Abstract 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.

中文翻译：

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气流聚焦搅打

摘要 我们从理论和实验上研究了在收敛-发散喷嘴中实现的轴对称气流聚焦中的摆动不稳定性。锥形弯月面和发射射流的横向振荡可以用方位数 m = 1 的横向模式的全局线性不稳定性来解释。与先前实验的比较显示出良好的一致性。在这些实验中考虑的条件下，进料毛细管和喷嘴颈部之间的距离几乎不会影响 m = 1 的稳定性极限。我们分析了喷嘴形状对导致鞭打的参数条件的影响。随着喷嘴收敛速率（直径减小发生的长度的倒数）增加，流动在 m = 1 扰动下变得更加稳定。上述结果与轴对称模式 m = 0 的结果形成鲜明对比。对于轴对称模式，最小流量随着喷嘴收敛速度的增加而增加，而毛细管到颈部的距离对喷射到滴落的转变有相当大的影响。我们还使用不同的喷嘴和毛细管到颈部的距离进行实验，以检查这些因素对喷射方式稳定性的影响。实验使我们能够区分绝对搅动，其中锥形弯液面和发射的射流都振荡，和对流搅动，其中射流振荡而弯液面几乎保持稳定。观察到水和 1-cSt 硅油集中在具有最小收敛率和毛细管到颈部距离的喷嘴上的绝对搅动。液体粘度的增加使液体弯液面稳定，产生从绝对搅打到对流搅打的转变。在高粘度情况下，远离排放孔的喷射射流的振荡受其颈部前方喷嘴形状的影响很大。事实上，会聚率和毛细管到颈部距离的增加也消除了对流鞭打。表面张力的降低增强了绝对搅打。我们根据颈部前面的喷嘴形状引起的流动模式来解释两种类型的鞭打的外观。远离排放孔的喷射射流的振荡受其颈部前方喷嘴形状的影响很大。事实上，会聚率和毛细管到颈部距离的增加也消除了对流鞭打。表面张力的降低增强了绝对搅打。我们根据颈部前面的喷嘴形状引起的流动模式来解释两种类型的鞭打的外观。远离排放孔的喷射射流的振荡受其颈部前方喷嘴形状的影响很大。事实上，会聚率和毛细管到颈部距离的增加也消除了对流鞭打。表面张力的降低增强了绝对搅打。我们根据颈部前面的喷嘴形状引起的流动模式来解释两种类型的鞭打的外观。