English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the diffusion-reaction-advection model for mobile chemical speciestogether with the dissolution and precipitation of immobile species in a porousmedium at the micro-scale. This leads to a system of semilinear parabolicpartial differential equations in the pore space coupled with a nonlinearordinary differential equation at the grain boundary of the solid matrices. Thefluid flow within the pore space is given by unsteady Stokes equation. Thenovelty of this work is to do the iterative limit analysis of the system bytackling the nonlinear terms, monotone multi-valued dissolution rate term,space-dependent non-identical diffusion coefficients and nonlinearprecipitation (reaction) term. We also establish the existence of a uniquepositive global weak solution for the coupled system. In addition to that, forupscaling we introduce a modified version of the extension operator. Finally,we conclude the paper by showing that the upscaled model admits a uniquesolution.

Limiting analysis of a crystal dissolution and precipitation model coupled with the unsteady stokes equations in the context of porous media flow