Fick's Laws of Diffusion

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Fick's Laws of Diffusion

By Paul A. Steward.

Diffusion is the mechanism by which components of a mixture are transported around the mixture by means of random molecular (Brownian) motion (cf. permeation: the ability of a diffusant to pass through a body - dependent on both the diffusion coefficient, D, and the solubility coefficient, S, ie, permeability coefficient, P = D.S). Flynn et al. cite Berthalot as postulating, at the beginning of the nineteenth century, that the flow of mass by diffusion (ie, the flux), across a plane, was proportional to the concentration gradient of the diffusant across that plane.  
[url=]In the mid-1800's,[/url]Fick introduced two differential equations that quantified the above statement for the case of transport through thin membranes. Fick's First Law states that the flux, J, of a component of concentration, C, across a membrane of unit area, in a predefined plane, is proportional to the concentration differential across that plane (see note), and is expressed by:  

Fick's Second Law states that the rate of change of concentration in a volume element of a membrane, within the diffusional field, is proportional to the rate of change of concentration gradient at that point in the field, as given by:  

where t = time.  

Adapted from: Modification of the Permeability of Polymer Latex Films., Nottingham Trent University PhD Thesis, 1995.
Copyright © Paul Steward, 1995.