Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development

The forced motion of semi-infinite axisymmetric thin inviscid annular liqui d sheets, exiting from a nozzle or atomizer into a surrounding void under z ero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Ph ys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent ("limit-cycle ") solutions to the pure boundary-value problem are presented as well as li near and nonlinear numerical (transient) solutions to the mixed boundary- a nd initial-value problem of initially undisturbed sheets harmonically force d at the orifice or nozzle exit. Group velocities for the six independent s olutions to the linear boundary-value problem are used to determine the loc ation of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on s heet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation frequency, modulated disturbance amplitude, Weber number, and annular radius is presented for various cases of the mixed problem, i.e., for linearly or nonlinearly stable and unstabl e, dilationally or sinusoidally forced sheets. Nonlinear effects often have significant effects on breakup times and lengths or on collapse times and lengths. Nonlinear wave forms can deviate substantially from linear predict ions resulting in major impacts on the size of the rings and shells that wi ll remain after breakup. (C) 2000 American Institute of Physics. [S1070-663 1(00)00406-2].