How it works
Reactions
Nitrogen fixation (fertilizer step)
e⁻ + O₂ → 2O ; e⁻ + N₂ → 2N
O + N₂ → NO + N ; N + O₂ → NO + O (Zeldovich)
2NO + O₂ → 2NO₂
3NO₂ + H₂O → 2HNO₃ + NO
2NO₂ + H₂O → HNO₃ + HNO₂
HNO₃ → H⁺ + NO₃⁻ (strong acid: pH falls)
Water splitting
2H₂O → 2H₂ + O₂ ΔG° = +237 kJ/mol, E° = 1.23 V
spark: H₂O → H + OH ; 2OH → H₂O₂
Ozone
3O₂ → 2O₃
O₃ + NO → NO₂ + O₂ ; NO₂ + O₃ → NO₃ + O₂
NO₃ + NO₂ → N₂O₅ ; N₂O₅ + H₂O → 2HNO₃
O₃ / H₂O₂ + NO₂⁻ → NO₃⁻
Mineral buffer: Ca²⁺/Mg²⁺ silicates and glass in regolith consume H⁺, so dirty meltwater resists acidification until its buffer capacity (≈0.5 mmol/L here) is used up, then the pH drops quickly. The result, Ca(NO₃)₂ / Mg(NO₃)₂, is itself a fertilizer.
Minimum voltage and spark duration
Breakdown follows Paschen’s law for a uniform gap:
V_B = B·p·d / ( ln(A·p·d) − ln(ln(1 + 1/γ)) )
A = 15 cm⁻¹Torr⁻¹, B = 365 V cm⁻¹Torr⁻¹, γ = 0.01
Air constants are used for every N₂/O₂ mix (a simplification).
Paschen breakdown voltage (kV), γ = 0.01
| Pressure | 0.1 mm | 1 mm | 3 mm | 5 mm | 10 mm |
|---|
| 101.3 kPa | 0.87 | 5.0 | 12.6 | 19.5 | 35.5 |
|---|
| 50 kPa | 0.55 | 2.9 | 7.0 | 10.7 | 19.3 |
|---|
| 10 kPa | 0.31 | 0.86 | 1.9 | 2.9 | 5.0 |
|---|
| 1 kPa | none | 0.31 | 0.41 | 0.55 | 0.86 |
|---|
| Lunar vacuum | no gas breakdown |
|---|
- Absolute minimum for air: 327 V at p·d ≈ 0.57 Torr·cm (≈7.5 µm at 1 atm) [P1]. The formula above gives ≈300 V at ≈0.8 Torr·cm.
- Rule of thumb: air insulates to about 3 kV/mm at 1 atm [R1].
- Water electrolysis needs only 1.23 V (thermodynamic); a ≈5 V droplet pulse was enough to split water in [R2].
- Droplet microspark [R2]: up to 1200 V per droplet, ≈900 V threshold at a 0.3 mm gap, ≈40 µs rise time.
- HKU/CityU fog system [R1]: ≈6 kV sparks every ≈3 s across a mm gap; 10 h → ≈30 mg/L NO₃⁻, 40 h → ≈100 mg/L, nitrite below 1 mg/L.
- Powered 1 L glow/spark reactor [R5]: ≈20 kV / 50 Hz supply, 15 min → 182 mg/L NO₃⁻, 148 mg/L NO₂⁻, 20 mg/L H₂O₂.
- Lowest reported for plasma-activated water [R6]: pulsed spark ≈4.6 kV; arc ≈3 kV. Corona on sharp points starts around 2–6 kV [P3].
- Duration: a single spark lasts nanoseconds to microseconds, but useful nitrate takes many sparks: hours at the HKU’s milliwatt power, or minutes at ≈100 W. In this model, cost ≈15 MJ per mol of dissolved NOx⁻ (spark mode).
Humidifier and vapour splitting
An ultrasonic mist maker on the reactor floor fills the headspace with water vapour and ≈3 µm droplets. In the spark, vapour is dissociated by electrons and excited N₂/O (plasma dissociation; the net result matches “vapour electrolysis”):
H₂O → H + OH
OH + OH → H₂O₂ ; H + H → H₂ (net 2H₂O → 2H₂ + O₂)
OH + NO → HNO₂
droplets dissolve NO₂ / HNO₂ / HNO₃ quickly
- Water-splitting share of the discharge energy: 2% with the humidifier off (≈40% RH) rising to ≈7.5% at 95% RH with mist, so more H₂, O₂ and H₂O₂ [H4].
- Droplets enlarge the gas–liquid interface: NOx absorption η_abs 0.30 → up to 0.75, so dissolved nitrate per joule roughly doubles [H2, H3, R1].
- Humid gas forms slightly less NOx per joule (−15% at saturation, est.; [H6] saw no change between 37% and 87% RH, [H8] a larger drop), shifts some NO to nitrite (HNO₂) [H2], and suppresses ozone [H5].
- Breakdown: humidity does not make a uniform gap easier to spark. H₂O attaches electrons, so V_B rises ≈0.3% per g/m³: about +3% at saturation [H1]. Droplets on or near an electrode can locally lower the inception voltage, but that is stochastic and not modelled. In the powered preset (20 kV, V_B 19.5 kV) the humidifier at ≥95% stops the spark.
The passive 40% RH, time constants and production multipliers are estimates (see research/humidity-findings.md). Vapour dilution of the N₂/O₂ inventory (≤5%) and the energy to evaporate the mist are neglected.
Why a pressurized reactor?
The lunar surface pressure is about 3×10⁻¹⁵ atm [L3]. With almost no molecules to ionize, p·d is far left of the Paschen minimum and no self-sustained spark can form; there is also no N₂ or O₂ to fix. The rover therefore carries a sealed reactor with an N₂/O₂ headspace above the water. Lunar nitrogen is scarce, so N₂ is shown as a consumable (“N₂ remaining”).
Model assumptions (est.)
- Energy per pulse ½CV² with C = 1 nF; power = ½CV²·f.
- Effective cost per mol dissolved NOx⁻: spark 15, arc 10, cold DBD 30 MJ/mol (gas-phase cost ÷ η_abs = 0.3). Calibrated to [R5] and inside the [R4] spark range. With full humidifier mist η_abs rises to 0.75.
- Nitrite share of fresh NOx⁻: spark 0.5, arc 0.6, cold 0.1 (up to +0.1 in humid gas).
- 2% of discharge energy splits water vapour (500 kJ/mol) with the humidifier off, rising to ≈7.5% at 95% RH; H₂O₂ calibrated to [R5] and scaled with that share.
- The HKU and powered presets run with the humidifier off, so their calibrations are unchanged.
- Ozone yield, nitrite oxidation rate, H₂O₂ decay, regolith buffer pKa 6.4 and dissolution rate are estimates.
- Headspace volume = max(0.25 L, 2 × water volume) at 250 K.
- pH from a full charge balance (HNO₃, HNO₂ pKa 3.3, regolith buffer, water).
- Fertilizer-grade target: ≥100 mg/L NO₃⁻. Water below pH 5 should be diluted or neutralised with regolith before use on pH-sensitive crops [R6].
References