Stability of a liquid jet in a longitudinal time-varying electric field.
Introduction r I^HE stability of a liquid jet under various conditions has •-*been examined by various investigators and their findings are summarized by Nayyar and Murty and by Schneider. These studies begin by assuming that the difference between the perturbed radius and the unperturbed radius is given as either A(t)exp(ikz) or as a exp(ikz + jt). Here A(t) is the amplitude of the deformation of the jet, a is the initial amplitude of the deformation of the jet, k is the wave number, and j is the growth constant. For the first type of perturbation mentioned previously, an equation of motion for A(t) results whereas, for the second type of perturbation, a dispersion equation for j results. Hence the effects of the various parameters under consideration on the stability of the jet are determined from a stability analysis of either the equation of motion for A (t) or the dispersion equation for j. These studies show that a time-independent longitudinal electric field can either help to stabilize or destabilize the jet depending whether the disturbances are of long or of short wavelengths compared to the circumference of the jet. To the best of this writer's knowledge, the condition of a timevarying electric field has never been investigated. Hence this Note is concerned with the effect of the frequency of a sinusoidal electric field on the stability of a liquid jet. In this case, since it is better to employ the equation of motion for the amplitude of the deformation of the jet, the equation of motion for a time-independent electric field as developed by Nayyar and Murty is first examined and then the equation of motion for a sinusoidal electric field is considered.