Sessile liquid drop evaporation: analytical solution in bipolar coordinates

The investigation of evaporating liquid drop deposited onto a flat surface is of great importance for physical, engineering and medical applications. Novel analytical expressions are proposed to calculate the evaporation rate of sessile drop (mass loss per unit surface area per unit time) and total evaporation rate (mass loss per unit time). To obtain these results, the H.M. Macdonald's solution for a flat wedge was transformed by method of inversion in a sphere originally developed by J.C. Maxwell in the Treatise on Electricity and Magnetism with further derivation the solution for a lens based on consideration given in bipolar coordinates by G.A. Grinberg. These solutions are mathematically equivalent to expressions proposed earlier by Yuri O. Popov [Phys. Rev. E 71, 036313 (2005)], but, in some cases, probably, the new solutions can be more useful from a computational point of view.