PEM Fuel Cell Water Management — 2D Cross-Channel View

Operating Conditions

Current density i 400 mA/cm²

Cell temperature T 70 °C

Inlet gas humidity RH 80 %

Anode feed

Membrane State (2D field)

Membrane well hydrated

Avg. hydration λ̄

7.0

Membrane R (Ω·cm²)

0.030

Avg. ohmic loss i·R

0.012 V

Cathode λ @ inlet

7.0

Cathode λ @ outlet

7.0

Anode λ @ inlet

7.0

Anode λ @ outlet

7.0

How it works

This is a genuine two-dimensional hydration field across the Nafion membrane: one axis is thickness (anode ⊖ → cathode ⊕, where protons hop by the Grotthuss mechanism), the other is position along the gas flow channel (inlet → outlet). The 3D version of this sim only resolves the thickness axis; here both directions carry real, independently-computed physics.

∂λ/∂t = D_w(λ,T)·(∂²λ/∂x² + ∂²λ/∂y²) − v_drag(λ,i)·∂λ/∂x

D_w(λ,T) = D₀(λ)·exp[2416·(1/303 − 1/T)]      (Motupally et al.)
σ(λ,T)   = (0.005139λ − 0.00326)·exp[1268·(1/303 − 1/T)] S/cm
a_cathode(y) = RH + 0.6·i·(y/L_channel)        product water accumulates downstream

Through-plane (x): electro-osmotic drag drags water anode→cathode with every proton (only in x — current flows straight through the membrane, not along it), opposed by back-diffusion down the concentration gradient. In-plane (y): water also diffuses along the channel direction, and the cathode's local equilibrium hydration rises from inlet to outlet as oxygen-reduction product water accumulates in the gas stream — a real, well-documented along-channel non-uniformity that a 1-D through-plane model cannot show at all.

Current density i — more drag pulling water toward the cathode, and faster product-water buildup along the channel.
Temperature — both diffusivity and conductivity follow Arrhenius terms.
Inlet RH — sets the equilibrium hydration the humidified anode boundary is clamped to at the channel inlet.
Anode feed toggle — Dry + high current is the classic failure mode, and it hits hardest near the channel inlet: the cathode there hasn't yet built up product water, so there is less back-diffusion to rescue the anode side. Watch the top-left corner of the map dry out first.

The heatmap shows λ(x,y) directly; bright dots are protons hopping anode→cathode at whatever channel position they were seeded, moving at a rate set by the local conductivity they're crossing through.

⊖ ANODECATHODE ⊕

GAS FLOW: INLET → OUTLET

Wet membrane (high λ) Dry membrane (low λ) Proton (H⁺)