Membranes - Principles of Chemical Separations with Environmental Applications - page 240

cc(STP)
cm

10 − 8

Q CO 2 = 3 . 465 × Note this is slightly reduced from

the pure component analysis.

· s · atm

9 . 86(0 . 070)

(0 . 349)

0 . 161

1

10 − 8 )

Q CH 4 = 0 . 161(0 . 444 × +

1 + 0 . 070(10) + 0 . 326(10)

cc(STP)
cm

10 − 10

Q CH 4 = 9 . 30 × This answer is also slightly lower

than the pure component analysis.

· ·

s atm

Q CO 2
Q CH 4 =

α mixture = 37 .

9.7 Porous membranes

Four types of diffusion mechanisms can be utilized to effect separation in porous mem-
branes. In some cases, molecules can move through the membrane by more than one
mechanism. These mechanisms are described below. Knudsen diffusion gives relatively
low separation selectivities compared to surface diffusion and capillary condensation.
Shape selective separation can yield high selectivities. The separation factor for these
mechanisms depends strongly on pore-size distribution, temperature, pressure, and inter-
actions between the solute being separated and the membrane surfaces.

9.7.1 Knudsen diffusion

Under viscous flow (Poiseuille flow), the mean free path of fluid molecules is small
compared to the pore diameter, and molecules undergo many more collisions with each
other than with the walls of the membrane. The molecules in a mixture do not behave
independently in viscous flow and no separation is possible. Thus, viscous flow is not
desirable. As the pressure is lowered, the mean free path ( ) of the molecules becomes

longer than the pore diameter (Figure 9.2(a)). As a result, the molecules undergo far
more collisions with the pore walls than with each other, and the molecules flow through
the pores independently from each other. The mean free path of a gas molecule can be
calculated as:

λ

kT
√ 2

λ =

P ,

(9.11)

σ

where k = Boltzmann's constant

T = absolute temperature

P = absolute pressure

σ = molar average collision diameter.