Shape of a small sessile drop and the determination of contact angle

Abstract

Free liquid surfaces in equilibrium are described by the Laplace capillary equation with suitable boundary conditions generally given in terms of the contact angle. By a fortuitous formulation in the axisymmetric case, the second order ordinary differential equation can be reduced to a pair of coupled first-order equations. For the case of a small liquid drop, the present formulation allows perturbation solutions to second order to be derived in closed form. Furthermore the solutions obtained can be used to calculate contact angles, if the height and maximum width of the drop is known, the method being equally simple whether the contact angle is less than or greater than 90°.