Capillary Surface
Capillary Surface is a physical surface model, of constant mean curvature, given by a parametrisation, immersed.
Open Capillary Surface in the interactive viewer →
aperiodic cmc def-parametric immersed implemented physical
Properties
- Family
- physical
- Given by
- a parametrisation
- Curvature
- constant mean curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: solved variationally (energy minimisation with a contact line) by the CMC generator; no formula. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- C. E. Delaunay, "Sur la surface de revolution dont la courbure moyenne est constante", Journal de Mathematiques Pures et Appliquees 6 (1841), 309-314 -- the classification of CMC surfaces of revolution (unduloid, nodoid, catenoid, cylinder, sphere).
- T. Young, "An essay on the cohesion of fluids", Philosophical Transactions of the Royal Society 95 (1805), 65-87 -- the contact-angle condition.
- P. S. de Laplace, "Traite de mecanique celeste", Supplement au livre X (1806) -- the Young-Laplace pressure law.
- J. Plateau, "Statique experimentale et theorique des liquides soumis aux seules forces moleculaires" (1873).
- R. Finn, "Equilibrium Capillary Surfaces", Grundlehren der mathematischen Wissenschaften 284, Springer (1986) -- sessile drops and capillary theory.
- P.-G. de Gennes, F. Brochard-Wyart, D. Quere, "Capillarity and Wetting Phenomena" (Springer, 2004) -- capillary length, Bond number, and the gravity-flattened puddle thickness h = 2 l_c sin(theta/2).