How does a shear boundary layer affect the stability of a capillary jet?

The stability of a capillary jetwith a shear boundary layer growing over its free surface is studied theoretically. The effect of an infinitely thin boundary layer is first examined from the corresponding singularly perturbed eigenvalue problem. Then, a linear stability analysis of the Navier-Stokes equations for a finite boundary layer thickness verifies the consistency of the previous asymptotic study. We show that, for sufficiently long distances from the boundary layer origin, Rayleigh's dispersion relation is recovered, which means that the layer does not affect the jet's stability in that case. However, for distances on the order of the jet's radius, the perturbation growth factor, the most unstable wave number, and the range of unstable wave numbers increase, while the convective-to-absolute instability transition delays drastically. These results establish a general framework to explain a variety of capillary jet phenomena, from the extended jetting regime of capillary jets in gas co-flows to fundamental features of the dripping faucet. (C) 2014 AIP Publishing LLC.