WFC water-capacitor cell model refined with EDL (Randles-cell) capacitance

Chris pushed back on treating the water capacitor as one lumped cap for the design-loop tank math — right call. Physical model is a Randles cell: two capacitances in series — my bulk geometric cap C_geo (tens-to-hundreds of pF, set by rod/tube annulus geometry) and the electrode double-layer cap C_dl at each plate face, sized by the Debye length: C_dl ~ eps*eps0/lambda_D per unit area.

Reveal: lambda_D runs nanometers-to-microns in real water; my plate gap runs millimeters -- three-plus decades apart. Two caps in series are dominated by the SMALLER one, so C_series ~ C_geo to a hair. That is exactly why the pure-pF resonance model held up clean through design sessions v6-v9 without ever carrying C_dl explicitly -- the EDL was there the whole time, just too large (small reactance) to move f_r.

Where it DOES matter: (1) Loss -- C_dl itself is reactive (~1 ohm of capacitive reactance at 50kHz vs C_geo's ~32k ohm), so the real dissipation is not the cap, it is the charge-transfer resistance R_ct and Warburg diffusion impedance riding parallel to it. Inert plates + pure water keep R_ct high, so this leakage path stays small -- but it is a real mechanism, not just bulk water resistance. (2) Step-charge timing -- EDL charging time constant tau_edl ~ lambda_D * L_gap / D lands around 0.5-1s, far longer than a single ~20us drive pulse. The layer cannot fully charge in one pulse; it creeps up over the whole pulse train. Likely part of the slow voltage creep observed building past 1000V during step-charging, and part of what the blocking diode is holding between pulses.

The lever: lambda_D is set by ionic strength. Purer/more inert water gives longer Debye length, smaller C_dl, higher R_ct, longer dielectric relaxation time tau_diel. Every arrow points the same direction -- keep the water clean. That is precisely why #5,149,407 calls for the water capacitor to be "preferably chemically inert."

Net effect on the design-loop numbers: v8's adopted geometry (15.9mm rod/22.3mm tube/101.6mm, C=1.31nF, Q=64.4, f_r=98.33kHz, 773V @ 625.6mA) stands -- the EDL correction to C_series is negligible at this scale separation, so this is not a retraction of v8. Open item, not yet run: fold an explicit C_dl(lambda_D) + R_ct/Warburg branch into the tank-circuit math as v10 and sweep lambda_D from distilled to tap water to see what it does to Q and to the step-charge baseline. Chris asked for the v8 remodel with this in mind -- that numeric pass is still owed, this entry captures the model reasoning behind it.