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Fick's First Law of Diffusion
Relates the diffusive molar flux of a species to the concentration gradient driving it across a stagnant medium.
Interpretation
Fick's first law (duplicate): J = −D·(dC/dx). Flux is proportional to concentration gradient. See id=30 for full explanation.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| J | Diffusive molar flux | mol/m2.s |
| D | Diffusion coefficient | m2/s |
| dC/dx | Concentration gradient | mol/m3 per m |
What it means
This is a duplicate entry of Fick’s first law (see id=30). For completeness, the law is repeated here. Fick’s first law is the fundamental equation for diffusive mass transfer. It states that the molar flux J of a species is proportional to the negative of the concentration gradient, with the diffusion coefficient D as the constant of proportionality. It is applicable to steady‑state diffusion and forms the basis of many mass transfer models. In practice, it is used to determine the rate of diffusion of gases through porous media, diffusion of solutes in liquids, and diffusion of atoms in solids. It is also used in the design of membrane separation processes and in understanding drug release from pharmaceutical formulations. The law is named after Adolf Fick, who first formulated it in 1855.
Worked example
Fick's First Law – Two Examples
Real‑World| Parameter | Value |
|---|---|
| D | 1×10⁻⁹ m²/s |
| dC/dx | 1000 mol/m⁴ |
| Parameter | Value |
|---|---|
| D | 1.5×10⁻⁵ m²/s |
| dC/dx | 200 mol/m⁴ |
Common mistakes
- Duplicate of ID 30 – see that entry.
- Note: Ensure you update the correct ID if you intend to keep separate content; otherwise, use the same as ID 30.
Applications
Fick's first law (as noted) is fundamental for diffusion analysis. Its duplicate entry reinforces the importance of this law in chemical engineering. It remains a cornerstone for modelling mass transfer in membranes, porous catalysts, biological tissues, and environmental systems. By applying Fick's law, engineers can design gas separation membranes, predict the release of active ingredients in pharmaceuticals, and model the spread of pollutants in air and water. The law also underlies the design of diffusion‑limited reactors and the analysis of corrosion and oxidation processes. Despite its simplicity, it provides a reliable starting point for more complex transport phenomena.
- Same applications as id=30: membrane separations, catalysis, drug delivery, corrosion, environmental transport
Frequently Asked Questions
Fick's first law states that the diffusive flux is proportional to the concentration gradient: J = –D·(dC/dx). It describes the spontaneous movement of molecules from regions of higher concentration to lower concentration, driven by the gradient.
In SI, D has units of m²/s. Other common units are cm²/s (1 cm²/s = 10⁻⁴ m²/s).
D generally increases with temperature, following an Arrhenius‑type equation: D = D₀·exp(–E_d/(RT)). This is used to estimate D at different temperatures.
Molecular diffusion occurs due to random thermal motion of molecules. Eddy diffusion (turbulent diffusion) occurs in turbulent flow and is much faster; it is described by an eddy diffusivity that is not a material property.
In gases, D is of the order 10⁻⁵ m²/s; in liquids, about 10⁻⁹ m²/s; in solids, 10⁻¹² to 10⁻¹⁶ m²/s. The large difference is due to the closer packing and stronger interactions in condensed phases.
For a membrane of thickness δ, with concentrations C₁ and C₂ on the two sides, the flux is J = –D·(C₂ – C₁)/δ (assuming linear gradient). This is used to calculate permeability.
- Using the law in a transient situation without the time derivative.
- Ignoring the effect of temperature on D.
- Assuming D is constant when it depends on concentration (non‑Fickian diffusion).
- Forgetting to include the negative sign, leading to a sign error in the flux direction.
The diffusion coefficient is related to the mean squared displacement of particles: D = ⟨x²⟩/(2t) in one dimension (Einstein relation). This connects macroscopic diffusion to microscopic particle motion.