Abstract
Equilibrium shapes and the stability of capillary bridges between parallel and nonparallel solid surfaces are determined. Asymptotic and computer-aided techniques from bifurcation theory are used to determine the limits of stability in terms of the minimum volume of fluid in the bridge. These critical values depend on the contact angle, θ c, its hysteresis range, and the dihedral angle between the plates, 2β. If gravity is present and acts away from the apex of the dihedral angle, then it is possible to balance the net surface tension force on the bridge even when the contact angle around the perimeter exhibits no hysterisis. Different shapes are grouped together into families of like symmetry, and values of volume are calculated for which no solution, or multiple solutions, exist. The relation of this problem to Rayleigh's stability of a liquid jet is discussed.
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