Fick's Law Of Diffusion

What is Fick’s law of diffusion?

Fick’s law of diffusion explains the diffusion process (movement of molecules from higher concentration to lower concentration region). In 1855, Adolf Fick described the Fick’s Law of Diffusion. A diffusion process that obeys Fick’s laws is called normal diffusion or Fickian diffusion. A diffusion process that does NOT obey Fick’s laws is known as Anomalous diffusion or non-Fickian diffusion.

Fick’s Law of Diffusion is used to solve the diffusion coefficient D.

There are two laws that are interrelated ie; Fick’s first law is used to derive Fick’s second law which is similar to the diffusion equation.

According to Fick’s law of diffusion,

“The molar flux due to diffusion is proportional to the concentration gradient”.

The rate of change of concentration of the solution at a point in space is proportional to the second derivative of concentration with space.

Fick’s First Law

Movement of solute from higher concentration to lower concentration across a concentration gradient.

\(\begin{array}{l}J = -D\frac{\mathrm{d} \varphi }{\mathrm{d} x}\end{array} \)


J: diffusion flux

D: diffusivity

φ: concentration

x: position

Fick’s Second Law

Prediction of change in concentration along with time due to diffusion.

\(\begin{array}{l}\frac{\partial \varphi }{\partial t} = D \frac{\partial^2 \varphi }{\partial x^2}\end{array} \)


D: diffusivity

t: time

x: position

Φ: concentration

Application of Fick’s law

    • Biological application:

\(\begin{array}{l}flux = -P(c_{2}-c_{1})\end{array} \)
(from Fick’s first law)


P: permeability

c2-c1: difference in concentration

  • Liquids: Fick’s law is applicable for two miscible liquids when they are brought in contact and diffusion takes place at a macroscopic level.
  • Fabrication of semiconductor: Diffusion equations from Fick’s law are used to fabricate integrated circuits.
  • Pharmaceutical application
  • Applications in food industries.

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