Fick's Law of Diffusion
Calculate the rate of diffusion using Fick's first law: J = -D(dC/dx).
Learn how concentration gradients drive molecular movement.
The Formula
Fick's first law of diffusion describes how molecules move from regions of higher concentration to regions of lower concentration. The flux J represents the amount of substance that flows through a unit area per unit time. The negative sign indicates that diffusion occurs in the direction opposite to the concentration gradient, meaning molecules naturally move from where they are more concentrated to where they are less concentrated.
Adolf Fick, a German physiologist, formulated this law in 1855. It has since become one of the most fundamental equations in biology, chemistry, and materials science. The law applies to any situation where particles spread out due to random thermal motion, a process known as passive diffusion.
In biological systems, Fick's law governs how oxygen and carbon dioxide exchange across lung membranes, how nutrients pass through cell walls, and how drugs are absorbed into the bloodstream. Pharmacologists use this equation to design drug delivery systems, ensuring medications reach target tissues at the correct rate. The diffusion coefficient D depends on the medium through which diffusion occurs, the size of the diffusing molecules, and the temperature. For example, small molecules like oxygen diffuse much faster than large proteins.
The concentration gradient dC/dx is the driving force behind diffusion. A steeper gradient means faster diffusion. This is why breathing faster increases oxygen uptake — it maintains a high concentration difference between the air in the lungs and the blood.
Fick's second law extends this to non-steady-state diffusion, where concentration changes over time. However, the first law is sufficient for most biological applications where steady-state conditions can be assumed.
Variables
| Symbol | Meaning |
|---|---|
| J | Diffusion flux — amount of substance per unit area per unit time (mol/m²·s) |
| D | Diffusion coefficient — depends on the substance and medium (m²/s) |
| dC/dx | Concentration gradient — change in concentration over distance (mol/m⁴) |
Example 1
Oxygen diffuses across a cell membrane. The diffusion coefficient is 2.1 × 10⁻⁹ m²/s, and the concentration drops from 8 mol/m³ to 2 mol/m³ over a membrane thickness of 10 μm (10 × 10⁻⁶ m). Find the diffusion flux.
dC/dx = (2 − 8) / (10 × 10⁻⁶) = −6 / 0.00001 = −600,000 mol/m⁴
J = −(2.1 × 10⁻⁹) × (−600,000)
J = 1.26 × 10⁻³ mol/m²·s
Example 2
A drug with diffusion coefficient 1.0 × 10⁻¹⁰ m²/s diffuses through skin. The concentration is 500 mol/m³ on the surface and 0 mol/m³ inside, across a 1 mm (0.001 m) thick layer. Find the flux.
dC/dx = (0 − 500) / 0.001 = −500,000 mol/m⁴
J = −(1.0 × 10⁻¹⁰) × (−500,000)
J = 5.0 × 10⁻⁵ mol/m²·s
When to Use It
Fick's first law of diffusion applies whenever you need to quantify how fast a substance moves through a medium due to a concentration difference.
- Calculating gas exchange rates in the lungs (oxygen in, carbon dioxide out)
- Designing transdermal drug patches and other drug delivery systems
- Modeling nutrient uptake in cells and tissues
- Analyzing pollutant dispersion in water or air
- Studying membrane permeability in laboratory experiments
- Engineering dialysis machines and filtration systems