[Elpmek]

Hi folks,
I've to talk about the diffusion of a molecule from a hydrogel due to enzyme cleavage and I'm struggling to get a grasp of the different models of diffusion (i.e. Fickian and non-Fickian). Could someone explain these to me in relatively simple terms?

What equations can be used by these models and which would would be relevant for the system I am looking at?

Any help at all would be really appeciated.

[Corribus]

Fickian diffusion is essentially based on the premise that the rate of mass movement at a point is linearly proportional to the concentration gradient. The constant of proportionality is the diffusion constant. In turn, the diffusion constant is usually based on the Stokes-Einstein relation, which is in turn based on simple Brownian motion. Generally speaking Fickian diffusion is applicable to simple fluids and application of the differential equations is straightforward (although the math can be laborious) for such things as diffusion across a thin film - in biological terms, a cell membrane qualifies here.  If you have access to Atkins and de Paula physical chemistry textbook, there is a nice section on application of Fick's laws to this kind of biological system. It's also used to model diffusion of small molecules or gasses in polymers, which has applications in packaging technology, particularly for foods.

Non-fickian diffusion is basically any diffusion scenario that cannot be modeled in this way. It is typically applicable to more complicated systems where the simple assumptions in Fickian diffusion don't apply. Some examples would be: diffusion in polymers or solids that are below the glass transition temperature, diffusion of substances at very high concentrations or when there is significant interaction between the diffusant and other nearby molecules (e.g., non-ideal solutions), diffusion through highly heterogeneous matrices possibly, and so forth.

You can find some preliminary information here: http://en.wikipedia.org/wiki/Fick%27s_law
But if you want a better explanation, especially with some applications, you'd be better off finding yourself a good physical chemistry text book.

The "bible" of diffusion mathematics is usually taken to be a book by John Crank (written way back in 1979) called "The Mathematics of Diffusion", but unless you are really good at following long (and I mean long) chains of differential equations, I'd stick to more elementary sources of information.