Laplacian drop shapes and effect of random perturbations on accuracy of surface tension measurement for different drop constellations.

Theoretical drop shapes are calculated for three drop constellations: pendant drops, constrained sessile drops, and unconstrained sessile drops. Based on total Gaussian curvature, shape parameter and critical shape parameter are discussed as a function of different drop sizes and surface tensions. The shape parameter is linked to physical parameters for every drop constellation. The as yet unavailable detailed dimensional analysis for the unconstrained sessile drop is presented. Results show that the unconstrained sessile drop shape depends on a dimensionless volume term and the contact angle. Random perturbations are introduced and the accuracy of surface tension measurement is assessed for precise and perturbed profiles of the three drop constellations. It is concluded that pendant drops are the best method for accurate surface tension measurement, followed by constrained sessile drops. The unconstrained sessile drops come last because they tend to be more spherical at low and moderate contact angles. Of course, unconstrained sessile drops are the only option if contact angles are to be measured.