Page 176 - Industrial Ventilation Design Guidebook

I 3 8 CHAPTER 4 PHYSICAL FUNDAMENTALS

According to the analogy model, it is valid that

This allows the mass transfer factor to be calculated. The above equation can
be refined to

It follows that

simplifying to

where Le = (D ABpCp)/X = Pr/Sc is the Lewis number (or Luikov's number in
the Russian literature).

4.3.8 Diffusion through a Porous Material

In a steady-state situation when gas flows through a porous material at a low ve-
locity (laminar flow), the following empirical formula, Darcy's model, is valid:

2
where k represents the permeability of the matter (m ). The kinematic viscos-
2
ity of the gas is denoted by i>(m /s), and p is the density of the gas for the to-
tal volume—or if the real density of the gas is d, p = <j>d t where <j> is the
volume percentage of the gas in the porous material. It is also seen that $ gives
the percentage of the free cross-sectional area of the gas in the material:

In Eq. (4.301) velocity u x is the real velocity of the gas in the pores: u x =
q v/A(g) = q v/((f))A, where q v is the volume flow.
From Darcy's equation we can determine a formula for the counterforce
produced by the porous material to the flowing or diffusing component A. If
this counterforce is found, it can be added to the diffusion resistance force
caused by component B to component A; hence the sum of these two forces
represents the total diffusion resistance.
For a porous material the linear momentum equation can be written as

where f mx represents the resistance force between the gas and the material, the
flow friction. The term (f> is important in Eq. (4.302). It comes from the fact
that while p appears on the left side of Eq. (4.302), the balance is constructed