û ûo 1 S(Pf Pb)
BASIC SEPARATION THEORY
The ability of a barrier to transmit gas is usually expressed as û (gamma), the
permeability. This is a measure of the total flow through a barrier and may be defined
as the ratio of the number of molecules which pass through the barrier to the number
which would pass through the space if the barrier were not there. This total flow
through a barrier is known to be a combination of several different types; namely,
diffusive flow, film flow, and viscous flow. As was previously explained, the type of
flow that is of greatest importance for a gaseous diffusion plant is diffusive flow.
However, as film flow and viscous flow affect the separation through a barrier, they
cannot be ignored.
Film flow refers to the transport of molecules under the influence of the force field
between the molecules and the barrier surface. When such force fields are significant,
a large number of molecules will not have sufficient velocity normal to the surface to
escape from this field so that their motion will be confined to the barrier surface and
barrier pore surface. Such molecules would pass through the barrier as a film on the
surface of the pores.
Viscous flow occurs when molecules flow as a group in the manner of ordinary flow
through a tube. Referring back to permeability, it is known that the flow through a
barrier increases as the pressure increases. Also, as the pressure increases, so does the
viscous component of flow. The relation between permeability and viscous flow can best
be shown by the following equation.
In this equation where P equals the fore or high side pressure and P equals the back or
low side pressure. û equals the permeability, û, when
P + P = 0.
S is called the slope factor and is inversely proportional to the viscosity of the gas.
In the above equation, the term S(P + P ) is a measure of the viscous component of
flow. Figure A-2 illustrates the variation of permeability with the slope factor and
changes in pressure.