Isothermal bubble pump heat engine II

No doubt someone wants a diagram. I think in words, usually. So a word picture:

Isothermal compression starts in a tube which is almost horizontal and slopes down to the right. The slope increases as the depth increases. The slugs of gas are at maximum volume for their temperature, which is cold because the isothermal compression tube is in thermal contact with the cold heat sink. The gas and liquid is moving at a reasonably constant velocity to the right and down. Farther down, the slugs of gas decrease in volume, because the liquid behind is being accelerated by gravity while the liquid ahead is being decelerated by the higher pressure gas ahead of it. The gas temperature increases and heat flows into the cold heat sink. If the temperature tends to continue rising (because the engine is running too fast for the cold heat sink to carry away heat) then the pressure will increase more and tend to slow down the engine. The hyperbolic shape of the curve will result in compression occuring as fast as possible without increasing the temperature.

Isobaric (constant pressure) heating occurs in a horizontal segment of tube at the maximum depth and maximum pressure of the engine. Ideally, the heat is obtained via countercurrent heat exchange with the isobaric cooling segment, but that segment operates at minimum pressure, at the top of the machine. Gravity feed heat pipes will not accomplish the job: capillary action heat pipes are needed. Countercurrent heat exchange is important because the heat capacity of the liquid may be substantial, and that heat should not be coming from the heat source or ending up in the heat sink, but should stay in the hot portion of the liquid.

After the gas and liquid are heated to the hot temperature, the isothermal expansion step begins. The liquid and gas slugs move suddenly upward and to the left, at a steep slope which decreases smoothly to a nearly horizontal path before connecting to the isobaric cooling unit. This phase produces the force which keeps the liquid and gas moving against friction and the electromagnetic load applied by the external field to the magnetic particles in the liquid, and of course, against the resistance of the compression step. As the weight of the liquid above the gas decreases, the applied pressure decreases and the gas expands. It does work on the slug of liquid ahead of it and behind it. The energy for this work comes from the heat absorbed in keeping the gas at constant temperature.

Does the isothermal bubble pump need a check valve in the circuit? With one, it shouldn't need to get a push start, but then we couldn't say the machine has no valves. Inertia serves a similar function to the check valve. When expanding gas warms back to the isothermal temperature, it applies additional force to the slug in front and the slug behind, decelerating the slug behind and accelerating the slug ahead.