Bond Number Revisited: Two-Dimensional Macroscopic Pendant Drop.

The definition of the Bond number, which is widely used for the qualitative description of the shape and stability of a macroscopic pendant drop, is revisited. Two new numbers, named Rbθ and Rbλ, are introduced for two kinds of two-dimensional pendant drops, which have a constant contact angle and a constant width of drop-solid contact, respectively. These numbers contain only input parameters such as the volume of the drop, gravitational acceleration, fluid densities, surface tensions, and contact angles. This distinguishes them from the traditional Bond number, which involves, in addition to the input parameters, prior unknown experimentally derived characteristics of the drop, e.g., height of the drop or radius of the curvature at the drop apex. It is shown that, when properly defined, the new numbers can be used, in particular, for predicting the breakup conditions of the drop and estimating their shape.