Theoretical and Experimental Analysis of the Equilibrium Contours of Liquid Bridges of Arbitrary Shape

Abstract

The equilibrium shape of the liquid bridge interface is analyzed theoretically and experimentally.Both axisymmetric and nonaxisymmetric perturbations are considered. The axisymmetric deviationsare those related to volume effects, the difference between the radii of the disks, and the axial forcesacting on the liquid bridge. The nonaxisymmetric deviations are those due to the eccentricity of thedisk and the action of lateral forces. The theoretical study is performed using three differenttechniques: ~i! an analytical expansion around the cylindrical solution, ~ii! a finite differencescheme, and ~iii! an approximate numerical approach valid only for slight nonaxisymmetricdeviations. The results of the three methods are compared systematically. There is a very goodagreement between the analytical and the numerical approaches for contours which are close tocylindrical, and the agreement extends to configurations with only moderate deviations fromcylindrical. Experiments are performed using the so-called neutral buoyancy or plateau technique.Theoretical and experimental contours are compared considering a wide range of values for theparameters characterizing the perturbations. In general, the finite difference method providesreasonably accurate predictions even for large deviations of the liquid bridge contour fromcylindrical.