Diffusion Coefficient: Definition, Equation & Units

Instructor: Nichole Miller

Nichole is a research scientist with a PhD in Materials Science & Engineering.

This lesson defines and explains the importance of the diffusion coefficient and shows the equation relating the diffusion coefficient to temperature.


What will happen if you add a drop of blue food coloring to a glass of water? The food coloring will gradually mix with the water until all of the water is the same blue color. This occurs because of diffusion.

The food coloring gradually mixes with the water due to diffusion.
Food coloring

Diffusion is the net movement of atoms or molecules from a high concentration region to a low concentration region. It is not surprising that the word diffusion comes from the Latin word diffundere, meaning ''to spread out,'' since diffusion causes the atoms or molecules to spread out and evenly disperse.

Diffusion in Gases, Liquids, and Solids

Diffusion can occur in gases, liquids, and solids. It's easy to imagine examples of diffusion in gases, such as the diffusion of perfume through the air, and diffusion in liquids, such as the diffusion of food coloring in a glass of water.

One example of diffusion is solids is case hardening, a method of strengthening the surface of steel while keeping its interior ductile. The case-hardening process involves the diffusion of carbon into the surface of the steel. Case hardening is often used to harden the surface of gears, valves, and other engine components.

Diffusion in gases and liquids can be very fast. That is why you can watch food coloring diffuse into water fairly quickly. Diffusion tends to be slower in solids since the atoms are bonded close to each other within a solid.

The Diffusion Coefficient

The diffusion coefficient, also known as the diffusivity, describes how fast one material can diffuse through another material. The higher the diffusion coefficient, the faster diffusion will be. Therefore, the diffusion coefficients for solids tends to be much lower than the diffusion coefficients for liquids and gases. The diffusion coefficient is an important variable in many equations, including Fick's First and Second Laws.

The diffusion coefficient has units of m2/s and can be calculated with the following equation.


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