Temporal analysis of capillary jet breakup

The temporal instability of a cylindrical capillary jet is analysed numerically for different liquid Reynolds numbers Re, disturbance wavenumbers k, and amplitudes ε₀. The breakup mechanism of viscous liquid jets and the formation of satellite drops are described. The results show that the satellite size decreases with decreasing Re, and increasing k and ε₀. Marginal Reynolds numbers below which no satellite drops are formed are obtained for a large range of wavenumbers. The growth rates of the disturbances are calculated and compared with those from the linear theory. These results match for low-Re jets, however 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 breakup time is shown to decrease exponentially with increasing the amplitude of the disturbance. The cut-off wavenumber is shown to be strongly dependent on the amplitude of the initial disturbance for amplitudes larger than approximately $\frac13$ of the initial jet radius. The stable oscillations of liquid jets are also investigated. The results indicate that liquid jets with Re ∼ O(1) do not oscillate, and the disturbances are overdamped. However, liquid jets with higher Re oscillate with a period which depends on Re and ε₀. The period of the oscillation decreases with increasing Re at small ε₀; however, it increases with increasing Re at large ε₀. Marginal Reynolds numbers below which the disturbances are overdamped are obtained for a wide range of wavenumbers and ε₀ = 0.05.