Mathematical Model for Moderately Dilute Electrolytes of Lithium Ion Battery

We formulate a model for transport (of both Li⁺ ions and a generic N^- ion species) in a moderately dilute electrolyte - i.e. an electrolyte in which ionic concentrations (of Li⁺ and N^-) are small compared to that of the solvent (so that solvent need not be treated explicitly), but are not sufficiently dilute to be treated with the Nernst-Planck theory. We approximate Nernst-Planck theory by assuming that the local concentrations of the various ion species are balanced (charge neutral) except in regions local to the electrolyte-electrode interface where the (de-) intercalation reaction occurs. The resulting model is similar in form to that presented by Newman [Adv. Lith. Batt. 2002], but contains considerably fewer physical parameters, namely: (i) the effective electrolyte diffusivity, (ii) the transference number and (iii) the electrolyte conductivity. This reduction in the number of parameters is possible due to our `averaged’ description of the porous electrode and thus facilitates a more straightforward comparison with experiment. We present numerical simulations of the model and these are shown to agree favourably with experimentally obtained characteristics of a graphite half-cell.