An experimental study of Worthington jet formation after impact of solid spheres

Abstract

The impacts of solid spheres with the free surface have been studied for over one hundred years. In this thesis, the Worthington jets resulting from the impacts of hydrophobic and hydrophilic spheres with the free surface are studied experimentally. Several impact velocities and three materials of differing mass ratios are used. The resulting jets are characterized in terms of common non-dimensional physical parameters. A single camera is used to image activity both above and below the free surface simultaneously. The resulting images provide measurements of the height and velocity of the Worthington jets, as well as information about the breakup of the columns of fluid into droplets. In the hydrophilic cases, two separate regimes of jet formation are observed. The heights of both the first and second jet are recorded with time, and the maximum heights of each jet are compared to the Froude number at impact. The maximum height of the second jet is found to scale linearly with We, which is calculated using the velocity of the jet tip rather than impact velocity. Viscosity is shown to be negligible while a dependence on gravity is indicated. The time at which the first jet breaks up is proportional to Froude number, while the time of breakup for the second jet is nearly constant. Comparisons to energy transfer are presented. In the hydrophobic cases, the Worthington jet results from the collapse of the cavity formed below the free surface. Heights of the continuous Worthington jet are recorded for each time step, and average maximum heights obtained are again compared to Froude and Weber numbers. The increased variability in these data hinder clear scaling, and experimental error is calculated from repeated trials of two representative cases. Unaffected by experimental variation, however, the lifespan of the Worthington jets is shown to depend linearly on Froude number. Energy comparisons are explored.