Ficks Law and Diffusion Coefficients

Fick's law states that the flux of nutrient particles across our imaginary planar section due to their random motion is approximately proportional to the local gradient in the concentration of particles. Together with a term, dc/dx, that describes the change in concentration over distance, the diffusion equation depends on D, a diffusion coefficient, whose magnitude does not depend on distances or concentration but instead describes the mobility of particles as a function of their size, charge, the nature of their interactions with the solvent, and the temperature.

Without solving the diffusion equations, we may say that the units for the diffusion constant, D, are distance squared per unit time. This observation alone says that the average distance through which diffusion operates in an interval of time is proportional to the square root of the product: D times time, and that the time taken to diffuse a distance, d, is proportional to the distance squared divided by the diffusion coefficient.

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