Rhythm in a saline oscillator

An oscillatory flow of water is generated when a cup containing saline water, with a small orifice in its base (ca. 1 mm in diameter), is placed within an outer vessel containing pure water. To clarify the mechanism of rhythmic fluid flow in this so-called saline oscillator, we performed a numerical simulation with the Navier-Stokes equation of this rhythmic flow in three dimensions. The essential features of the rhythmic flow were reproduced with the numerical simulation. We concluded that the pressure term is the most important for driving the oscillation, whereas the inertia and viscosity terms always depress oscillation. It becomes clear that osmotic pressure has a negligible contribution. Based on this analysis of the contributions of individual components to the rhythmic flow, the system dynamics can be reduced to a second-order ordinary-differential equation, i.e., the Rayleigh equation.