Fick's first law - part II
Mathematically, dC/dx represents the change in concentration (C) with respect to distance (x). Suppose we are located in one place that we will call our starting point or x0, which happens to be in a rain forest close to a tropical beach. Let's say that the amount of mosquitoes in this place is very high. Then we walk toward the beach. We notice that the amount of mosquitoes remains unchanged. This means that at this point, x0+dx, the change in concentration (or gradient) is 0, in other words dC/dx=0. Notice that the gradient of mosquitoes (dC/dx) is zero even if the concentration (C) of them is high, over the distance (x). Soon, we are very close to the beach and happily, we see how the amount of mosquitoes decreases noticeably because of the breeze. Now, there is a gradient of mosquitoes which decreases as we walk toward the beach. In math, dC/dx<0, because C gets lower as x, with respect to the origin (x0), increases. In other words, dC/dx is negative. But, this is not the end of the story. After enjoying a great afternoon at the beach, we notice that the breeze, which was keeping the mosquitoes in the forest, fails to blow any longer. Later, the red sky of the sunset attracts mosquitoes to the beach. At that time, we observe a positive net flux (F > 0) from the forest to the beach. In other words, the mosquitoes start "diffusing" from the forest to the beach (F > 0) downhill along the gradient of concentration (dC/dx < 0). During diffusion, the mosquitoes found a lot of obstacles along their way to the beach (trees, leaves, spider webs, etc). The higher the number of obstacles, the smaller the flux would be. In fact, if we could wrap the whole forest with a huge screen, mosquitoes would never get to the beach. Therefore, the flux is also determined by how mobile the particles are inside the space (medium) that contains them. The mobility of the particles, represented by D in the equation above, which is a constant and depends on the nature of the interaction between each particle and the components of the medium. The constant D is normally referred as the diffusion coefficient.
In summary, Fick's first law established that a net flux (F) of particle take place between two contiguos region in space when there is a gradient of concentration (dC/dx) in between them. This tendency is a consequence of the random movement of the particle rather than interaction among them that "inform" the particle where they are located. The magnitude of the F is linearly proportional to -dC/dx, and de proportionality is given by a constant factor (D) known as diffusion coefficient.