Electric batteries and fuel cells modeled by Bondgraphs

In an electric battery, electric charge flows against the electric field, driven by the concentration gradient or chemical tension. Outside it flows with the electric field through the load resistor to which it supplies energy. The whole is well represented by a Bondgraph (BG) and we develop the associated equations, especially for the element SPAC (see Section 2), which affords the coupling of chemical and electric flows. So it is a case of coupled reactions, driven by the concentration gradients between the two battery compartments. The electric charge is taken in ions against its potential gradient, driven by the chemical tension or potential.

The BG has an electrical and a chemical part, connected by two elements SPAC. There is also a flow source in the chemical part, which is driven when an external current flows. The reaction proceeds between two multiport C which represent chemical effort sources and entrains the electric charge. The whole is programmed and simulated by the 20SIM program and shows the switching on and off of electric current and the gradual equalization of concentrations with depletion of the voltage: the battery is discharged.

Essential is the selective membrane, that divides two compartments with different concentrations, and lets one species of ions run through. Fuel cells are similar but have two constituents, hydrogen and oxygen, and one product, water. Other substances can be used.