NONLINEAR SPATIAL INSTABILITY OF A SLENDER VISCOUS JET

A perturbation analysis combined with one-dimensional equations is carried out to study the nonlinear spatial instability of a slender viscous jet. The solutions and wave profiles of the second order to third order have been presented. The result indicates that, as the perturbation expression proceeds to higher orders, the main swellings become narrow and the secondary swellings are flattened, resulting in the formation of a level liquid ligament. In addition, there exist two different nonlinear regions, named herein as the strong nonlinear region and the weak nonlinear region. The division of the two regions can be explained as a result of the interactions between the higher order harmonics transferred from lower orders and the inherent higher order disturbances. In addition, as Weber number decreases or Reynolds number increases, the growth rate of the jet increases significantly; the nonlinear amplitudes increase in the strong nonlinear region but remain constant in the weak nonlinear region, resulting in a shorter breakup length and a nearly identical waveform. The critical frequency, below which the jet is in the strong nonlinear region and above which it is in the weak nonlinear region, is not affected by Weber number but decreases noticeably as the Reynolds number reduces to less than 10. The theoretical waveforms are in agreement with previous experiments and simulations.