{
  "abstract": "We study a coupled Stokes-reaction-diffusion-advection system in a three dimensional domain perforated by a large number of evolving spherical inclusions with radii of order $\\varepsilon^α$ for $α\\in(1,3]$. Their centers are separated on the order of $\\varepsilon$ but are not assumed to form a periodic lattice. The inclusions grow or shrink through an interfacial adsorption-desorption mechanism, so that the evolution of the geometry is coupled to the Stokes-reaction-diffusion-advection system. We first establish well-posedness on arbitrary large time intervals for sufficiently small $\\varepsilon$. We then derive quantitative homogenization limits in terms of the limiting empirical measure describing the spatial distribution and size of the inclusions. Its evolution is governed by a continuity equation in the radius variable, and the convergence of the empirical measures is controlled in the $2$-Wasserstein distance. In the critical case, $α=3$, the Stokes system converges to a Brinkman system, while non-vanishing concentration boundary layers modify the microscopic exchange law for the reaction-diffusion-advection equation. For $α\\in(1,3)$, the limit is of Darcy type and the original exchange law is retained. The homogenization results are quantitative and provide explicit error estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28489",
  "author_total": 2,
  "authors": [
    {
      "name": "Michael Eden"
    },
    {
      "name": "Richard M. Höfer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ean6twc6stc7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28489",
  "fulltext_url": null,
  "id": "3ean6twc6stc7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28489",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7204805957",
  "pdf_url": "https://arxiv.org/pdf/2608.28489",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ean6twc6stc7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2608.28489",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28489"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Reactive Flow around Spherically Evolving Particles in Critical and Supercritical Dilute Regimes",
  "title_text": "Reactive Flow around Spherically Evolving Particles in Critical and Supercritical Dilute Regimes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/3ean6twc6stc7",
  "venue": "arXiv",
  "versions": []
}