Abstract
A laminar inviscid liquid (typically water) jet issuing from a circular nozzle into otherwise quiescent air disintegrates into droplets periodically at a distance from the nozzle. The Plateau-Rayleigh instability theory and others cannot determine this breakup length because they do not have any logic that determines the initial amplitude of the unstable wave responsible for the breakup. In this paper, a closed spatial evolution solution is derived for a uniformly issued liquid jet by applying a theory that identifies the origin of the unstable wave. This solution describes the self-destabilizing mechanism of the liquid jet in the steady breakup state, showing that the initial amplitude of the unstable wave is determined by the capillary wave with upstream propagating speed that is created by the tip contraction at every breakup. Finally, the developed theory is extended to allow for the self-destabilizing mechanism of a liquid jet issuing from a long nozzle, which initially has a parabolic velocity profile and results in a long breakup length.
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