EDL Capacitance
EDL Capacitance in Water
Calculating the actual capacitance of a water fuel cell requires understanding how the Electric Double Layer contributes to the total capacitance. This page explains how to account for EDL effects in your VIC circuit calculations.
Total WFC Capacitance Model
The total capacitance of a water fuel cell is not simply the geometric parallel-plate capacitance. It includes contributions from multiple components:
Series Combination of Capacitances:
1/Ctotal = 1/Cgeo + 1/Cedl,anode + 1/Cedl,cathode
Where:
- Cgeo = geometric (parallel-plate) capacitance
- Cedl,anode = double layer capacitance at anode
- Cedl,cathode = double layer capacitance at cathode
Geometric Capacitance
The geometric capacitance depends on electrode geometry and water's dielectric constant:
For Parallel Plate Electrodes:
Cgeo = ε₀ × εr × A / d
Where εr ≈ 80 for water at room temperature
For Concentric Tube Electrodes:
Cgeo = (2π × ε₀ × εr × L) / ln(router/rinner)
Where L is the tube length, r is the radius
EDL Capacitance Density
The EDL capacitance is typically specified per unit area:
| Electrode Material | Cdl (µF/cm²) | Notes |
|---|---|---|
| Stainless Steel 316 | 20-40 | Common WFC electrode |
| Stainless Steel 304 | 15-35 | Also commonly used |
| Platinum | 25-50 | High catalytic activity |
| Graphite/Carbon | 10-20 | Lower EDL capacitance |
| Titanium | 30-60 | Oxide layer affects value |
Calculating Total EDL Capacitance
EDL Capacitance for an Electrode:
Cedl = cdl × A
Where:
- cdl = specific EDL capacitance (µF/cm²)
- A = electrode surface area (cm²)
Example Calculation
Given:
- Electrode area: 100 cm²
- Electrode gap: 1 mm
- cdl: 25 µF/cm² (for stainless steel)
Calculate:
Geometric capacitance:
Cgeo = (8.854×10⁻¹² × 80 × 0.01) / 0.001 = 7.08 nF
EDL capacitance per electrode:
Cedl = 25 µF/cm² × 100 cm² = 2500 µF = 2.5 mF
Total capacitance:
1/Ctotal = 1/7.08nF + 1/2.5mF + 1/2.5mF
Ctotal ≈ 7.08 nF (EDL contribution is negligible when Cedl >> Cgeo)
When EDL Matters Most
The EDL capacitance becomes significant when:
| Condition | EDL Impact | Reason |
|---|---|---|
| Very small electrode gap | Minimal | Cgeo becomes very large |
| Large electrode gap (>5mm) | Minimal | Cgeo is small, dominates total |
| Small electrode area | Significant | Cedl becomes comparable to Cgeo |
| High frequency operation | Significant | EDL may not fully form |
Frequency Dependence
The EDL capacitance is not constant with frequency:
- Low frequency (<100 Hz): Full EDL capacitance available
- Medium frequency (100 Hz - 10 kHz): EDL partially developed
- High frequency (>10 kHz): EDL contribution decreases; diffuse layer can't follow
This frequency dependence is modeled using the Cole-Cole relaxation model (covered in Chapter 3).
Effect of Water Purity
The ionic content of water affects both conductivity and EDL behavior:
| Water Type | Conductivity | EDL Thickness | Cdl Effect |
|---|---|---|---|
| Deionized | <1 µS/cm | ~100 nm | Lower Cdl |
| Distilled | 1-10 µS/cm | ~30 nm | Moderate Cdl |
| Tap water | 200-800 µS/cm | ~1 nm | Higher Cdl |
| With electrolyte (NaOH, KOH) | >1000 µS/cm | <1 nm | Highest Cdl |
In the VIC Matrix Calculator
The VIC Matrix Calculator's Water Profile settings account for EDL effects:
- Electrode material: Determines specific Cdl
- Water conductivity: Affects EDL thickness and capacitance
- Temperature: Influences dielectric constant and ion mobility
- EDL thickness parameter: Allows fine-tuning based on measurements
Practical Tip: For most VIC calculations using typical electrode gaps (1-3mm), the geometric capacitance dominates. However, for very close electrode spacing or when precise tuning is needed, including EDL effects can improve accuracy.
Next: The Helmholtz Model →