Orange Battery
This tutorial model serves as an introduction to electrochemistry modeling in COMSOL Multiphysics and models the currents and the concentration of dissolved metal ions in a battery (corrosion cell) made from an orange and two metal nails.
Figure 4: Modeled geometry. Orange and two metal nails.
This type of battery is commonly used in chemistry class demonstrations. Instead of an orange, lemons, or potatoes can also be used.
Model Definition
The citric acid and various other ions in the orange serve as electrolyte, and using nails of different metals as electrodes creates a galvanic potential over the cell.
In this example a zinc nail is used as one of the electrodes, giving rise to the following electrode reaction:
The other nail consists of copper, and here hydrogen evolution is assumed to take place:
Eeq,0 above denotes the equilibrium potentials at standard conditions versus a standard hydrogen electrode (SHE). In the model, the equilibrium potentials are corrected for the pH and zinc concentration of the orange pulp using the Nernst equation.
The model for the currents in the orange and electrodes is set up using the Secondary Current Distribution interface. The electrolyte current in the orange is thereby solved for by Ohm’s law. The conductivity of the metal nails is so high that the electrode domains are not included in the model, instead boundary conditions on the nail surfaces are used to set the nail potentials. One nail is grounded and the other one is set to a cell potential to comply with a total current condition. This would correspond to a situation where the cell is controlled galvanostatically, for instance by the use of a potentiostat.
Butler–Volmer type expressions, with concentration dependent exchange current density for the zinc reaction, are used for the electrode kinetics on the surface of the nails within the orange.
The initial electrolyte potential value is set to correspond to the potential of a cell at open circuit (that is, no activation potential). Following the definition of the overpotential:
the initial value becomes:
In an extension of the model, the diffusion and migration of the dissolved zinc ions in the orange from the zinc electrode reaction are modeled by the Transport of Diluted Species interface in a time-dependent simulation. This assumes that the zinc ion transport can be described by diffusion according to Fick’s law. In addition, the zinc electrode kinetics are modified to be dependent on the zinc concentration, which increases in the orange as more and more zinc is dissolved. The cell current is set to a constant value of 1 mA and the zinc concentration is set to 0.001 mol/m3 at the start of the simulation.
All boundaries except the nail electrodes are insulated.
Results and Discussion
Figure 5 shows the potential field in the orange. The potential decreases as the current flows from the zinc electrode (left) to the upper electrode (right). The main part of the cell voltage loss is due to ohmic losses in the electrolyte.
The performance of the battery could probably be increased by using an electrolyte of higher conductivity (for example, a lemon instead of an orange) or by decreasing the distance between the nails.
Figure 5: Potential field in the electrolyte at t=0.
Figure 6 shows a polarization plot as the total current of the battery increases from 0 to 1 mA. The potential has a nearly linear correlation to the applied current, pointing to ohmic losses in the electrolyte.
Figure 6: Polarization plot for the initial concentrations.
Figure 7 shows an isosurface for the 0.2 mol/m3 concentration level of zinc ions after running the battery for five minutes.
Figure 7: 0.2 mol/m3 zinc concentration isosurface after five minutes.
Figure 8 shows how far the 0.2 mol/m3 isosurface level has reached after one hour.
Figure 8: 0.2 mol/m3 zinc concentration isosurface after one hour.
Figure 9 shows how the cell current evolves with time. Due to the increase of zinc ions at the zinc nail electrode, the battery current decreases for a constant cell current.
Figure 9: Cell current vs. time.
Suggested Exercises and Extensions of the Model
Change the radius of the nails and the value of the electrolyte conductivity and investigate how this affects the polarization plot.
The proton concentration is not included in the model. Add the proton concentration under Dependent Variables on the Transport of Diluted Species node and couple the flux of protons on the copper surface by using an Electrode Surface Coupling node. In this manner, the change in pH of the cell can be monitored.
The dissolved zinc ions may form a layer of zinc hydroxide on the zinc surface, giving rise to an additional potential drop. You can use the Film Resistance section on the Electrode Surface Boundary node to include this potential drop. The value of the film resistance could, for instance, be a function of the zinc ion concentration variable in the pulp. Alternatively, you can add a Surface Reactions interface or the to model the buildup of the surface concentration of zinc hydroxide.