RECOVERY OF THE RAYLEIGH CAPILLARY INSTABILITY FROM SLENDER 1-D INVISCID AND VISCOUS MODELS

For either inviscid or viscous jets, Rayleigh proved cylindrical jets are linearly unstable due to surface tension of the interface, with in stability precisely in all wavelengths greater than the jet circumfere nce. As an alternative to linearized analysis, many past sind present studies of surface tension-driven-jet breakup are based on slender asy mptotic 1-D models; here we clarify two issues regarding this approach . First, self-consistent, leading-order models of inviscid or viscous slender jets do not have a finite instability cutoff. Indeed, the invi scid 1-D equations exhibit unbounded exponential growth in the small s cale limit, while the viscous,counterparts bound the growth rate but r emain unstable in all wavelengths. Second, one can recover a finite in stability cutoff by extending the asymptotic analysis to higher order. The linearized growth rate corrections at each finite order arise as algebraic approximations to Rayleigh's exact exponential rate. We expl icitly match, at leading and subsequent order, the slender longwave ex pansion of the exact results with the linearized behavior of I-D slend er asymptotic equations. (C) 1995 American Institute of Physics.