An approximate theory describing the profile of a sessile drop

Abstract

The profile of an axisymmetric sessile drop is described by an analytically insoluble second-order differential equation, which can be obtained either from Laplace's equation or by employing the calculus of variations to minimise the free energy of the solid/liquid/fluid system. Most reported methods of solution involve numerical integration and although some very accurate data have been calculated in this way, the purpose of the present study is to present a simple method of obtaining approximate sessile drop profiles by applying a form of first-order perturbation theory. Provided that certain conditions are satisfied, the technique allows contact angles to be calculated without recourse to tables or elaborate calculation facilities. Although the method is neither as precise nor as general as studies involving numerical integration on computers, it has the advantage of reducing the subjectivity of direct contact angle measurement. The technique, in its present form, is applicable to drops for which the contact angle is < 90°.