Figure 2.2.2 represents the simplest diffusion system and shows the diffusion of atoms of a gas through a metal plate, where the concentrations (or pressures) of the diffusion component on both surfaces are maintained constant. Figure 2.2.2 could be a schematic representation of the process used to purify hydrogen (H), which diffuses through palladium (Pd) sheets. As hydrogen is very small (atomic radius 0,46Å) it diffuses quickly through palladium sheets (atomic radius 1,376Å and CFC structure).
The flux J of the diffusing atom, in Figure 2.2.2, is positive from left to right, because it moves from a region of high concentration to a region of lower concentration, over a distance. The flux is defined as the quantity of mass (m) that passes through a unit of area (A) perpendicular to the flux direction (the flux is a vector) per unit of time (t):
\[J =\frac{m}{At} \tag{2.1} \]
The units of flux are:
\[[(quantity of mass).(length^{-2}).(time^{-1})]\]
for example:
\[(\frac{mol}{m^{2}.s})\]
If the flux doesn’t vary over time it is said to be in a steady state. In the present case, the concentrations CA and CB are constant, the gradient of concentration \(\frac{dC}{dx}\) is constant and as \(C_{A}>C_{B}\), the gradient of concentration is negative from left to right. The gradient of concentration is the inclination of tangent, or angular coefficient, at any point under a known curve known as the concentration profile, which is a curve of concentration C as a function of the position (or distance) of the point considered to be in the interior of solid, x.
The quantity of mass that passes through the membrane in Figure 2.2.2 increases when the area A increases and when the gradient \(\frac{dC}{dx}\) becomes more negative. The proportionality coefficient for this system is known as diffusivity or diffusion coefficient D. The equation that describes the flux is known as Fick’s First Law1.
\[J =-D \frac{dC}{dx} \tag{2.2} \]
1Adolf Eugen Fick (1829-1901), german scientist and physiologist, author of the Fick Laws of Diffusion. He also made important contributions in Physiology, like being the first to propose measuring cardiac output, the rate of blood flow though the heart.
