Thermogravitational cycle

A thermogravitational cycle is a reversible thermodynamic cycle using the gravitational works of weight and buoyancy to respectively compress and expand a working fluid.
Theoretical framework.
Consider a column filled with a transporting medium and a balloon filled with a working fluid. Due to the hydrostatic pressure of the transporting medium, the pressure inside the column increases along the "z" axis (see figure). Initially, the balloon is inflated by the working fluid at temperature "T"C and pressure "P"0 and located on top of the column. A thermogravitational cycle is decomposed into four ideal steps:
For a thermogravitational cycle to occur, the balloon has to be denser than the transporting medium during 1→2 step and less dense during 3→4 step. If these conditions are not naturally satisfied by the working fluid, a weight can be attached to the balloon to increase its effective mass density.
Applications and examples.
An experimental device working according to thermogravitational cycle principle was developed in a laboratory of the University of Bordeaux and patented in France. Such thermogravitational electric generator is based on inflation and deflation cycles of an elastic bag made of nitrile elastomer cut from a glove finger. The bag is filled with a volatile working fluid that has low chemical affinity for the elastomer such as perfluorohexane (C6F14). It is attached to a strong NdFeB spherical magnet that acts both as a weight and for transducing the mechanical energy into voltage. The glass cylinder is filled with water acting as transporting fluid. It is heated at the bottom by a hot circulating water-jacket, and cooled down at the top by a cold water bath. Due to its low boiling point temperature (56 °C), the perfluorohexane drop contained in the bag vaporizes and inflates the balloon. Once its density is lower than the water density, the balloon raises according to Archimedes’ principle. Cooled down at the column top, the balloon deflates partially until its gets effectively denser than water and starts to fall down. As seen from the videos, the cyclic motion has a period of several seconds. These oscillations can last for several hours and their duration is limited only by leaks of the working fluid through the rubbery membrane. Each time the magnet goes through the coil produces a variation in the magnetic flux. An electromotive force is created and detected through an oscilloscope. It has been estimated that the average power of this machine is 7 μW and its efficiency is 4.8 x 10−6. Although these values are very small, this experiment brings a proof of principle of renewable energy device for harvesting electricity from a weak waste heat source without need of other external energy supply, e.g. for a compressor in a regular heat engine. The experiment was successfully reproduced by undergraduate students in preparatory classes of the Lycée Hoche in Versailles.
Several other applications based on the thermogravitational cycles could be found in the literature. For example:
Cycle efficiency.
The efficiency "η" of a thermogravitational cycle depends on the thermodynamic processes the working fluid goes through during each step of the cycle. Below some examples:
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