Absolute lateral instability in capillary coflowing jets

We examine the stability of coflowing capillary jets under lateral (m=1) perturbations of small amplitude. Two models are considered for the perturbed basic flow: the Kelvin-Helmholtz (KH) and the outer boundary layer (OBL) models. We revisit the temporal analysis of the KM model and show that the flow is unstable if and only if the (conveniently defined) Weber number is greater than unity. On the contrary, the OBL flow becomes unstable for Weber numbers much smaller than unity, although the growth rate of the perturbations is very small in that case. The spatiotemporal analysis of the dispersion relations shows that both the KH and OBL flows become absolutely unstable (absolute whipping) for sufficiently large values of the Weber number and the ratio between the outer and inner stream velocities. Absolute whipping dominates the behavior of high-viscosity jets for large velocity ratios and prevents the jetting regime from being reached even when varicose perturbations are convected downstream. For sufficiently large values of the Reynolds number, the flow becomes absolutely unstable if the velocity ratio exceeds a critical value, which is almost independent of the Weber number. For small values of the velocity ratio, the flow is stable or at most convectively unstable independently of the Reynolds and Weber numbers. For sufficiently large values of the velocity ratio, there is a critical Reynolds number above which jetting can not be reached because the flow becomes absolutely unstable due to the modes m=0 and/or m=1. That critical Reynolds number decreases as the velocity ratio increases. These results have important implications in technological applications such as steady high-viscosity liquid microjet production and fiber spinning using coflowing gas conformation. (C) 2010 American Institute of Physics. [doi:10.1063/1.3447800]