Book Description

The capillary instability of an infinitely long jet with respect to temporally growing disturbances was analyzed by Rayleigh. Keller et al. examined the capillary instability of a semi-infinite jet with respect to spatially growing disturbances. They found that the temporal and spatial disturbances are analytically related if the Weber numbers is sufficiently large. For sufficiently small Weber numbers, Leib and Goldstein found that the state of convective instability obtained by Keller et al. actually cannot be reached by a given initial disturbance in the sense of Briggs and Bers. The effect of the ambient gas density on the onset of absolute instability in a viscous liquid jet is examined. The critical Weber number, above which the instability is convective and below which the instability is absolute, is determined as a function of Reynolds number and the density ratio of gas to liquid. It is shown that the gas density has the effect of raising the critical Weber number. It also raises the cutoff wavenumber below which disturbances are spatially amplified and above which they are damped. Reprints.