you mean 10:1 reduction from 50:5.
No. Volume. 4/3*25³*pi = 65450 microns³; 4/3*2.5³*pi = 65.45 microns³ 1000:1.
One of the papers I read mentioned 10^6:1. I think 300µm to 3µm. I'll try to re-find the reference.
I don't know exactly what outcome you want and then to define the piezo specs and input you need. But your question started from the input without defining the output.
I did identify very early on that I wasn't at all sure about the parameters. You moved so fast with expanding the electronics side of this -- to which I am still trying to catch up with even the basic understanding -- that I have been neglecting the electro-mechanical side.
It doesn't help that as soon as the PZT manufacturers hear that there is no company, no multi-billion/year target market, and no big order in the immediate offing, they stop responding. I'm probably going to end up buying a few different size PZT elements off alibaba and sucking to see. Which means I'll need flexibility in the electronics to vary the frequency and output impedance widely.
No. In fact there is no 'it'. There are a bunch of possible 'its', with one I'm particularly interested in but don't want to discuss.
By way of example, without wishing to turn this thread into a discussion about this either, one of the problems with ICE engines is incomplete combustion producing noxious substances. Some injectors already use piezo elements to inject the ~0.1ml of fuel per cyclinder per cycle.
Imagine if between the closing of the injector valve at the end of one cycle, and its opening 2 cycles later those same piezo elements were driven with a high frequency low voltage signal so the valve remained closed, but the ultrasound induced cavitation within the closed cylinder. Partial vaporisation within the injector raises the temperature and pressure, so that when the valve opens, the fuel instantly vapourises as it escapes into the air flow. Better mixing? Better combustion?
Cavitation seems to be the phase-change avalanche effect analogy to dielectric breakdown of
Partial Discharge that eventually destroys oil-filled transformers by creating H2 and other HC combustible gases, due to contaminants in the dielectric(=insulation) , or voids in dry types.
Mostly over my head, and far outside my experience, but it sounds about right.