Axisymmetric capillary waves on thin annular liquid sheets. I. Temporal stability

A reduced-dimension approach is employed to analyze the nonlinear distortion and disintegration of axisymmetric thin inviscid annular liquid sheets in a surrounding void with nonzero gas-core pressure at zero gravity. Linear and nonlinear solutions for the free motion of periodically disturbed infinite linearly stable and unstable sheets are obtained and compared in this first paper. (The forced motion of semi-infinite annular sheets exiting from a nozzle or atomizer is considered in the second paper.) Both sinuous and dilational modes are studied. Both modes are dispersive unlike the planar case where only the dilational mode is dispersive. These modes are coupled even in the linear representation although for sufficiently large annular radius, a pure dilational linear oscillation is found. The sinuous oscillation always excites the dilational mode. Nonlinear effects can modify the wave shapes substantially, causing an increase in breakup time for the dilational mode and a decrease in breakup time for the sinuous mode. The capillary sheet instability due to the nonlinear interaction of harmonic and subharmonic dilational disturbances, originally observed on planar sheets, is also observed and analyzed for the annular geometry. Parametric studies on the influence of annular radius, disturbance wavelengths, and their ratios are reported. (C) 2000 American Institute of Physics. [S1070-6631(00)00306-8].