Fick's first law

Diffusive flux
1. Fick's law determines the density and direction of the diffusion flux j - so let's first define what it is: It is a vector quantity, the size of which tells us how many moles of a given substance will pass through a unit area S per unit time t:
 * $$j = \frac {n} {S \cdot t} $$

As can be seen, the unit of diffusive flux density in the SI system is mol.m -2 .s -1.

The direction of the diffusion flux then tells us the mean direction of the particle flow. So it is clear that it must be a vector quantity. It formally becomes this if we multiply the value from the previous equation by the unit vector in the flow direction.

The flow density over a surface can also be expressed from the average velocity of particles flowing over this surface and the particle concentration:
 * $$\mathbf{j}=c\cdot \mathbf{v}$$

1. Fick's law
1. Fick's law states that the diffusion flux density j is proportional to the negative concentration gradient :
 * $$\mathbf{j} = -D \cdot \mathrm{grad}\, c$$

A gradient can be intuitively understood as a mathematical operation that receives as an argument a scalar function in space, i.e. a scalar field, and returns a vector function in space, i.e. a vector field. The gradient at a given point is actually a vector in the direction of greatest gradient. Diffusion coefficient D is a constant characterizing how easily a given substance diffuses through a given environment.

Worth mentioning the fact that the diffusive flux j is a vector quantity, nevertheless is not surprising even with a cursory thought, because in diffusion process it is not only important how much substance is moved, but also where it is moved.

For the one-dimensional case and for the approximation of the gradient by small but final changes, a much simpler shape can be used:
 * $$j = -D \cdot \frac {\Delta c} {\Delta x} $$

, where Δc is the difference in molar concentrations of two nearby locations Δx away from each other. the unit of the concentration gradient is therefore mol.m -4.

Diffusion coefficient
The proportionality constant in Fick's 1st law is the so-called diffusion coefficient D expressing the number of moles of a substance that pass through a cross-section of 1 m 2 in a time of 1 s at a concentration gradient of 1 mol/m.