Membranes - Introduction to Carbon Capture and Sequestration - page 318

species. At very low concentrations the thermodynamic factor, which
relates the Maxwell-Stefan diffusion coeffi cient to the Fick diffusion coef-
fi cient, is one. Hence, at the limit of very low concentrations all three
diffusion coeffi cients are identical.

Random walk

A different way of looking at diffusion is to assume that because of collisions
our molecule is performing a random walk. If we assume a random walk on
a cubic lattice, if our molecule jumps from one lattice point to another, we
can defi ne the mean squared displacement as (see Figure 7.4.4 ):

2

N

2

() ()

∑

z N − z 0 = I ,

i

i = 1

where l i is a random step on the lattice. If we now take an average over
many random walks:

2

() ()

...

z N − z 0 = II + II + ... I I + I I +

11 12 2 1 2 2

Figure 7.4.4 Diffusion as a random walk
One can envision the motion of a labelled particle (red) as a random walk on a lattice.
The orange arrows give the random step l i and the black arrow shows the displacement
after N steps.