Free vibration of a spherical liquid drop attached to a conical base in zero gravity

Free vibration analysis of a spherical liquid drop attached to a conical base is presented. Assuming the liquid is incompressible and inviscid, and introducing a velocity potential, axisymmetric and asymmetric vibration characteristics are clarified, considering two liquid contact conditions: slipping edge and anchored edge. In the numerical calculations, for a wide range of conical base apex angles, the natural frequency and vibration mode of a liquid drop are presented. From these parameters, the vibration characteristics of a liquid drop attached to a conical base with general apex angle can be easily predicted. When the apex angle tends to 180°, natural frequencies are found to converge to those of a spherical drop under both slipping and anchored edge conditions, except in the axisymmetric mode with meridian mode number m=0 in the anchored edge case and asymmetric mode m=1 and n=1 in the slipping edge case.

► Liquid drop on a conical base are presented for a wide range of conical base apex angle α.
► Two liquid contact conditions: slipping edge and anchored edge, are considered.
► Both the axisymmetric and asymmetric modes are considered.
► Limiting cases when the apex angle α tends to 90° or 180° are considered.