The Transport of Concentrated Species Interface

The interface (

), found under the 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 physics interface solves for the mass fractions of all participating species. Transport through convection, diffusion, and migration in an electric field can be included.

It supports simulations of transport by convection, migration, and diffusion in 1D, 2D, and 3D as well as for axisymmetric components in 1D and 2D. The physics interface defines the equations for the species mass fractions, including a diffusion model (Mixture-averaged, Maxwell–Stefan, or Fick’s law).

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

Some examples of what can be studied with this physics interface include:

When this physics interface is added, the following default nodes are also added in the — , , and . Then, from the toolbar, add other nodes that implement, for example, boundary conditions and reactions. You can also right-click to select physics features from the context menu.

The is the default physics interface name.

The 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 field. The first character must be a letter.

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

The basic equation for the conservation of mass of a species i is:

Using the continuity equation, the sum of all species equations, the equation can be re-cast in its non-conservative form:

This form of the equation is the one used in the Transport of Concentrated Species interface. The equation displayed in the interface changes depending on the active transport mechanisms, the selected diffusion model, and the type of reactions modeled.

For 2D components, the field (default value: 1 m) defines a parameter for the thickness of the geometry perpendicular to the two-dimensional cross-section. Both constant and varying thicknesses are supported. The value of this parameter is used, among other things, to automatically calculate mass flow rates from the total mass flux.

For 1D components, enter a Ac (SI unit: m2) to define a parameter for the area of the geometry perpendicular to the 1D component. Both constant and varying areas are supported.The value of this parameter is used, among other things, to automatically calculate mass flow rates from the total mass flux. The default is 1 m2.

The Transport of Concentrated Species interface always accounts for transport due to convection and diffusion.

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

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The option employs the most detailed diffusion model, but is also the most computationally expensive. The model is intended for diffusion dominated models, and requires that the multicomponent Maxwell–Stefan diffusivities of all component pairs are known. No stabilization is available when selecting this model.

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The option is less computationally expensive than the Maxwell–Stefan model. It is a simpler model that can be used when variations in the partial pressures and temperature can be assumed to not affect the multicomponent diffusion. The model includes stabilization but requires the multicomponent Maxwell–Stefan diffusivities of all component pairs.

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The model is a general model that should be used when the diffusion is assumed Fickian, or when no multicomponent diffusivities are available. Also, when molecular diffusion is not the dominating transport mechanism and a robust but low order model is wanted, the Fick’s law options should be used. The model includes stabilization.

Under , click to select or clear any combination of check boxes as needed.

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

For and , it is possible to include . 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 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.

The diffusional driving force is defined as

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 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 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 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 diffusion model, the diffusive flux is formulated in terms of a Fickian diffusion coefficient. The 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 3-132 (that is, its value comes from the fact that the sum of all mass fractions must equal 1). In the 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 button (

) and select .

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Two consistent stabilization methods are available — and . Both are active by default.

The setting applies to both the consistent stabilization methods. is the default setting and it means that derivatives of the diffusion tensor components are neglected. This setting is usually accurate enough and computationally faster. If required, select instead.

To display this section, click the button (

) and select . Normally these settings do not need to be changed.

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

Regularized mass fractions are used for the calculation of composition-dependent material properties, such as the density.

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

When the 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 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 option adds pseudo time derivatives to the equation when the equation form is used in order to speed up convergence. When selected, a CFL number expression should also be defined. For the default 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 button (

) and select .

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

	In the COMSOL Multiphysics Reference Manual see Table 2-4 for links to common sections and Table 2-5 to common feature nodes. You can also search for information: press F1 to open the Help window or Ctrl+F1 to open the Documentation window.

Add or remove species in the model and also change the names of the dependent variables that represent the species concentrations.

Specify the . There must be at least two species. To add a single species, click the button (

) under the table. To remove a species, select it in the list and click the button (

) under the table. Edit the names of the species directly in the table.