Modeling of a density oscillator.

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.