Fick’s second law

Example

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Use in Lemonergy

Specify phase, direction and boundaries.

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Fick’s first law

J = −D dc/dx: diffusive flux is proportional to the concentration gradient and points down it. It is a constitutive law, valid at one instant; Fick’s second law follows from it when mass is conserved.

Newman model

The standard physics-based lithium-ion cell model: porous-electrode theory across the cell thickness, with solid diffusion solved in a representative spherical particle at every point — hence pseudo-two-dimensional. It predicts voltage from first principles but needs dozens of parameters.

Single-particle model

A simplified physics model that represents each electrode as one spherical particle and neglects electrolyte gradients. It runs fast enough for a BMS and is accurate at low to moderate currents.

Solid-state diffusion

Lithium moving through the crystal lattice of an active-material particle, with diffusion coefficients of about 10⁻¹⁶ to 10⁻¹³ m²/s — three or more orders of magnitude slower than the 10⁻¹⁰ m²/s of the liquid. It is usually the rate-limiting step for thick electrodes and large particles.

References & further reading

Technical references

1. Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing

   IUPAC · 2011

   Technical reference · Physical-chemistry notation, thermodynamics, electrochemistry and transport quantities.

Further reading on this topic

These sources provide broader context; they are not presented as citations for every statement in this entry.

2. Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell

   Marc Doyle, Thomas F. Fuller, John Newman · Journal of The Electrochemical Society · 1993

   Topic background · Porous-electrode transport and insertion-cell modeling; foundational work rather than a specification for a particular commercial cell.