Bridge equilibrium solutions connecting a liquid lens and a sessile drop

DIEZ, JAVIER A.; RAVAZZOLI, PABLO D.; GONZÁLEZ, A. G.

Indianapolis

Congreso; 75th Annual Meeting of the Division of Fluid Dynamics; 2022

American Physical Society

We study the deformation of an axisymmetric sessile drop of liquid A on a horizontal substrate when the surrounding liquid B partially covers it. Thus, the drop adopts the shape of a liquid bridge that connects the substrate with the interface between the surrounding liquid and the air (fluid C). By applying both the Neumann´s law at the triple point where fluids A, B and C meet and the Young´s law at the contact line formed by the interface between liquids A and B at the solid, we find set of six second order differential equations along with the corresponding twelve boundary conditions. Aside from the symmetry conditions, we also apply no--flow conditions at the wall of the cylindrical container of liquid B. We numerically solve the equations by determing the nine unknowns parameters of the system, and we find the shape of the three interfaces (AB, BC and AC). We find two solutions with a neck. One of the solutions has at least one inflection point, while the other one does not. By performing an energy analysis, we find that the former is more likely to be found in nature (less energetic). In order to assert if a neck rupture is likely to occur, we compare the bridge energies with that of the corresponding separate drops configuration (a sessile drop plus a liquid lens).