Membranes - Principles of Chemical Separations with Environmental Applications - page 241

Table 9.1 Mean free paths for various gases.

Mean free path (nm)

500 K 800 K

Gas σ (nm) 0.1 MPa 1.0 MPa 5.0 MPa 0.1 mPa 1.0 MPa 5.0 MPa

H 2 0.2915 183 18.3 3.7 293 29 5.9

CO 0.3706 113 11.3 2.3 181 18.1 3.6

N 2 0.3749 111 11.1 2.2 177 17.7 3.5

CO 2 0.3897 102 10.2 2.0 164 16.4 3.3

Transient
gap between
chains in
matrix allows
penetrant
to diffuse

Upstream Upstream Upstream

Upstream

Downstream

Downstream Downstream Downstream

Size (diffusivity) and
condensibility (solubility)
selectivity factors
interact to determine
which component passes
the fastest.

Knudsen diffusion
allows separation
on the basis of the
square root ratio of the
molecular weight of
components A and B.

Size-selective
molecular sieving
allows passage of
the smallest of the
two components.

Selective sorption of
more-condensable
component in pores
can exclude the
transport of the
smaller components.

(b) (c) (d)

(a)

Knudsen diffusion Selective surface

adsorption with
surface diffusion

Molecular sieving

Sorption-diffusion

transport

transport

transport

Figure 9.2 The four possible general mechanisms for selective-membrane-based
gas and vapor separations [3]. Reproduced with permission of AIChE.

Table 9.1 indicates some representative values of the mean free path of several gases at
various pressures and temperatures.
For a circular capillary of radius r and length l , the molar flux of component i in the
Knudsen diffusion regime is given by:

8 π

M i RT

r 3 P i

l

J i =

3 √ 2

, (9.12)

π