Calculation of Liquid Droplet Profiles from Closed-Form Solution of Young-Laplace Equation

A closed-form solution is obtained for a two-dimensional version of the Young-Laplace equation governing the shape of the interface between immiscible liquids. This solution enables designers of liquid junctions (in, for example, soldering or ink printing applications) to calculate profiles using certain junction dimensions as boundary conditions in the equations. Calculated profiles are superimposed on silhouettes of liquid junctions to show the accuracy of the solutions (±5%). The paper also introduces a parameter called the coefficient of retardation which was found convenient in accounting for all the factors that permit variable contact angles to be observed in a given solid-liquid-air system.