MES — Sporomusa-style acetate biocathode

Acetate productivity and the acetate / H₂ / CH₄ Faradaic split for a poised CO₂-reducing biocathode — not power.

Each relation is transcribed from the implementation. Where the code cites no source, the source line says so.

1. $$j_{kin} = j_0\,\exp\!\left(\frac{\alpha_c F \eta}{RT}\right) \exp\!\left[-\left(\frac{L - 0.05}{0.08}\right)^{2}\right], \qquad \eta = \max\left(0,\ -0.28 - E_{WE}\right)$$

   Source: Tafel form with an UNCITED biofilm prefactor: the 0.05 mm optimum and 0.08 mm width have no source (flagged 2026-08-19 in mes.ts, pinned by biofilm-prefactor-provenance.test.ts).

   The Gaussian thickness term is symmetric and uncited, and may double-count the CO₂ supply limit below.

   Symbol	Meaning	Unit
   $j_{kin}$	kinetic cathodic current density (magnitude)	A/m²
   $j_0$	strain exchange current density (S. ovata 0.02)	A/m²
   $\alpha_c$	cathodic transfer coefficient, 0.5	1
   $\eta$	driving force below the CO₂ → acetate floor	V
   $E_{WE}$	poised cathode potential vs SHE (default −0.6)	V
   $L$	biofilm thickness, floor 0.005	mm
   $F, R, T$	Faraday constant 96 485, gas constant 8.314, temperature	C/mol, J/(mol·K), K

2. $$j = j_{kin}\,\frac{C}{K_s + C}\, f_{mt}, \qquad f_{mt} = \frac{r}{1+r}, \quad r = \frac{k_La}{10\,\max\left(1,\ j_{kin}/5\right)}$$

   Source: Unsourced engineering default in mes.ts (2026-10 citation audit).

   The CO₂ Monod term scales the current; no biomass growth (μ_max) enters the calculation.

   Symbol	Meaning	Unit
   $C$	dissolved CO₂ under sparging, fixed at 30	mM
   $K_s$	strain half-saturation constant for CO₂ (S. ovata 1.5)	mM
   $f_{mt}$	gas-liquid mass-transfer factor	1
   $k_La$	CO₂ volumetric mass-transfer coefficient (default 20)	h⁻¹

3. $$FE_{ac} = \max\left(0,\ FE_{max} f_{mt} - p_{HER}\right), \qquad p_{HER} = \min\left(0.2,\ 0.5\max(0,\ \eta - 0.3)\right)$$

   Source: FE ceiling informed by Nevin et al. 2010, mBio 1:e00103-10 (over 85 % of electrons recovered in products); penalty form is in-house. · doi:10.1128/mbio.00103-10

   Symbol	Meaning	Unit
   $FE_{ac}$	Faradaic efficiency to acetate	1
   $FE_{max}$	strain acetate ceiling (S. ovata 0.92)	1
   $p_{HER}$	hydrogen-evolution penalty for an over-negative cathode	1
   $\eta$	driving force below −0.28 V vs SHE	V

   Worked example

   These inputs, passed to the predictor, return the output below. A test re-runs the example on every change, so this number is the one the code produces.

   input	value	unit
   temperatureC	30	°C
   ph	7	pH
   electrodeSpacingCm	2	cm
   hrtHours	24	h
   codMgL	1,000	mg/L
   workingElectrodePotentialVsSheV	-0.6	V vs SHE

   Output · mes.feAcetate = 47.06 %, within ±0.1 %

   By hand · S. ovata, η = −0.28 − (−0.6) = 0.32 V. j_kin = 0.02 × exp(0.5 × 96 485 × 0.32 / (8.314 × 303.15)) × 1 = 0.02 × e^6.125 = 9.145 A/m² (L = 0.05 mm puts the Gaussian at 1). r = 20 / (10 × 9.145/5) = 1.093, f_mt = 0.522. p_HER = 0.5 × 0.02 = 0.01. FE_ac = 0.92 × 0.522 − 0.01 = 0.4706, i.e. 47.06 %.

   Reproduce · Pinned by libs/shared/electrochemistry/src/predictors/worked-examples.test.ts. Run it from the repository root:

   pnpm exec jest -c libs/shared/electrochemistry/jest.config.js worked-examples.test.ts -t "mes.feAcetate"

4. $$r_{ac} = \frac{j\,A\,FE_{ac}}{8F} \cdot 86\,400 \cdot \frac{M_{ac}}{V}$$

   Source: Faraday's law with CO₂ → acetate stoichiometry.

   Symbol	Meaning	Unit
   $r_{ac}$	acetate productivity	g/L/day
   $A$	cathode area (default 0.003)	m²
   $8$	electrons per acetate: 2 CO₂ + 8 H⁺ + 8 e⁻ → CH₃COOH + 2 H₂O	1
   $M_{ac}$	molar mass of acetic acid, 60.05	g/mol
   $V$	chamber volume (default 100 mL)	L

• Sporomusa ovata as the canonical acetogen; μ_max ≈ ln(2)/24 h⁻¹ is assumed, informational only, and not verified against Nevin et al. 2010.
• Gas–liquid CO₂ transfer k_L·a = 20 h⁻¹ (range 5–50) — an unsourced engineering default.
• Dissolved CO₂ fixed at 30 mM (sparged, 1 atm, pH ~7).
• Thermodynamic floor −0.28 V vs SHE for CO₂ → acetate; at or above it the predictor returns zeros.

• Methanogen contamination lowers FE_acetate (CH₄ branch).

• Chain elongation (acetate → butyrate → caproate via reverse β-oxidation); needs a follow-on predictor per Jourdin 2018.
• Bicarbonate buffer speciation (HCO₃⁻ / CO₃²⁻) at the cathode surface — pH-dependent CO₂ availability is approximated.

• Nevin et al. 2010, mBio 1:e00103-10 · doi:10.1128/mbio.00103-10
• Marshall et al. 2013, Environ. Sci. Technol. 47:6023
• Jourdin et al. 2018, Front. Energy Res. 6:7

libs/shared/electrochemistry/src/predictors/mes.ts

heuristic_fixed_fraction — A fixed ±25 % placeholder band. It is NOT a calibrated interval; when served through /api/ml/predict it is replaced by the benchmark band below, or withheld. How served intervals are built

• Benchmark out-of-fold residual quantiles: bes-benchmark-v1 · gkf5 · generated 2026-09-09
• Split-conformal calibration: split-conformal · generated 2026-05-21
• Hierarchical-priors v2 trust snapshot: populated · generated 2026-05-16

Each row is a stratum with n ≥ 30 residuals at nominal level 90%. Coverage is the cross-validated share of held-out points inside the band.

The state the lab badge shows for each served parameter and system, from the v2 priors fit.

pnpm verify:science runs these rules over the committed priors and validation artifacts in pre-commit. Known violations are baselined per rule and slug; a new one blocks the commit. Baseline from hierarchical-priors-v2.json@2026-10-26T00:10:47.721880+00:00.