Bond Number Revisited: Axisymmetric Macroscopic Pendant Drop

Identities for droplets with circular footprint on tilted surfaces

Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface). The identities are put under test both by the available solutions of a linear response approximation at small Bond numbers as well as the ones obtained from numerical solutions, making use of the Surface Evolver software. The subtleties to obtain certain angle-averages appearing in identities by the numerical solutions are discussed in detail. It is argued how the identities are useful in two respects. First is to replace some unknown values in the Young-Laplace equation by their expressions obtained from the identities. Second is to use the identities to estimate the error for approximate analytical or numerical solutions without any reference to an exact solution.

An Analytical Two-Dimensional Linearized Droplet Shape Model for Combined Tangential and Normal Body Forces

In view of emerging research on forced wetting under complex applied forces, a simple model for a droplet shape evolution is developed here. In particular, the model refers to droplet spreading under quasisteady conditions. The corresponding linearized two-dimensional Young–Laplace equation is solved analytically resulting in a system of two equations that relates the droplet shape features to each other. Despite its simplicity, the final model produces a wealth of droplet behaviors when combined with the physical requirement that the contact angle should be within a particular range of values. Indicative results of the droplet behavior under several forces scenarios are examined here exhibiting why the present model is useful for designing experimental campaigns on forced spreading.