# Heat transfer and diffusion of particles

# Particle scattering

### Fondamental : Fick's law and equation of particle scattering

Fick's three-dimensional law :

with the coefficient of scattering and the particle density.

This law shows that scattering can only take place in a medium where the particle density is not uniform.

Moreover, the gradient being oriented towards the increasing , the - symbol in Fick's law indicates that particles spontaneously scatter from the more concentrated places to the less concentrated ones.

Let's determine the one-dimensional equation of scattering without internal source of creation of particles.

A reasoning similar to the one of thermal transfers (we write the conservation of matter considering a cube, which has a volume ) :

It results in the equation of conservation of matter :

Using Fick's law, we obtain the one-dimensional equation of scattering :

In three dimensions, we have (see the lesson about "Vector calculus") :

And the equation of scattering (without source) :

### Attention : Fick's law and equation of particle scattering

**Fick's law :**

**Equation of scattering (without source) :**