Page 74 - Adsorption Technology & Design, Elsevier (1998)

Rates of adsorption of gases and vapours by porous media 71

coefficient. The classical kinetic theory of gases (Present 1958) reveals that
the diffusion of a gas is determined by the mean velocity of molecules and
the distance they travel before they collide either with another molecule
(molecular or Maxwellian diffusion) or with the wall of a narrow capillary
(Knudsen diffusion). When the mean free path A, is smaller than the
dimensions of a containing conduit, unconstrained molecular transport
occurs; if, on the other hand, the mean free path is greater than the radius of
a narrow channel (for example, pores within a porous solid) through which
molecules are travelling, then Knudsen diffusion obtains.
Pore size distribution data obtained from gas desorption (Barret et al.
1951) and mercury porisimetry experiments together with a knowledge of
adsorbate molecular size thus enables the mode of diffusive transport to be
ascertained. It should be noted that both molecular and Knudsen diffusion
may occur in the same porous medium when the porous medium contains
both macropores and micropores (revealed from an analysis of a bimodal
pore size distribution curve). Unconstrained molecular diffusion, DM, and
Knudsen diffusion, DK, coefficients are subsequently calculated from
formulae derived from transport properties of fluids (gaseous and liquid)
and the kinetic theory of gases. The molecular diffusivity for a binary gas
mixture of A and B is evaluated from the Chapman-Enskog theory
(Chapman and Cowling 1951) equation
(1.858 x 10-7)T 3/2 ((lIMA) + (lIMB)) t/2
DM = pO.2AB I (4.9)

in which DM is expressed in units m 2 s -1, MA and MB are the molecular
masses of the species A and B, Crab is a constant in the Lennard-Jones
potential function and I is the collision integral (see Section 3.1). The
Knudsen diffusivity, in contrast to the bulk diffusion coefficient, is
calculated from the kinetic theory formula
2 2 (8Re, T] '/2
DK = -~- re = --3 r trM ] (4.10)

where r is the pore radius, C" the average molecular velocity and M the
molecular mass. When the mean free path and pore radius are of a similar
magnitude the resultant diffusivity is calculated in proportion to the individual
bulk and Knudsen diffusivities. According to Pollard and Present (1948), for
adsorption and desorption, equimolar counterdiffusion occurs and so the
resultant resistance to diffusion is the sum of the resistances to bulk diffusion
and Knudsen diffusion. Thus the net diffusion coefficient D is given by

I/D = (I/DM) + (I/DK) (4.11)