{
  "abstract": "We investigate theoretically the propagation of dendrites along an undercooled solid substrate. Our approach takes into account the heat diffusion in the substrate, and the solid and liquid domains, coupled by the Stefan condition at the solid–liquid interface. Using dimensional and asymptotic analysis, we deduce a simplified model in which diffusion in the liquid and horizontally in the substrate can be neglected. We obtain a self-similar solution consisting of a half-parabolic dendrite shape propagating at constant speed. We derive a scaling law for the maximum velocity, set by the Gibbs–Thomson and kinetic effects, which is in good agreement with experimental results from the literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Ellen Luckins"
    },
    {
      "name": "Christophe Josserand"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2pt9c9bkf09t9.bib",
  "cited_by": 0,
  "doi": "10.1017/jfm.2026.11944",
  "fulltext_url": null,
  "id": "2pt9c9bkf09t9",
  "issns": [
    "0022-1120",
    "1469-7645"
  ],
  "landing_url": "https://hal.science/hal-05805058v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.nlin"
    ],
    [
      "openalex",
      "2505|Solidification and crystal growth phenomena"
    ]
  ],
  "openalex": "W7171346587",
  "pdf_url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6715A2F1CFEA5B5489CBEEE40102F0EB/S0022112026119442a.pdf/div-class-title-modelling-the-growth-of-dendrites-on-cold-substrates-div.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": "Cambridge University Press (CUP)",
  "ris": "https://research.draconitic.com/paper/2pt9c9bkf09t9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05805058",
      "source": "hal",
      "url": "https://hal.science/hal-05805058v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "hal:0.nlin",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Modelling the growth of dendrites on cold substrates",
  "title_text": "Modelling the growth of dendrites on cold substrates",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/2pt9c9bkf09t9",
  "venue": "Journal of Fluid Mechanics",
  "versions": []
}