Chlor-Alkali Membrane Cell (2D)

Cell Operation

Current density 4.0 kA/m²

Membrane Na⁺ selectivity 96%

Anolyte NaCl feed 300 g/L

Live Readouts

Cell voltage

3.00 V

Current efficiency

96.0%

NaOH (catholyte)

0.0 wt%

Cl₂ / H₂ rate

0.0 mol/s

NaOH purity

100.0%

Na⁺ transported

Na⁺ crossing membrane

Cl₂ gas (anode)

H₂ gas (cathode)

Cl⁻ leakage (low selectivity)

How it works

This 2D cross-section engine implements the same real chlor-alkali electrochemistry as the 3D version, viewed edge-on: an anode (brine) compartment, a cation-exchange membrane, and a cathode (caustic) compartment.

Anode (Ti, anolyte = NaCl brine):
  2Cl⁻ → Cl₂(g) + 2e⁻

Cathode (Ni, catholyte = dilute NaOH):
  2H₂O + 2e⁻ → H₂(g) + 2OH⁻

Membrane transport:
  Na⁺ migrates anolyte → catholyte to balance charge
  Net cell reaction: 2NaCl + 2H₂O → Cl₂ + H₂ + 2NaOH

Every electron pulled at the cathode must be matched by a cation arriving through the membrane. Gas evolution follows Faraday's law: moles of Cl₂ or H₂ per second = I/(n·F) with n = 2 and F = 96,485 C/mol — doubling the current density genuinely doubles the gas rate, since the integral is linear in I. The theoretical Na⁺ transport rate needed for 100% current efficiency is exactly 2× the gas rate (2 mol e⁻ per mol gas ⇒ 2 mol Na⁺ per mol gas at unit charge).

The selectivity slider sets the membrane's Na⁺ transport number t₊. A fraction t₊ of that theoretical rate crosses as genuine Na⁺ and pairs with cathode OH⁻ to build clean NaOH; the remaining fraction (1 − t₊) is modeled as Cl⁻ co-ions leaking through the membrane, which do not carry useful current and instead contaminate the catholyte with NaCl. Both species are integrated over time with a first-order washout (continuous product takeoff), so NaOH purity = NaOH accumulated / (NaOH + NaCl contaminant accumulated) — a genuinely time-integrated ratio, not an instantaneous readout, so it lags realistically when you move the selectivity slider mid-run and settles toward t₊·100% at steady state.

Cell voltage is the thermodynamic decomposition voltage (~2.19 V) plus an ohmic/overpotential term that scales with current density, plus a small extra resistive penalty when the brine feed is diluted below saturation (~300 g/L) — a real effect of lower electrolyte conductivity.

t = 0.0 s