Shape of sessile drops at small contact angles

The shape of a sessile drop on horizontal substrate depends upon the Bond number $Bo$ and contact angle $\alpha$ . Inspired by puddle approximations at large (Quéré, Rep. Prog. Phys. , vol. 68, 2005, p. 2495), we address here limit small angles fixed volume arbitrary It readily leads to pancake approximation, where height radius scale as $\alpha ^{-1/2}$ respectively, with capillary forces being appreciable only near edge. approximation breaks down for $Bo=\textrm {ord}(\alpha ^{2/3})$ In that distinguished limit, gravitational are comparable throughout, ^{2/3}$ ^{-1/3}$ respectively. For $Bo\ll \alpha these scalings remain, turning into spherical cap. asymptotic results compared numerical solution exact problem.