The diffusion coefficient
As was discussed on the previous chapter, the description made by Adolf Fick regarding diffusion established that the net fluxes of matter are determined by the gradient of the concentrations of such matter in space. Hopefully, we have already understood that,
Excellent!... But, wait a minute!... The previous expression has no information about how the diffusion will take place in time.
Well, that seems to be a very clever observation. However, it's not accurate. Sorry!
The flux, F, intrinsically contains temporal information because it says how much matter will "translate from one place to another" per unit of time. The temporariness of F is given by D, the diffusion coefficient. Yes, that "D" that we carry out all the way in the previous chapter with no further explanation except to relate it with trees and leaves in the path of a cloud of mosquitoes, is treally the bearer of the clock. In order to illustrate this concept, let's look at an example. Suppose we have a glass of water and just for fun we pour a drop of Food Coloring into it (you pick the color!). What we'll see is that slowly but steadily the dye will start dissolving in the water, going everywhere. Voila! We were a witness to diffusion. Now, suppose we try to do the same in Jello (a dye-free one). Although Jello is mostly water, what we will see is that the Food Coloring barely moves... just as expected. In terms of Fick's first law, we have for both cases, the initial gradients of concentration are the same because the initial concentration of dye in the drops are identical, and the water, as the Jello, has none. Therefore the difference in the "speed" of the diffusion depends on the Diffusion Coefficient.
This conclusion leads us to an understand an interesting feature of the Diffusion Coefficient. This scalar is not only related to the nature of the diffusing matter, but it also depends on the characteristics of the medium that contains it. This is an important concept to embrace. D is only meaningful when it is referred to with respect to a solvent or medium. For example, the diffusion coefficient of Calcium in water, or the one for fluorescein in ethanol. It always has to be referred to in relation to something else.
Back to : Fick's first law or Fick's first law - part II