Fick's Laws
Also known as: diffusion equation, Fickian diffusion
Fick's Laws describe how species diffuse through media due to concentration gradients. The First Law (steady-state) relates diffusion flux to concentration gradient, while the Second Law (transient) describes how concentration changes over time. These laws are fundamental to mass transfer analysis, applying to gases, liquids, and solids. Fick's Laws are analogous to Fourier's Law of heat conduction, replacing temperature with concentration.
Key highlights
- Simple, mathematically elegant formulation
- Extensive library of analytical solutions for standard geometries
- Applicable to diverse phenomena (gases, liquids, solids)
- Integrates readily with heat transfer (thermal-diffusion analogy)
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use Fick's Laws for analyzing any mass diffusion process: gas absorption, liquid-liquid extraction, drying of solids, adsorption, ion transport, and chemical reaction with diffusion. Apply First Law for steady-state, Second Law for transient analysis. For binary mixtures in most cases; for multicomponent systems, consider Stefan-Maxwell equations.
Strengths & limitations
- Simple, mathematically elegant formulation
- Extensive library of analytical solutions for standard geometries
- Applicable to diverse phenomena (gases, liquids, solids)
- Integrates readily with heat transfer (thermal-diffusion analogy)
- Assumes constant or weakly concentration-dependent diffusion coefficient
- Less accurate for multicomponent systems (Stefan-Maxwell more rigorous)
- Cannot account for pressure-driven or thermophoretic effects
- Assumes isotropic diffusion; does not capture anisotropic materials
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What is the diffusion coefficient and what are typical values?
The diffusion coefficient D characterizes how fast a species diffuses through a medium. Typical values: gases in gases ~10^-5 m²/s, gases in liquids ~10^-9 m²/s, liquids in liquids ~10^-9 m²/s, ions in solutions ~10^-9 m²/s. Temperature dependence is strong (proportional to T^1.75 for gases).
How do I distinguish between steady-state (First Law) and transient (Second Law) diffusion?
Steady-state diffusion occurs when concentration doesn't change with time—a quasi-equilibrium has formed. This is relevant when time scales are long enough and boundaries are maintained at constant concentration. Transient diffusion occurs when concentration changes over time, relevant in early stages or when boundaries change.
What is the error if I ignore bulk flow in diffusion?
If bulk flow velocity is comparable to diffusion velocity, Fick's Law becomes inaccurate. When one component diffuses much faster than others, it induces bulk flow that Stefan-Maxwell equations account for. For equimolar counter-diffusion or dilute solutes, bulk flow effects are negligible.
Sources
- 1.Fick, A. (1855). On liquid diffusion. Philosophical Magazine, 10(63), 30-39.
- 2.Incropera, F. P., DeWitt, D. P., Bergman, T. L., & Lavine, A. S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.). Wiley.ISBN 978-0470055540
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Fick's Laws. ScholarGate. https://scholargate.app/thermodynamics/ficks-laws