Resolution of the Young–Laplace equation by a geometrical method using curvatur

Mathieu Gentes (1) , Germain Rousseaux (1) , Pierre Coullet (1) , Pierre-Gilles de Gennes (1, 2, 3)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 Institut Curie [Paris]
3 CdF (institution) - Collège de France

We revisit from a modern viewpoint a graphical method of resolution of the Young–Laplace equation proposed by Thomson in 1886 and improved by Boys in 1893. This method, relying on some axisymmetry properties, was applied to the case of pendant drops, drops on a horizontal plane and meniscii. The several initials conditions necessitated a numerical implementation of the Thomson's algorithm, particularly in order to obtain pendant drops with multiple bulges. A scaling law for the variation of the drops radii forming this rosary (string of drops) is presented.

Mots clés: Young–Laplace equation; Thomson's algorithm; Pendant drop; String of drops

Domaines: Dynamique des Fluides [physics.flu-dyn]

Mathieu Gentes, Germain Rousseaux, Pierre Coullet, Pierre-Gilles de Gennes. Resolution of the Young–Laplace equation by a geometrical method using curvatur. Comptes Rendus. Physique, 2005, 6, pp.1027-1033. ⟨10.1016/j.crhy.2005.11.009⟩. ⟨hal-00016262⟩