Inlet and concentration restraines

[daklauss]

In Issue #16 we described a model, that is abel to model a dead end filter.

Because of calculating the viscosities with Arrhenius:

$$ \ln \mu^P = \frac{\sum _{i \in \Omega} n_i \ln \mu_i} {\sum _{i \in \Omega} n_i} $$

it is mandatory to know the Amount of substance $n_i$ of every component in our system. This implies that we know each concentration $c_i$ of our solution, even of the solvent. This is not provided in CADET, where $c_i$ is only given for Particles. If we want to give the concentration of every component $c_i$ in our system, it has some unexpected consequences for our Inlet. In CADET we where able to simulate any concentration profile by approximating it with a third degree polynomial that assumed pretty much any form of function. Now we have another restriction because we can't just vary a concentration of one component without changing the concentration of every other component, because the volumes of our Particle matters now.

The concentration is given by:

$$ c_i = \frac{\sigma_i \cdot \rho_i}{ M_i} $$

Where $\rho_i$ is the density [ $kg/m^3$ ] and $M_i$ the Molar mass [ $kg/mol$ ]. $\sigma_i$ is the partial volume of component $i$ in a Volume:

$$ \sigma_i = \frac{V_i}{V} $$

$V_i$ ist the Volume [ $m^3$ ] of component $i$ in its Volume $V$ [ $m^3$ ]. This means $\sigma$ is a distribution. So if we want to use an Inlet as a boundary supplier for concentration $c$, we have to give the inlet a distribution of our Volume.