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

A reduced-dimension approach is employed to analyze the nonlinear distortio n 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 infin ite linearly stable and unstable sheets are obtained and compared in this f irst 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 c ase where only the dilational mode is dispersive. These modes are coupled e ven in the linear representation although for sufficiently large annular ra dius, a pure dilational linear oscillation is found. The sinuous oscillatio n always excites the dilational mode. Nonlinear effects can modify the wave shapes substantially, causing an increase in breakup time for the dilation al mode and a decrease in breakup time for the sinuous mode. The capillary sheet instability due to the nonlinear interaction of harmonic and subharmo nic dilational disturbances, originally observed on planar sheets, is also observed and analyzed for the annular geometry. Parametric studies on the i nfluence of annular radius, disturbance wavelengths, and their ratios are r eported. (C) 2000 American Institute of Physics. [S1070-6631(00)00306-8].