Remarks on quiescent systems

The following observations show that in contrast with heat conduction, mass diffusion processes seldom occur in quiescent systems. Therefore mass diffusion in quiescent systems has less practical meaning compared to heat conduction. We understand mass diffusion to be mass transport as a result of the natural movement of molecules from one region of a system to another. Correspondingly, heat conduction can be described as the energy transport due to the statistical movement of elementary particles caused by an irregular temperature distribution. In this respect a close relationship between mass diffusion and heat conduction exists. 

In contrast to heat conduction, in mass diffusion the average velocity of the particles of the individual materials in a volume element can be different from each other, so that a relative movement of the individual particles to each other is macroscopically perceptible. In general this results in a macroscopic movement of all particles in a volume element and therefore convection. As these considerations show, in contrast to heat conduction quiescent systems cannot always be assumed for mass diffusion. This can only be assumed under certain conditions, which we will now discuss. 

We will limit ourselves to a discussion of systems where the reference velocity for the determination of the mass diffusional flux disappears, cf. (1.153). As a 

The model considered here is that of an incompressible body. This is defined by the fact that the density of a volume element in the material does not change during its movement, i.e. g = g(x,t) = const and therefore dg/dt = 0, which is fulfilled in our case, because due to w = 0 and dg/dt = 0 

As an example we will take a porous body into which hydrogen diffuses. A volume element in the porous body has a certain mass and therefore a certain density, e.g. p = 7.8 103 kg/m3. According to this a volume element of 1 mm3 has a mass of 7.8 10-3 g. We assume that the volume element is at the ambient temperature 298 K with a partial pressure of hydrogen of p = 1 hPa. The equation of state for ideal gases is used to find the hydrogen absorbed by the volume element, which is 

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