Fickâ€™s Law of Diffusion relates diffusion flux to the diffusion coefficient, change in concentration and change in position. The diffusive flux of a substance goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the change in concentration and the change in position, or put together the concentration gradient.
Fickâ€™s Law of Diffusion is commonly written as:
J = -D(delta[C]/delta[x])
where,
J is the diffusion flux
D is the diffusion coefficient
C is the concentration
x is the position
The negative sign in the above equation indicates that the diffusion is moving down the concentration gradient, for a net positive diffusion flux.
For example, if the concentration is 10^5 units/cm^3, which drops by 20% over a distance of 2 cm. Then the gradient (delta[C]/delta[x]) is -10^5. Assume the diffusion coefficient is 10^5. Then the diffusion flux equals:
J = -(10^5)(-10^5) = 10^10 units cm^-2 s^-1
Fickâ€™s Law of Diffusion is very important for understanding the motion of gases with respect to external factors such as the concentration gradient, and the diffusion coefficient which is an intrinsic value unique to a particular gas. However, this law is not limited to just gases in Physical Chemistry, as it can be applied to liquids diffusing across biological membranes in Biology. Thus, understanding this law is crucial for understanding the overall process of diffusion.
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# Fickâ€™s Law of Diffusion

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### Fick's law

We can treat a single ion channel as a cylindrical pore through the cell membrane. The channel is of length L = 5 nm and is filled with water. The concentration differences of sodium ions across the membrane is Ã¢??c = 100 mM. This concentration difference produces a flux of ions through the channel, given by FickÃ¢??s Law.

### Estimation of diffusion coefficient using Fick's law

Estimate the diffusion coefficient, D, of skin, given that 350 mL of water diffuses through the skin each day, that the surface of the skin is 1.73 m2, and that the skin is 20 um thick. Assume that there is pure water inside the skin.