On a toroidal method to solve the sessile-drop oscillation problem

We present a fully analytical solution for the natural oscillation of an inviscid sessile drop with small Bond number (surface tension dominates gravity) and a fixed contact line on a flat horizontal plate. The governing equations are expressed in terms of the toroidal coordinate system which yields solutions involving hypergeometric functions. Resonant frequencies are identified for zonal, sectoral and tesseral vibration modes. The predictions show excellent agreement with experimental data reported in the literature, particularly for flatter drops (lower, but not so low as to incur significant viscous dissipation) and higher modes of vibration. ©