Teaching Rayleigh–Plateau instabilities in the laboratory
The breakup of a liquid jet into spherical droplets via the Rayleigh–Plateau instability is a common and fundamental part of fluid mechanics. However, teaching this instability in a laboratory setting is challenging, requiring sophisticated methods to generate and study the jet dynamics. Recently, toroidal droplets were shown to break into one or more spherical droplets in the thin-drop limit via the Rayleigh–Plateau instability. We propose a simple experimental setup to generate toroidal droplets that break up on the order of tens of seconds, allowing for easy video capture using a basic CCD camera. With this setup, it is possible to quantify the Rayleigh–Plateau instability in a pedagogical laboratory setting. In addition, the role of curvature on jet breakup can be explored using thick toroidal droplets. We envision this setup as a powerful teaching tool for one of the most fundamental fluid dynamics processes.
In this paper,the stability of a class of stage structure SIS model with small delay is studied.The sufficient conditions for asymptotical stability of the equilibrium are given.Some simulations are carried out by matlab software to support the correctness of our analysis results.Owing to the small delay,the results are the continuation and complement of the previous authors.