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Peer-reviewedCC BY-NC 4.0Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées

On the structure of the critical Reynolds number for roll-wave instability in generalized Newtonian falling films

  • François Rousset
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Abstract

We investigate the critical Reynolds number for the onset of long-wave instability in gravity-driven flows of generalized Newtonian fluids. A new factorized representation is derived, revealing the underlying structure of the problem and reducing the analysis to a small number of dimensionless quantities. This framework yields a universal lower bound valid for all admissible rheologies, together with several explicit upper and lower bounds. Sharper bounds are obtained for shear-thinning fluids in the presence of a yield stress. In the shear-thinning case, we establish an optimal universal upper bound. The optimal constant is attained in the Newtonian case.

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Cite

BibTeXRIS
BibTeX
@article{rousset2026structure,
  title = {{On the structure of the critical Reynolds number for roll-wave instability in generalized Newtonian falling films}},
  author = {François Rousset},
  journal = {Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées},
  year = {2026},
  month = oct,
  doi = {10.1007/s00033-026-02957-9},
  url = {https://hal.science/hal-05838814v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - JOUR
TI  - On the structure of the critical Reynolds number for roll-wave instability in generalized Newtonian falling films
AU  - François Rousset
PY  - 2026
DA  - 2026/10/23
JO  - Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées
DO  - 10.1007/s00033-026-02957-9
UR  - https://hal.science/hal-05838814v1
AB  - We investigate the critical Reynolds number for the onset of long-wave instability in gravity-driven flows of generalized Newtonian fluids. A new factorized representation is derived, revealing the underlying structure of the problem and reducing the analysis to a small number of dimensionless quantities. This framework yields a universal lower bound valid for all admissible rheologies, together with several explicit upper and lower bounds. Sharper bounds are obtained for shear-thinning fluids in the presence of a yield stress. In the shear-thinning case, we establish an optimal universal upper bound. The optimal constant is attained in the Newtonian case.
SN  - 0044-2275
SN  - 1420-9039
ER  -