The sessile liquid drop. I. Symmetric case

Quantitative estimates are derived, describing the size and shape of a symmetric (idealized) liquid drop, resting in gravitational equilibrium on a plane surface 77. The free surface interface is determined by the conditions that its mean curvature be a given (increasing) linear function of distance from , that it enclose with a prescribed volume V, and that the angle formed with be a prescribed constant . The estimates apply to drops of all sizes, and some are asymptotically exact in the limiting cases of large or small wetted area on 77. It is shown that a number of qualitative features of behavior are determined by the ratio F/sin /2. This ratio is in turn related to a ratio that appears in the study of the circular capillary tube, thus indicating a reciprocity between th,e two problems, which becomes exact in both limiting cases.