Membranes - Principles of Chemical Separations with Environmental Applications - page 243

9.7.3 Capillary condensation

When one of the components in a mixture is a condensable vapor and the pores are
small enough, the condensate can block gas-phase diffusion through the pores. This is the
limiting case of surface diffusion where the adsorbed layer fills the pore. This condensate
will evaporate on the low partial pressure side of the membrane. The Kelvin equation
predicts that condensation can occur in small pores even through the partial pressure of
that component is below its vapor pressure. The Kelvin equation represents thermodynamic
equilibrium between the gas phase and fluid in the pore:

exp −

2 γ cos

P / P s = , (9.15)

ρ rRT

where P = vapor pressure in bulk phase in the presence of capillary pores

P s = normal vapor pressure in the bulk phase

γ = surface tension of the condensed fluid in the pore

= contact angle between the condensed fluid and the pore wall

ρ =

molar density of the condensed liquid

=

r mean pore radius.

As a result of capillary condensation, the pores can completely fill with that component
(Figure 9.2(c)). For a narrow distribution of pore sizes, all pores will be filled and the
fluxes of the other components through the membranes will be quite small and limited
by their solubility in the condensable component. Thus, extremely high separation factors
are possible.

9.7.4 Molecular-sieve separation

Molecular-sieve membranes can yield high separation factors by permitting small
molecules to diffuse while essentially excluding or severely restricting the accessibility
of larger molecules (Figure 9.2(d)). This type of diffusion, where the pores are of molecular
size, has been referred to as shape selective or configurational diffusion.

9.8 Membrane configurations

Membrane processes operate in two basic modes. In Figure 9.3(a), the permeate stream
is solely the components of the feed stream that transport across the membrane.
Figure 9.3(b) illustrates the case where a sweep stream is introduced on the permeate
side to collect the permeate. The sweep stream can operate cocurrent or countercurrent to
the feed stream. One limiting case is when the streams on both sides of the membranes are
perfectly mixed and there is no axial variation in solute concentration. These basic modes
are then incorporated into various geometric configurations (Figure 9.4).