WFC design session v17: reasoning

Lab note, 3 July — ppm/surface sweep at low temp.

Findings confirm the ionic-branch knee sits right at 0.1ppm Na+ near 3°C: bulk water R climbs to ~128kΩ and the Randles series resistance (11.1Ω) is now dominated entirely by the double-layer geometry, not the electrolyte. What's interesting is that surface_factor (0.25 through 0.7) had zero effect on the top-line numbers — C_dl scales with area as expected (1.9µF→5.3µF) but since displacement current is already 99.1% and the tank is capacitively dominated, cell series R and hence current draw don't move. That tells me at this ppm/temp point the double-layer area is not the current-limiting lever anymore — I was hoping reducing surface area would buy back margin below 983.6mA, but it's flat. The real degrees of freedom left are ppm and temperature: dropping from 3°C to 4°C (candidate #5) cost me Q (97.5→94.3) and pushed current down only marginally (983.6→948.6mA) while raising f_r slightly. Breakdown margin stayed enormous (×143-147) across the board, so I'm not breakdown-limited here — I'm current-limited by design intent, sitting deliberately just under 1A.

Adopting #1: identical performance to #2-4 but minimum surface_factor (0.25) means least electrode area/cost for the same result — no reason to pay for more Cdl area when it buys nothing.

Next session: hold surface_factor fixed at 0.25, sweep ppm below 0.1 (toward near-deionized) and temperature down toward 0°C to see if the knee moves further and current drops below the 900mA mark with margin to spare.