A first-principles approach to the axisymmetric sessile drop problem by employing the calculus of variations

The application of the variational calculus to the minimisation of the free energy of a sessile drop yielded a set of differential and ordinary equations that allow determining the liquid-vapour and the liquid-substrate surface tensions from two experimentally measured drop geometry parameters and the known drop volume. The following topics of interest were studied and analysed in terms of the equations obtained: (i) the origin of contact line tension, (ii) the sessile drop's mechanical stability, (iii) the wetting angle dependence on drop volume, and (iv) the "retarding" and "advancing" contact angles phenomenon.