DiffusionS

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Interface.Transport.DiffusionS

The component generates the diffusional fluxes for Stefan-Maxwell surface diffusion (Ross Taylor and R. Krishna, 1993) due to gradients in surface concentrations.

$\begin{equation*} \frac{d\gamma_{i}}{dz} = \sum_{\stackrel{i \neq j}{j}}^{N} \frac{\Theta_{i} \, J_{j} - \Theta_{j} \, J_{i}}{\dcal_{ij}} + \frac{J_{i}}{\dcal_{i}} \quad \text{for} \quad i=1,\dots,N \end{equation*}$

Note: The fluxes are based on the interface width. Thus, the molar flow rates become

$\begin{equation*} F_{i} = w \, J_{i} \qquad \text{for} \quad i=1,\cdots,N \end{equation*}$

Ports

Conserving

Interface conserving port
```
Port_A = Interface;  %
```
Interface conserving port
```
Port_B = Interface;  %
```

Input

Physical signal that represents the interface width
```
wIn = {0,'m'};
```
Dependencies: The port is only visible when wInputOutput is set to Input.

Output

Physical signal that represents the interface width
```
wOut = {0,'m'};
```
Dependencies: The port is only visible when wInputOutput is set to Output.

Parameters

Options

Option to select interface width input/output
```
wInputOutput = InOut.Off;
```
Input | =Output | Off

Geometry

Interface width
```
w0 = {1,'m'}; 
```
Dependencies: The port is only visible when wInputOutput is set to Off.
Transport Distance
```
delta  = {1.0e-03,'m'};
```

Mass Transport

Counter-Sorption Diffusion Coefficients
```
Dsbin = {ones(2,2),'m^2/s'};
```
Note Initially only two species are considered. As the number of species can be changed via the properties dialogue, the size of the array must be adjusted accordingly.
Surface Diffusion Coefficients
```
Ds = {ones(2,1),'m^2/s'};
```
Note Initially only two species are considered. As the number of species can be changed via the properties dialogue, the size of the array must be adjusted accordingly.

Nomenclature

$\dcal_{ij}$	binary counter sorption diffusion coefficient
$\dcal_{i}$	surface diffusion coefficient of species A_i
$F_{i}$	molar flow rate of species A_i
$J_{i}$	diffusional flux of species A_i
$N$	total number of species
$u$	interface velocity
$w$	interface width
$\alpha$	impact parameter
$\gamma_{i}$	surface concentration of species A_i
$\Theta_i$	surface converage of species A_i

Bibliography

Ross Taylor and R. Krishna (1993). Multicomponent Mass Transfer, Wiley.