Blog
About

14
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Homogenization of a pore scale model for precipitation and dissolution in porous media

      Preprint

      , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a coupled system of evolution equations, involving a parabolic equation and an ordinary differential equation. The former models ion transport and is defined in a periodically perforated medium. It is further coupled through the boundary conditions to the latter, defined on the boundaries of the perforations and modelling the dissolution and precipitation of the precipitate. The main challenge is in dealing with the dissolution and precipitation rates, which involve a monotone but multi-valued mapping. Due to this, the micro-scale solution lacks regularity. With \(\ep\) being the scale parameter (the ratio between the micro scale and the macro scale length), we adopt the 2-scale framework to achieve the convergence of the homogenization procedure as \(\ep\) approaches zero.

          Related collections

          Most cited references 22

          • Record: found
          • Abstract: not found
          • Article: not found

          Homogenization and Two-Scale Convergence

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            A General Convergence Result for a Functional Related to the Theory of Homogenization

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              The Periodic Unfolding Method in Homogenization

                Bookmark

                Author and article information

                Journal
                27 January 2014
                Article
                1401.7025

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                CASA Report 13-32, Eindhoven University of Technology (2013)
                math.AP

                Comments

                Comment on this article