Electrolysis Simulation

Category: Coupled Analysis – Electrochemistry | Revised 2026-10-01

Theory: bubbles lower electrolyte conductivity

Overview

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Besides electrode reactions, what must an electrolysis simulation calculate?

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Bubbles. In water electrolysis hydrogen leaves the cathode and oxygen the anode as bubbles. Bubbles don't conduct, so when they mix into the electrolyte near the electrodes, the cross-section available to ions shrinks and voltage loss grows. Bubbles also rise, so their amount differs between bottom and top of an electrode and so does voltage loss. Current avoids high-loss areas and shifts toward the bottom, where it then makes even more bubbles. Electrochemical reaction, electrolyte and bubble flow, and current distribution all influence one another — coupling them is the heart of electrolysis simulation.

Void fraction and effective conductivity

$$ \varepsilon = \frac{j_g}{j_g + j_l + u_d},\qquad j_g(z) = \frac{i\,V_m\,z}{nF\,d},\qquad \kappa_{eff} = \kappa\,(1-\varepsilon)^{1.5} $$

j_g and j_l are superficial gas and liquid velocities, u_d the speed at which bubbles rise faster than liquid (0.20 m/s), V_m molar gas volume at 80 °C and 1 atm, n electrons per mole of gas (2 for hydrogen, 4 for oxygen) and d the electrode–diaphragm gap (3 mm). κ is bubble-free electrolyte conductivity (1.2 S/cm, illustrative).

Gap voltage loss

$$ \Delta V_{gap}(z) = \frac{i\,d}{\kappa_{eff,c}(z)} + \frac{i\,d}{\kappa_{eff,a}(z)} $$
Coffee Break Trivia

The word "electrolysis"

Faraday showed in 1833–1834 that the amount of substance produced by electrolysis is proportional to the quantity of electricity. At the same time, consulting the scholar Whewell, he settled words still used today — electrode, anode, cathode, electrolyte, ion — and electrolysis itself. Organising the idea of splitting matter with electricity, together with its vocabulary, helped the electrochemical industry that followed to grow.

Worked examples

Example 1: height, bubbles and voltage loss (0.3 A/cm², 1 m tall)

Height from bottomCathode voidAnode voidGap lossBubble increment
0 m0%0%0.150 V0
0.25 m11%6%0.172 V+0.022 V
0.5 m20%11%0.195 V+0.045 V
1.0 m34%20%0.244 V+0.094 V

Averaged over height the gap loss is 0.196 V (0.046 V above bubble-free). Since 1 V corresponds to 26.6 kWh per kg of hydrogen, the gaps cost 5.2 kWh/kg, of which bubbles account for 1.2 kWh/kg. Uniform current is assumed here.

Example 2: gap versus zero-gap

DesignGap loss (average)Per kg of hydrogen
3 mm gap, no bubbles (hypothetical)0.150 V4.0 kWh
3 mm gap with bubbles0.196 V5.2 kWh
Zero-gapabout 0 (diaphragm resistance remains)about 0
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Does zero-gap make the bubble problem go away?

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Gap electrolyte loss disappears, but the bubble problem moves rather than vanishes. In zero-gap cells bubbles pass through perforated electrodes to the back, but bubbles clinging to the surface or inside holes reduce active area and concentrate current on what remains. If bubbles accumulate in the rear channels, electrolyte struggles to reach the electrode. Hole size and shape, rear channel width and electrolyte flow rate all change how bubbles escape, and that is what simulation investigates. Raising current density increases gas, so designers check that bubbles don't build up excessively near the top or outlet. High void fraction also affects how much hydrogen and oxygen cross the diaphragm and mix, so bubble distribution matters for safety too.

Modelling workflow

  1. Give electrolyte conductivity as a function of temperature and concentration.
  2. Represent electrode reactions with polarization curves and solve electrolyte potential.
  3. Derive gas generation from current distribution and solve bubble–liquid (two-phase) flow.
  4. Update conductivity with void fraction and re-solve current distribution.
  5. Compute temperature from heat and feed back into conductivity and reactions until converged.
Coffee Break Trivia

“An electrode darkened only on its upper half”

On disassembling an alkaline electrolyser, only the upper half of the electrodes was discoloured, with a thinned catalyst layer. Coupled bubble–current analysis showed bubbles accumulating at the top, starving the electrode of electrolyte and holding local voltage high for long periods. Increasing electrolyte circulation and widening the rear channels so bubbles escaped more easily reduced the top-to-bottom bubble difference, and later inspections found no discolouration.

Common mistakes

Mistakes and fixes

MistakeEffectFix
Ignoring bubblesVoltage underestimatedReduce conductivity by void fraction
Equal bubble and liquid speedVoid fraction overestimatedInclude bubble rise velocity
Uniform currentUpper-electrode damage missedSolve current distribution
Equal hydrogen and oxygen gasCathode side underestimatedVolumes are 2 to 1
Constant temperatureConductivity wrongCouple with heat
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