Some carnivorous mammals (e.g., cats and dogs) lap water with their tongues to drink water at high frequencies. Such a fast moving tongue creates a liquid column out of a bath which is bitten by the mouth for drinking. Presumably, the animals bite just before the pinch-off time of the water column to maximize the water intake. Otherwise, the water column falls back to the bath before being bitten. Such a pinch-off phenomenon in the liquid column can be described as the acceleration-induced (i.e., unsteady) inertia balances with the capillary force. The classical Rayleigh-Plateau instability explains the competition of the steady inertia with the capillarity, but not with the acceleration-induced inertia. In this study, we modify the Rayleigh-Plateau instability in the presence of the fluid acceleration, and show that the most unstable wavenumber and growth rate increase with acceleration. The pinch-off time is theoretically predicted as the $-1/3$ power of the Bond number (i.e, a ratio of the acceleration-induced inertia to capillarity). Finally, measured pinch-off times from previous physical experiments and dog and cat jaw-closing times are shown to be in good agreement with our theoretical pinch-off time. Therefore, our study shows that animals presumably modulate their lapping and jaw-closing time to bite down on the water column before the pinch-off to maximize the water intake.

中文翻译：

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阐明动物拍打的夹断动力学

一些食肉哺乳动物（例如猫和狗）用舌头舔水以高频喝水。如此快速移动的舌头从浴缸中产生液体柱，被嘴咬住以饮用。据推测，动物在水柱夹断时间之前咬人，以最大限度地摄入水。否则，水柱会在被咬之前回落到浴缸中。液柱中的这种夹断现象可以描述为加速度引起的（即不稳定的）惯性与毛细管力的平衡。经典的 Rayleigh-Plateau 不稳定性解释了稳态惯性与毛细作用的竞争，而不是与加速度引起的惯性的竞争。在这项研究中，我们修改了存在流体加速度的 Rayleigh-Plateau 不稳定性，并表明最不稳定的波数和增长率随着加速度的增加而增加。夹断时间理论上预测为$-1/3$邦德数的幂（即加速度引起的惯性与毛细作用的比率）。最后，从之前的物理实验中测量的夹断时间以及狗和猫的下颌闭合时间与我们的理论夹断时间非常吻合。因此，我们的研究表明，动物可能会调节它们的拍打和下颌闭合时间，以便在夹断之前咬住水柱，以最大限度地摄入水。