Bond Number Revisited: Axisymmetric Macroscopic Pendant Drop

The numbers Rb_θ and Rb introduced recently (Berim, G.O.; Ruckenstein, E. J. Phys. Chem. 2019, 123, 10294-10300) to characterize the cylindrical pendant drops hanging from the solid surface are modified for characterization of axisymmetric pendant drops which are more common in experiment. Similar to the case of cylindrical drops, Rb_θ and Rb are defined on the basis of rigorous solution of Young-Laplace equation for the drop profile. As a consequence, they contain only the input parameters of the drop-solid system such as the volume of the drop, gravitational acceleration, fluid densities, surface tension, and contact angle. This constitutes the main difference between Rb numbers and traditional Bond and Bond-like numbers which involve the dimensions of the drop unknown prior to the experiment (e.g., height of the drop or radius of curvature at the drop apex). It is shown, that the new numbers can be used, for example, for predicting the breakup conditions of the drop, determining the surface tension, and estimating the deviation of drop shape from the circular one. A good agreement between theoretical predictions and experimental results known from the literature was demonstrated.