A direct relation between bending energy and contact angles for capillary bridges

Abstract

The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line.

Keywords

• Distortion of nonaxisymmetric capillary bridges
• Mean and Gaussian curvatures impact
• Euler characteristic
• Generalized Young–Laplace equation
• Bending effects
• Fenchel’s theorem in differential geometry
• Gauss–Bonnet Theorem
• Geodesic curvature
• Bending stress
• Influence of the contact angles