Linear response of a viscous liquid to translational excitation

Abstract

Forced oscillations of a viscous liquid with a free liquid surface in a circular cylindrical container have been treated by observing various boundary conditions. The response of the velocity distribution, the free surface elevation and response force of the liquid due to translational excitation of the tank have been determined. Three cases have been treated and compared with each other. One is the case of slipping liquid at the side wall, where the contact line is free to slip, while the other case considers an anchored contact line. Finally all adhesion conditions at the side wall of the container have been satisfied, while at the tank bottom only the normal velocity condition is satisfied. The first two cases are valid for small liquid filling rates, while the last treatment renders good results for large aspect ratio containers. It was found that a new phenomenon appears for low filling rates, where the liquid is only capable to perform an aperiodic motion.