Surface

Chemical Reactor Design Toolbox Reference Manual

The component represents a surface of fixed size.

$\begin{equation*} \frac{dn_{i}}{dt} = F_{i} \end{equation*}$ 1

initial conditions

$\begin{equation*} n_{i}(t=0) = \frac{\Theta_{i_{0}} \, A_{0}}{{\overline A}_{i}} \quad \text{for} \quad i=1,\dots,N \end{equation*}$ 2

The fractional coverages are obtained as

$\begin{equation*} \Theta_{i} = \frac{n_{i} \, {\overline A}_{i}}{A_{0}} \quad \text{for} \quad i=1,\cdots,N \end{equation*}$

It is noted, that

$\begin{equation*} \sum_{i}^{N} \Theta_{i} = 1 - \Theta_{0} \end{equation*}$

with $\Theta_{0}$ as the fractional coverage of the free sites.

Physical signal that represents the total surface area
```
Aout = {0,'cm^2'};   % A
```
Dependencies: The port is only visible when areaOutput is set to On.

Option to select total area output
```
areaOutput = OnOff.Off; 
```
On | Off

Initial Surface Area

A0 = {1,'cm^2'};         % Surface Area

Initial Fractional Coverages
```
Theta0 = {[0;0],'1'};    % Initial Fractional Coverages
```
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.

$A_{0}$	cross sectional area
${\overline A}_{i}$	specific surface area of species A_i
$F_{i}$	molar flow rate of species A_i
$N$	total number of species
$n_{i}$	number of moles of species A_i
$t$	time
$\Phi$	energy flow rate
$\Theta_{i}$	fractional coverage of species A_i
$\Theta_{0}$	fractional coverage of free sites
$\Theta_{i_{0}}$	initial fractional coverage of species A_i