In the present paper we carried out several experiments in oxygen or dry air, at low
temperature of some metallic samples. In order to be able to extend or estimate the corrosion
phenomenon we made use of the modelling of oxygen diffusion through rust layers (oxides) and of
solving the parabolic equations of diffusion, respectively. The diffusion equation is important for
modelling the oxygen diffusion within biological systems and for modelling the neutron flux from
nuclear reactors.
3. =0.003997 [cm], for t=1.5552x107[s]).
3. MATHEMATICAL MODELLING OF DIFFUSION
The equations that describe the diffusion are parabolic partial derivatives, and the
mathematical models are based on three remarkable laws:
- the equation of heat or the Fick second law for diffusion
, (1)
- convection-diffusion equation
, (2)
- and parabolic-diffusion equation
, (3)
where w(x,t) represents the practical value of a concentration, expressed in [mg/cm3], x is a
distance and t, time.
As a particular case, there is the function f(x)=e-x, n order to explain the decrease of
concentration in time: this decreases from the air-rust interface (outer air) towards rust-metal
interface (towards the interior). The study in one dimension has been imposed by a diffusion named