis, two-scale convergence, boundary unfolding

DOI: 10.3233/ASY-221763

Journal: Asymptotic Analysis, vol. 130, no. 3-4, pp. 553-587, 2022