Toy geyser experiment: periodicity, operating conditions and coupling

A natural geyser can be reproduced by a toy experiment composed of a water pool located above a water reservoir, the two being connected by a long and narrow tube. When the bottom reservoir is heated, the system may experience periodic eruptions of hot water and steam at the top similarly to the geyser effect occurring in nature. The eruption frequency of a toy geyser is inspected experimentally as a function of the heating power and the height of the setup. We propose a thermodynamic model of this system that predicts the time between eruptions. A phase diagram that takes into account the thermal energy provided to the geyser and the geometry was constructed for the toy geyser. The conditions to obtain the geyser effect have been determined. The study of the toy geyser is then extended to the case of two reservoirs connected to the same tube. Such a coupled system adopts a complex time evolution that reflects the dynamics of natural geysers. We analyze the behavior of a toy geyser with two reservoirs by way of statistical tools and develop a theoretical model in order to rationalize our observations.