Shape analysis of a sessile drop on a flat solid surface

The shape of a liquid drop on a flat solid surface is examined by using the minimization of free energy. This free energy consists of the contributions from the gravitational potential energy of the drop mass and the energy of the interfacial surfaces. The minimization of free energy is solved by the Lagrange multipliers method keeping the drop volume constant. The generic differential equation for the shape of the drop and a relation among the contact angles (Young equation) are determined as a result of the minimization via the variation of a functional and by imposing the condition for equilibrium of the drop. The differential equation is solved analytically around the origin of the selected coordinate axis and for two special cases. For the general solution, the differential equation is solved numerically to obtain the general shape of the sessile drop. Furthermore, a new Axisymmetric Drop Shape Analysis method is proposed for non-wetting sessile drop.