Kano T, Kinoshita S
Graduate School of Frontier Biosciences, Osaka University, Suita, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046217. doi: 10.1103/PhysRevE.80.046217. Epub 2009 Oct 27.
A density oscillator is a well-known system, which exhibits relaxation oscillation. It alternately exhibits up and down flows through a pipe that connects two containers filled with fluids that have different densities. Although the up-flow, down-flow, and flow-reversal processes have been studied separately, the entire oscillatory dynamics has not been modeled quantitatively. In this study, we derive a model of a density oscillator by considering all the above mentioned processes. The model thus obtained describes the oscillatory behavior in a unified manner, and its viscosity and pipe-length dependence is well described. Moreover, for the demonstration of this model, we have extended it to describe the dynamical behaviors observed in coupled density oscillators. Thus, this model provides a general expression for density oscillators.
密度振荡器是一种众所周知的系统，它表现出弛豫振荡。它通过连接两个装有不同密度流体的容器的管道交替呈现向上和向下的流动。尽管上升流、下降流和流反转过程已分别进行了研究，但整个振荡动力学尚未进行定量建模。在本研究中，我们通过考虑上述所有过程推导出了密度振荡器的模型。由此获得的模型以统一的方式描述了振荡行为，并且很好地描述了其对粘度和管道长度的依赖性。此外，为了演示该模型，我们对其进行了扩展，以描述在耦合密度振荡器中观察到的动力学行为。因此，该模型为密度振荡器提供了一个通用表达式。
