Profile and departure size of condensation drops on vertical surfaces

The problem of the equilibrium shape and departure size of two-dimensional dropwise condensation drops on a vertical surface is considered. The equation of the surface of the drop is obtained by minimizing (for a given volume) the total energy of the drop, consisting of surface and gravitational energy, using the techniques of variational calculus. The solution is tractable once the advancing contact angle is known, and is taken as an approximation to the axial meridian profile of a three-dimensional drop. The receding contact angle is obtained as part of the solution. The drop size is specified by imposing its vertical length. Upon increasing this vertical length, a point is reached at which no real solution exists, and this is taken as the departure size of the drop. Comparison with measured departure sizes under various body forces from standard to 100 times earth gravity are good.