Asymptotic reduction of a porous electrode model for lithium-ion batteries
We present a porous electrode model for lithium-ion batteries using Butler-Volmer reaction kinetics. We model lithium ion concentration in both the solid and fluid phase along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially h...
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| Fformat: | Journal article |
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Society for Industrial and Applied Mathematics
2019
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| Crynodeb: | We present a porous electrode model for lithium-ion batteries using Butler-Volmer reaction kinetics. We model lithium ion concentration in both the solid and fluid phase along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially homogeneous which decouples the problem into a series of time-dependent problems. These problems can be solved on three distinguished time scales, an early time scale where capacitance effects in the electrode dominate, a mid-range time scale where a spatial concentration gradient forms in the electrolyte, and a long-time scale where each of the electrodes saturate and deplete with lithium respectively. The solid phase concentration profiles are linear functions of time and the electrolyte potential is everywhere zero which allows the cell potential to be determined analytically. Results are compared with numerical simulations and agree favourably. |
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