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Multi Component Linear Driving Force Freundlich

A multi-component extension to the classical Freundlich adsorption model. A linear driving force approach is applied to obtain a kinetic form.

\[\begin{split}\begin{aligned} \frac{\mathrm{d} q_i}{\mathrm{d} t} &= k_{\text{ldf},i}\: \left(q_i^* - q_i \right) & i = 0, \dots, N_{\text{comp}} - 1 \\ q_i^* &= k_{F,i} c_{p,i} \left( \sum_j a_{ij} c_{p,j} + \tau \right)^{1 / n_i - 1}. \end{aligned}\end{split}\]

Here, \(\tau > 0\) is a small constant that ensures numerical stability.

In a rapid-equilibrium setting with a diagonal matrix (i.e., \(a_{ii} = 1\) and \(a_{ij} = 0\) for \(j \neq i\)), the traditional Freundlich isotherm is recovered.

For more information on model parameters required to define in CADET file format, see Multi Component Linear Driving Force Freundlich.