Instability and fragmentation of expanding liquid systems

This analysis pursues the underlying physics governing the expansion, dispersal and breakup of a thin walled steel right circular cylinder filled with liquid after being impacted by a high velocity aluminum sphere. The impact generates a radially expanding coherent thin shell of liquid which stays together to at least a diameter 8 times that of the original cylinder. An instability criterion is proposed and developed based on the opposing forces of stabilizing inertial pressures and destabilizing viscous resistance. This criterion is compared to test data where possible in order to ascertain its ability to predict liquid breakup of the shell. The breakup theory developed here predicts the extensive expansion of the unthickened liquid prior to fragmentation as observed in the experiments. This result lends some credence to the underlying physics pursued here and its ability to predict the onset of liquid fragmentation.