From Steve Shrubb
You express surprise that the valveless pump appears to have an auto reverse (2 February, p 38). Some 30 years ago I played with such devices while studying for my electronics degree—and realised that the solution was similar to the electronic circuits with which I was familiar.
Consider the hydrodynamic impedances looking in either direction from the squeezed portion. Clearly, it would be difficult to make them exactly equal. Unequal impedance in opposite directions will provide the equivalent of a diode, and hence allow a preferential flow in one direction.
The tricky part of the problem is in the calculation of the impedance. The ring is a lossy circuit—it dissipates energy. In electronics terms, it has relatively low Q. With some tedious but not difficult mathematics it is possible to show that the variation of impedance varies with pulse rate and follows an “S” curve. In other words, low frequencies meet a “diode” facing one way and higher frequencies a “diode” facing the other way.
I am not surprised that the circuit could have several reverses. You’d expect the number of pulses in the system to cyclically vary the impedance, making the “S” curve one part of a sine wave, although I didn’t take my considerations that far.
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