Bending effects distorting axisymmetric capillary bridges. Generalized Young–Laplace equation and associated capillary forces

This study proposes a theoretical contribution to the problem of the various distortions affecting axisymmetric capillary bridges, due to gravity or to bending effects linked to the Gaussian curvature. We deduce a clear hierarchization of effects between various reference configurations and put in a prominent position an exact first integral for the Young–Laplace equations, classical or generalized. These relationships are taken advantage of to obtain the theoretical expression of the varying inter-particle force, quantified effects of flexural strength. Finally, we establish a generalization of the classical “gorge method” to calculate accurately the capillary force of a profile subjected to distorsion due to bending when the gravity effects are negligible or not taken into account.