Lemonergy · Core equation

ficks_first_law_flux

One-dimensional diffusive molar flux for a supplied concentration gradient.

Implementation ID: ficks_first_law_flux
Reviewed: 2026-10-27

Behavior

Diffusivity must be finite and nonnegative; the gradient must be finite. Scalar and broadcastable array inputs are supported. This evaluates a constitutive law, not a spatial PDE, gradient estimator or boundary-condition solver.

Interface

Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.

Ports and observed outputs
Name	Direction	Unit	Meaning
`return`	output	mol/(m^2 s)	Scalar float or NumPy array following broadcasting.

Parameters

Defaults are initial model values. Select values for your own model and operating conditions.

Configuration fields
Parameter	Unit	Default	Meaning and limits
diffusivity `diffusivity`	m^2/s	Supplied by the user	Finite nonnegative diffusion coefficient.
concentration gradient `concentration_gradient`	mol/m^4	Supplied by the user	Finite spatial concentration gradient.

Equations and rules

J = -D * dc/dx

Worked example

Calculate diffusion flux

For D = 1 × 10⁻¹⁰ m²/s and dc/dx = 2 × 10⁶ mol/m⁴, J = −2 × 10⁻⁴ mol/(m²·s).

Open the worked lesson →

Use in a workflow

Calculate diffusion flux

Lemonergy Core evaluates this relation.

ficks_first_law_flux: Core equation
- D (m²/s)
- dc/dx (mol/m⁴)

Open the worked lesson

Connected concepts

Limits and interpretation

This does not solve second-law time evolution or specify boundary conditions.

Implementation sources

This reference follows Lemonergy implementation sources. Scientific articles support the linked concepts separately.

Repository: battery-core · Revision: main

src/battery_core/diffusion.py

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