Diffusion areal speed

Now examine the case of diffusion of a species i in a three-dimensional zone. We can define the speed of diffusion by the flow of molecules of / that cross a surface (fictitious) perpendicular to the direction of diffusion. Then the flux of diffusion/, will be an areal speed because we have the following expression ... 

A zone of diffusion is a three-dimensional one, but taking into account the preceding expression of the voluminal speed, we will distinguish the diffusion length parallel with the flux, which is included in the expression of this flux, from the surface perpendicular to the direction of displacement. Thus, the areal speed of diffusion, that is, the flux, also depends on the geometry of the zone through the diffusion length. 

We choose to express flux at the internal interface. But this flux, which plays the role of an areal speed, not oidy depends on intensive variables, but also contains a geometrical term as shown in the second colunm of Tables 7.1 and 7.2 for various geometries. In order to separate the two contributions, we introduce Go, the space number of diffusion and we can write flux in the form ... 

As we did for the diffusion in the chemical conversions, we will introduce a factor G without dimension into the space function and we will define the reactivity starting from areal speed as follows ... 

To calculate the reactivities, we calculate areal speeds or flux of diffusions in case of the modes with a rate-determining step. However, it is to be noticed that steps [12.Et.a] and [12.Et.c] are exactly reverse of each other and that we will not be able to consider that only one of them is with infinite rate constant and not the other. Then, it will be necessary to consider the case of the pseudo-steady state mixed modes [12.Et.a] and [12.Et.c] as we did in the cases studied above (see section 12.6.1.3). 

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See also in sourсe #XX -- [ ]

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