Shape analysis of an axisymmetric pendant drop using minimization of free energy

Abstract

The shape of a pendant drop is studied by employing free energy minimization. This free energy includes the gravitational potential energy and the interfacial surface energy. We employed the Lagrange multipliers method to minimize free energy while maintaining drop volume as constant. The differential equation for the shape of any pendant drop was established as a function of one dimensionless parameter only. This novel dimensionless parameter is defined as the shape factor. Around the origin of the chosen coordinate axis, an analytical solution to the differential equation was found. For a general solution, a numerical approach was followed to estimate drop shape. Furthermore, we calculated the detached volume from the bulk pendant drop. Comparison of the results with the experimental findings shows good agreements. A new Axisymmetric Drop Shape Analysis method is suggested, which can help users estimate any unknown of the problem if one geometrical data of the drop is known