The Transport of Concentrated Species (tcs) interface (), found under the Chemical Species Transport branch () when adding a physics interface, is used to study gaseous and liquid mixtures where the species concentrations are of the same order of magnitude and none of the species can be identified as a solvent. In this case, properties of the mixture depend on the composition, and the molecular and ionic interactions between all species need to be considered. The physics interface includes models for multicomponent diffusion, where the diffusive driving force of each species depends on the mixture composition, temperature, and pressure.

The available transport mechanisms and diffusion models differs between various COMSOL products (see http://www.comsol.com/products/specifications/).

When this physics interface is added, the following default nodes are also added in the Model Builder — Transport Properties, No Flux, and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and reactions. You can also right-click Transport of Concentrated Species to select physics features from the context menu.

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first physics interface in the model) is tcs.

The basic equation for an individual species i is:

The available diffusion models and the additional transport mechanisms differs between various COMSOL products (see http://www.comsol.com/products/specifications/).

Under Additional transport mechanisms, click to select or clear any combination of check boxes as needed. The Convection check box is selected by default. The second term on the left-hand side of Equation 6-32 represents mass transport by convection.

Select the Migration in electric field check box to activate migration of ionic species due to an electric field. The resulting migration term is part of the relative mass flux vector.

The Mass transport in porous media check box activates functionality specific to species transport in porous media. When selected the following features are enabled:

For Mixture-averaged and Fick’s law, it is possible to include Knudsen diffusion. This mechanism accounts for species collisions with the surrounding media, for example, the pore walls the species pass through. It is also an important component when setting up a Dusty gas model.

When using the Maxwell-Stefan diffusion model the relative mass flux vector is

where (SI unit: m2/s) are the multicomponent Fick diffusivities, dk (SI unit: 1/m) is the diffusional driving force, T (SI unit: K) is the temperature, and (SI unit: kg/(m·s)) is the thermal diffusion coefficient.

where gk is an external force (per unit mass) acting on species k. In the case of an ionic species, the external force due to the electric field, which is added by selecting the Migration in electric field check box, is

where zk is the species charge number, F (SI unit: A·s/mol) is Faraday’s constant and (SI unit: V) is the electric potential.

When using the Mixture-averaged diffusion model, the diffusive flux is formulated in terms of a mixture-averaged diffusion coefficient representing the diffusion of each species into the resulting mixture. The diffusion coefficient is based on the multicomponent Maxwell-Stefan diffusivities Dik. The Mixture-averaged diffusion model is computationally less expensive, and significantly more robust than the Maxwell-Stefan Diffusion Model, but constitutes an approximation of the multicomponent flux. For information on the flux formulation in this case see Multicomponent Diffusion: Mixture-Averaged Approximation.

When using the Fick’s law diffusion model, the diffusive flux is formulated in terms of a Fickian diffusion coefficient. The Fick’s law diffusion model is computationally less expensive and significantly more robust than the Maxwell-Stefan Diffusion Model, but constitutes an approximation of the multicomponent flux. For information on the flux formulation in this case see Multispecies Diffusion: Fick’s Law Approximation.

Select the species that this physics interface solves for using the mass constraint in Equation 6-35 (that is, its value comes from the fact that the sum of all mass fractions must equal 1). In the From mass constraint list, select the preferred species. To minimize the impact of any numerical and model introduced errors, use the species with the highest concentration. By default, the first species is used.

To display this section, click the Show button () and select Stabilization.

To display this section, click the Show button () and select Advanced Physics Options. Normally these settings do not need to be changed.

From the Regularization list, select On (the default) or Off. When turned On, regularized mass fractions are calculated such that

The Diffusion settings are available for the approximate diffusion models Mixture-averaged and Fick’s law.

When the Mixture diffusion correction is enabled, a flux correction is added to ensure that the net diffusive flux is zero. This typically also mean that the solution becomes less sensitive to the species selected to be computed from the mass constraint in the Species section. More information on this correction is available in the theory section Multicomponent Diffusion: Mixture-Averaged Approximation.

The Diffusion flux type list controls the whether the molecular flux is assumed proportional to the mole fraction or the mass fraction. See Multicomponent Diffusion: Mixture-Averaged Approximation or Multispecies Diffusion: Fick’s Law Approximation for information on the diffusive flux formulation.

The Use pseudo time stepping for stationary equation form option adds pseudo time derivatives to the equation when the Stationary equation form is used in order to speed up convergence. When selected, a CFL number expression should also be defined. For the default Automatic option, the local CFL number (from the Courant–Friedrichs–Lewy condition) is determined by a PID regulator. For more information, see Pseudo Time Stepping for Mass Transport.

To display all settings available in this section, click the Show button () and select Advanced Physics Options.

For more information about these settings, see the Discretization section under The Transport of Diluted Species Interface.

Specify the Number of species. There must be at least two species. To add a single species, click the Add concentration button () under the table. To remove a species, select it in the list and click the Remove concentration button () under the table. Edit the names of the species directly in the table.