Abstract
The weakly nonlinear instability of a liquid ring is investigated by perturbation method and illustrates several important features at the early stage of evolution after destabilization. When the centerline maintains circular, the ring would transform into a droplet chain during its shrinkage, but tends to possess some local pinching during the expansion. If there is an additional distortion of the centerline, an evident tendency to protrude spikes, on each of which a droplet may be formed, is predicted. The analysis concentrates on inviscid cases, because the viscosity of ring liquid is proven to merely affect the base state. Besides, the interaction between instability modes is studied to understand the irregularity of perturbed surface and centerline, and the four locations where the irregularity appears to the maximum extent are discovered. All these results are confirmed by numerical simulations of the same model and experimental observations on ring-shaped the rim of drop-splash ejecta, and hence are related intrinsically with the spike formation process.
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