TEMPORAL ANALYSIS OF CAPILLARY JET BREAKUP

The temporal instability of a cylindrical capillary jet is analysed nu merically for different liquid Reynolds numbers Re, disturbance wavenu mbers k, and amplitudes epsilon(0). The breakup mechanism of viscous l iquid jets and the formation of satellite drops are described. The res ults show that the satellite size decreases with decreasing Re, and in creasing k and epsilon(0). Marginal Reynolds numbers below which no sa tellite drops are formed are obtained for a large range of wavenumbers . The growth rates of the disturbances are calculated and compared wit h those from the linear theory. These results match for low-Re jets, h owever as Re is increased the results from the linear theory slightly overpredict those from the nonlinear analysis. (At the wavenumber of k = 0.9, the linear theory underpredicts the nonlinear results.) The br eakup time is shown to decrease exponentially with increasing the ampl itude of the disturbance. The cut-off wavenumber is shown to be strong ly dependent on the amplitude of the initial disturbance for amplitude s larger than approximately 1/3 of the initial jet radius. The stable oscillations of liquid jets are also investigated. The results indicat e that liquid jets with Re similar to O(1) do not oscillate, and the d isturbances are overdamped. However, liquid jets with higher Re oscill ate with a period which depends on Re and epsilon(0). The period of th e oscillation decreases with increasing Re at small epsilon(0); howeve r, it increases with increasing Re at large epsilon(0). Marginal Reyno lds numbers below which the disturbances are overdamped are obtained f or a wide range of wavenumbers and epsilon(0) = 0.05.