Oscillations of captured spherical drop of viscous liquid

Abstract

The complex frequencies of a viscous spherical drop where part of the free surface is embedded in a rigid spherical cap of the same radius have been determined as a function of the cap angle and the free surface tension parameter. With increasing cap angle α , the oscillation frequencies and decay magnitudes increase. This is also true for liquid drops of larger surface tension parameters. It also could be found, as has been found previously for a free floating sphere of viscous liquid, that the oscillations may cease to exist for certain diameters and low surface tension parameters, a fact not present in the treatment of frictionless liquid. In such cases, the captured liquid globule performs just an aperiodic motion. Three different liquid systems have been considered. In addition, the response of a captured spherical drop due to harmonically forced vertical translational excitation of the cap has been determined. Only a liquid sphere embedded in a spherical cap of the same radius has been evaluated numerically. The results reveal that for the mode n = 1 the geometry of a liquid sphere in a spherical cap of equal radius represents—depending on the magnitude α of the cap—for small surface tension parameters σ * ≡ σ a ρ / η 2 , a stable configuration, while for large σ * -values the spherical geometry is unstable, indicating that for those large cases the free liquid surface assumes a different geometry.