Axisymmetric slosh frequencies of a liquid mass in a circular cylinder

Spectral eigenvalue methods along with some lower-dimensional techniques are used to determine the natural frequencies of a liquid slug in a circular tube. The contact lines are either pinned or governed by a slip coefficient assumed small. Corresponding physical experiments are conducted for a borosilicate glass tube and a treated water slug. Gravitational and viscous effects are neglected for the analyses. The spectral results agree well with a simple spherical end cap approximation (zero dimensional) for large aspect ratio slugs and with a membrane approximation (one dimensional) for small aspect ratios. The experimental observations for different aspect ratios agree well with the predictions, although the gravity, viscosity and/or slip are neglected in the analyses.