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Peer-reviewedCC BYJournal of Fluid Mechanics

Modelling the growth of dendrites on cold substrates

  • Ellen Luckins
  • Christophe Josserand
Open at sourcePDFDOICite

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.

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Cite

BibTeXRIS
BibTeX
@article{luckins2026modelling,
  title = {{Modelling the growth of dendrites on cold substrates}},
  author = {Ellen Luckins and Christophe Josserand},
  journal = {Journal of Fluid Mechanics},
  year = {2026},
  month = aug,
  doi = {10.1017/jfm.2026.11944},
  url = {https://hal.science/hal-05805058v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Modelling the growth of dendrites on cold substrates
AU  - Ellen Luckins
AU  - Christophe Josserand
PY  - 2026
DA  - 2026/08/28
JO  - Journal of Fluid Mechanics
DO  - 10.1017/jfm.2026.11944
UR  - https://hal.science/hal-05805058v1
AB  - 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.
SN  - 0022-1120
SN  - 1469-7645
ER  -