Battery knowledge · Transport and modelling
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. [1]
- Unit
- mol/(m²·s)
- Relationship
- J = −D · dc/dx
Example
Read the direction of a flux
With D = 1×10⁻¹⁰ m²/s and dc/dx = 1×10⁶ mol/m⁴, J = −1×10⁻⁴ mol/(m²·s). The negative sign means diffusion points toward decreasing concentration.
Explore the graph
The minus sign in Fick’s law sends material down its concentration gradient.
Flux J = 500 μmol/(m²·s), toward increasing position.
J = −D dc/dx
Illustrative model. The profile is imposed and static. Time evolution requires Fick’s second law and boundary conditions.
Use in Lemonergy
Lemonergy Core equation
Calculate diffusion flux
Lemonergy Core evaluates this relation.
Equation or tool to use
- ficks_first_law_flux
Core equation
Inputs & settings
- D (m²/s)
- dc/dx (mol/m⁴)
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
- Open the lesson and inspect the equation.
- Change one input while holding the others fixed.
Example. For D = 1 × 10⁻¹⁰ m²/s and dc/dx = 2 × 10⁶ mol/m⁴, J = −2 × 10⁻⁴ mol/(m²·s).
Observe. Compare the result with the equation and units.
This does not solve second-law time evolution or specify boundary conditions.
Open the worked lesson →References & further reading
Technical references
- 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.
- 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.