Abstract
An optimization process for the solution of the Laplace equation of capillarity by numerical analysis is described. The approach is based on the image analysis of droplets that provides the “best” initial graphical estimate from parameters of the system, which are then optimized. This optimization process yields the contact angle, the surface tension, and the work of adhesion for any experimental droplet that has an equilibrium axisymmetric shape (i.e., a sessile or pendant drop). For the optimization, the Levenberg-Marquardt (LM) and the Gauss-Newton (GN) methods are compared through an objective function. The LM has the lowest number of iterations and produces the smallest errors for the optimization. It can converge to a solution even when different combinations of initial parameters are chosen for optimization. The best results are obtained when all the parameters are optimized to generate a solution. To illustrate the process, sessile drops of molten aluminum resting on sapphire single crystal (0001) are described and analyzed.
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