# Fick's law of diffusion

 related topics {math, energy, light} {acid, form, water} {math, number, function}

Fick's laws of diffusion describe diffusion and can be used to solve for the diffusion coefficient, D. They were derived by Adolf Fick in the year 1855.

## Contents

### Fick's First Law

Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). In one (spatial) dimension, this is

where

• J is the diffusion flux in dimensions of [(amount of substance) length−2 time−1], example $(\tfrac{\mathrm{mol}}{ \mathrm m^2\cdot \mathrm s})$. J measures the amount of substance that will flow through a small area during a small time interval.
• $\, D$ is the diffusion coefficient or diffusivity in dimensions of [length2 time−1], example $(\tfrac{\mathrm m^2}{\mathrm s})$
• $\, \phi$ (for ideal mixtures) is the concentration in dimensions of [(amount of substance) length−3], example $(\tfrac\mathrm{mol}{\mathrm m^3})$
• $\, x$ is the position [length], example $\,\mathrm m$

$\, D$ is proportional to the squared velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid and the size of the particles according to the Stokes-Einstein relation. In dilute aqueous solutions the diffusion coefficients of most ions are similar and have values that at room temperature are in the range of 0.6x10−9 to 2x10−9 m2/s. For biological molecules the diffusion coefficients normally range from 10−11 to 10−10 m2/s.