The evolution of capillary fountains

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Abstract
In this paper we consider the dynamics of a growing capillary fountain. We assume that at some time t = 0 an inviscid incompressible fluid is ejected vertically upwards through a circular nozzle. The subsequent dynamics of the resulting fountain is studied numerically using the boundary-element technique. The rate at which fluid is discharged from the nozzle and the Bond number (a measure of gravitational and surface tension forces) are the parameters that govern the dynamics of the fountain. For small discharge rates the fountain assumes the form of a slowly growing sessile drop, with dynamic effects not modifying the shape of the drop significantly. For large discharge rates we find that close to the symmetry axis a region develops with a high curvature. This strongly curved region results in a physical instability which can take on one of two forms: either a liquid drop is ejected from the free surface or the capillary surface entrains a bubble. For intermediate values of the discharge rate we find that fluid lobes develop which fall over the side of the nozzle. A number of experimental results are also presented showing the evolution of water fountains for different Bond numbers and discharge rates. Some of our numerical predictions are confirmed by the experimental results.