Fick's law of diffusion

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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.

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