Meniscus shape and contact angle of a slightly deformed axisymmetric drop

Although the meniscus of a pure liquid drop placed on a perfectly smooth and homogeneous solid surface is a spherical cap (when gravity is negligible and the contact angle finite), the general solution of Laplace's capillary equation represents a complex mathematical task. The author obtains a formulation for the limited class of problems in which an essentially axisymmetric sessile drop of low intrinsic contact angle is perturbed by weak heterogeneities, either chemical or physical, on the solid surface. The contact line is disturbed from its circular form by local (positive) heterogeneities and an effect of 'digitation' results. Modification of the meniscus, although becoming attenuated, extends to the drop centre.