Membranes - Introduction to Carbon Capture and Sequestration - page 311

30

D Fick

20

D MS

10

D S

0

0 2 4 6 8
Molecules/cage

Figure 7.4.1 The different diffusion coeffi cients of hydrogen
Diffusion coeffi cients of hydrogen in the zeolite FAU. The top curve is the Fick diffusion
coeffi cient ( D Fick ), followed by the Maxwell-Stefan diffusion coeffi cient ( D MS ), and fi nally
the self-diffusion coeffi cient ( D S ). Figure based on data from Jobic et al. [7.5].

Figure 7.4.1 shows experimental data for hydrogen diffusing in the
zeolite FAU. For this system Jobic and coworkers [7.5] simultaneously
measured the Fick diffusion coeffi cient and the self-diffusion coeffi cient
using quasi elastic neutron scattering (QENS) [7.6]. We see that the three
diffusion coeffi cients are indeed different. There are two important obser-
vations. In the limit of very low loading, the three different diffusion coef-
fi cient converge to the same value. We will demonstrate that this holds for
all systems. In addition, we see that if we increase the loading, the Fick
diffusion coeffi cient increases. This is counterintuitive! It seems to suggest
that at rush hour in New York Central Station people will diffuse faster! At
the end of this section you should be able to explain what is going on here.
Let us now consider these three different diffusion coeffi cients and
show how they are related. Let's start with Fick's defi nition of the diffu-
sion coeffi cient. From a practical point of view this is the most important
defi nition as it directly relates to mass transport. Suppose that we take a
material and apply a concentration gradient; we will observe a fl ux (in
molecules per unit area per unit time, see Figure 7.4.2 ). If the concentra-
tion gradient is not too large, this fl ux is proportional to the concentration
gradient driving force, or:

D d ρ

d

Fick

j = − ,