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PreprintCC BY 4.0arXiv

Fluid deformable surfaces with variable thickness - a Surface Shallow-Water-Helfrich model

  • Jan Magnus Sischka
  • Axel Voigt
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Abstract

Epithelial tissues play a fundamental role in morphogenesis. Mechanically they can be viewed as thin soft materials exhibiting a solid-fluid duality. The Surface Navier-Stokes-Helfrich model accounts for these properties by combining bending and surface hydrodynamics. In order to account for varying cell thickness we incorporate a thickness field in the spirit of a shallow-water equation, but defined on the (self-)evolving surface. This replaces the inextensibility constraint of the two-dimensional fluid and with it the conservation of surface area by an incompressibility constraint of the thin film fluid allowing for changes in surface area. We develop a numerical scheme based on surface finite elements, perform convergence tests, demonstrate the impact on shape evolution of closed surfaces with a constant enclosed volume and discuss implications on modeling morphogenesis.

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Cite

BibTeXRIS
BibTeX
@misc{sischka2026fluid,
  title = {{Fluid deformable surfaces with variable thickness - a Surface Shallow-Water-Helfrich model}},
  author = {Jan Magnus Sischka and Axel Voigt},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11903},
  eprint = {2610.11903},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11903},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fluid deformable surfaces with variable thickness - a Surface Shallow-Water-Helfrich model
AU  - Jan Magnus Sischka
AU  - Axel Voigt
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11903
UR  - https://arxiv.org/abs/2610.11903
AB  - Epithelial tissues play a fundamental role in morphogenesis. Mechanically they can be viewed as thin soft materials exhibiting a solid-fluid duality. The Surface Navier-Stokes-Helfrich model accounts for these properties by combining bending and surface hydrodynamics. In order to account for varying cell thickness we incorporate a thickness field in the spirit of a shallow-water equation, but defined on the (self-)evolving surface. This replaces the inextensibility constraint of the two-dimensional fluid and with it the conservation of surface area by an incompressibility constraint of the thin film fluid allowing for changes in surface area. We develop a numerical scheme based on surface finite elements, perform convergence tests, demonstrate the impact on shape evolution of closed surfaces with a constant enclosed volume and discuss implications on modeling morphogenesis.
ER  -