Tank resonant frequency is a live void-fraction gauge; low choke Q is what keeps it alive across the swing

Derived on-bench with Scotchn (2026-09-13), his build: bifilar stainless chokes L_total = 39.48 mH, distributed self-cap 35 face pairs x 50 pF = 1.75 nF (bare-choke SRF = 19.15 kHz), R ~1.925 kOhm per choke.

1. CELL CAPACITANCE SWINGS WITH VOID FRACTION. Injector annulus per notebook #3373 geometry (probe .156 in OD, housing .176 in ID, .993 in exposed, 0.254 mm parallel gap), vic_calc kind=cell tubular: water-filled (er = 78.4) C = 912 pF; vapour-filled (er ~ 1) C ~ 11.6 pF. An 80:1 swing.

2. TANK FREQUENCY THEREFORE MOVES. C_total = 1.75 nF (choke self-cap) + load:

   • wet tube 2.4 nF -> 4.15 nF -> f_r = 12.43 kHz
   • injector water-filled -> 2.66 nF -> f_r = 15.5 kHz
   • injector vapour-filled -> 1.76 nF -> f_r = 19.1 kHz Direction: more capacitance = LOWER f_r. Gas formation RAISES f_r.

3. IT IS A CONTINUOUS SLIDE, NOT A STEP. A foam/mist ("cold milk / shaving foam" gas) is a dielectric mixture, so effective er tracks void fraction continuously. Therefore the ringing period of the tank reads how much gas is in the gap, in situ, in real time, with no added hardware. This is the missing sensor for closed-loop relaxation pulsing control.

4. LOW Q IS A FEATURE HERE. Q = 2pif*L/R = 1.23 at 12.43 kHz with R = 2.5 kOhm; -3 dB bandwidth = f/Q ~ 10 kHz. A high-Q tank would fall off its peak as soon as dissociation started and the load capacitance moved. A Q ~ 1 tank rides the entire 15.5-19.1 kHz excursion. Cost: voltage multiplication is only ~1.2x, so the stainless DCR still has to come down - but not so far that the tank loses the tolerance.

Open: confirm experimentally by logging ringdown period against measured gas volume.