The Concentration Dependent Diffusivity script approximates a diffusion process where the local diffusivity depends on the concentration of the diffusing species. This is achieved by using the existing constant diffusivity solver in an iterative process, where the local diffusivity in one iteration depends on the local concentration computed in the previous iteration.

The window below the selection box shows the description of the script and its input parameters. Open Macro / Script File opens the underlying Python script in a text editor. Be aware that administrator privileges would be required to change the macro if GeoDict has been installed in the default location for all users.

Run starts the computation. When the simulation is finished, a DiffuDict result file is opened in the Result Viewer.

Clicking Edit… opens the dialog to enter the available parameters.

Under Concentration to Diffusivity Function, define how the diffusivity depends on concentration. Linear, Exponential, and Quadratic are predefined concentration to diffusivity functions. These predefined functions are stored as text file in the GeoDict installation folder in the subfolder C:\Program Files\Math2Market GmbH\GeoDict 2026\GeoApps\General\Physical Properties\DiffusivityFuncs.

If you want to define your own concentration to diffusivity function select Custom.

Create a text file (*.txt) describing the relationship between diffusivity value (D_i) and concentration value (u_i) as follows.

For example, copy one of the predefined files to a project specific file location and edit it in a text editor. Since the diffusivity is given in bins of a specific range, the number of elements differs by 1 with respect to the number of concentration values. Therefore, the diffusivity value-pairs must start with a sentinel, e.g. (0.1, -1), followed by the desired values.Due to the iterative process described below, after the sentinel 15 different value pairs must be given.

The Maximum Number of Iterations can be specified in order to increase the degree of convergence. For the solver choose between the EJ and the LIR solver.

The effective diffusivity of the material for the chosen concentration difference is always computed in z-direction according to

Here, is the concentration and the concentration-dependent diffusivity. For the surfaces, no-slip boundary conditions are applied. In Z-direction, constant Dirichlet-boundary conditions are applied where the constants are taken from the given diffusivity file as minimum and maximum values. In the tangential directions, symmetric boundary conditions are used. The solution to the non-linear equation (153) is found in an iterative manner by dividing the pore space into 15 different materials according to the values of u and assigning diffusivity, then solve a linear approximation to (153) for and repeat until convergence is reached, i.e., when the distribution of the materials does not need to be adjusted anymore for the newly computed .

Please contact support@math2market.de for more help and information regarding concentration dependent diffusivity simulations, if you are interested in this topic.