Temporal analysis of capillary jet breakup

Abstract

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.