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Physical Sciences
Physics
1855
Intermediate

Diffusion Equation

∂C∂t=D∇2C\frac{\partial C}{\partial t} = D \nabla^2 C

Concentration spreads over time—molecules diffuse from high to low concentration regions.

By Adolf Fick

Physical Sciences
Diffusion Equation
1855 · Adolf Fick
Why it matters: Explains smell spreading, semiconductor doping, and biological signaling.

Discoverers: Adolf Fick (1855)

What does it mean?

Concentration spreads over time—molecules diffuse from high to low concentration regions.

Why should I care?

Explains smell spreading, semiconductor doping, and biological signaling.

Variables & Units

SymbolNameUnitMeaning
CCConcentration—Substance concentration
DDDiffusion coefficientm²/sDiffusivity
ttTime—Time

Worked Example

Perfume molecules spread: σ = √(2Dt) after time t.

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Sources & further reading

Search WikipediaSearch Wolfram MathWorldOpen in Wolfram|AlphaWatch explainers on YouTube

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Equation Universe

Diffusion Equation

∂C∂t=D∇2C\frac{\partial C}{\partial t} = D \nabla^2 C

Real-world impact

Modern electronics

Electrostatic design at nanometer scales.

Photo: Unsplash — microchip

Concentration spreads over time—molecules diffuse from high to low concentration regions.

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