Whipping in gaseous flow focusing

We study both theoretically and experimentally the whipping instability in axisymmetric gaseous flow focusing realized in a converging-diverging nozzle. The lateral oscillation of both the tapering meniscus and emitted jet is explained in terms of the global linear instability of the lateral mode with the azimuthal number m = 1. A comparison with previous experiments shows good agreement. The distance between the feeding capillary and the nozzle neck hardly affects the m = 1 stability limit for the conditions considered in those experiments. We analyze the influence of the nozzle shape on the parameter conditions leading to whipping. As the nozzle convergence rate (the inverse of the length over which the diameter reduction takes place) increases, the flow becomes more stable under m = 1 perturbations. The above results are in marked contrast with those of the axisymmetric mode m = 0. For the axisymmetric mode, the minimum flow rate increases with the nozzle convergence rate, while the capillary-to-neck distance has considerable influence on the jetting-to-dripping transition. We also conduct experiments with different nozzles and capillary-to-neck distances to examine the effect of those factors on the stability of the jetting regime. The experiments allow us to distinguish between absolute whipping, in which both the tapering meniscus and the emitted jet oscillate, and convective whipping, in which the jet oscillates while the meniscus remains practically steady. Absolute whipping is observed for water and 1-cSt silicone oil focused with the nozzle with the smallest convergence rate and capillary-to-neck distance. The increase of the liquid viscosity stabilizes the liquid meniscus, producing the transition from absolute to convective whipping. In the high-viscosity case, the oscillation of the emitted jet far away from the discharge orifice is considerably affected by the shape of the nozzle in front of its neck. In fact, the increase of the convergence rate and capillary-to-neck distance eliminates the convective whipping as well. The reduction of surface tension enhances absolute whipping. We explain the appearance of the two types of whipping in terms of the flow pattern induced by the nozzle shape in front of the neck. (C) 2020 Elsevier Ltd. All rights reserved.