Transport Properties

The is the main node used to model mass transfer in a fluid mixture with the Transport of Concentrates species interface. The node adds the equations governing the mass fractions of all present species, and provides inputs for the transport mechanisms and for the material properties of the fluid mixture.

The settings in this node are dependent on the check boxes selected under Transport Mechanisms in the Settings window of the Transport of Concentrated Species interface.

When the check box is selected, the Turbulent Mixing subnode is available from the context menu as well as from the toolbar, menu.

The options available in this feature differs between COMSOL products. (See http://www.comsol.com/products/specifications/).

Specify the temperature and pressure to be used in the physics interface. The temperature model input is used when calculating the density from the ideal gas law, but also when thermal diffusion is accounted for by supplying thermal diffusion coefficients. The pressure model input is used in the diffusional driving force in Equation 3-101 (that is, when a Maxwell-Stefan Diffusion Model is used) and when calculating the density from the ideal gas law.

Select the source of the field T:

Select the source of the p:

Define the density of the mixture and the molar masses of the participating species.

Select a way to define the density from the list — or :

Here M is the mean molar mass of the mixture and Rg is the universal gas constant. The absolute pressure, p, and temperature, T, used corresponds to the ones defined in the Model Inputs section.

Enter a value or expression for the Mw for each species. The default value is 0.032 kg/mol, which is the molar mass of O2 gas.

This section is available when the check box is selected.

Select the source of the u:

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Select a velocity field defined by a Fluid Flow interface present in the model (if any). For example, select to use the velocity field defined by the node fp1 in a Single-Phase Flow, Laminar Flow interface with spf as the Name.

Specify the molecular and thermal diffusivities of the present species based on the selected .

When using a Maxwell-Stefan Diffusion Model or a Mixture-Averaged Diffusion Model, select the (Table or Matrix) and specify the in the table or matrix, then enter the

When using a Fick’s Law Diffusion Model, specify the

and the

for each of the species.

Using a Maxwell-Stefan Diffusion Model or a Mixture-Averaged Diffusion Model, the Dik (SI unit: m2/s) can be specified by a table or matrix. For a simulation involving Q species the Maxwell-Stefan diffusivity matrix is a Q-by-Q symmetric matrix, where the diagonal components are 1. Enter values for the upper triangular components, Dij, which describe the inter-diffusion between species i and j. For the table input type, only upper triangular components (Dij) are listed. The name of species pair consists of species in the first and second column. For the matrix input type, the numbering of the species corresponds to the order, from top to bottom, used for all the input fields for species properties (see for example the molar mass fields in the Density section). The Maxwell-Stefan diffusivity matrix is used to compute the multicomponent Fick diffusivities as described in Multicomponent Diffusivities.

Using a Fick’s Law Diffusion Model, the diffusion is by default assumed to be isotropic and governed by one

(SI unit: m2/s) for each species. To allow for a general representation, it is also possible to use diffusion matrices (diagonal, symmetric, or anisotropic).

To model thermal diffusion, prescribe the

(SI unit: kg/(m·s)), by entering one thermal diffusion coefficient for each species in the corresponding field. In a multicomponent mixture, the sum of the thermal diffusion coefficients is zero. The default value for all thermal diffusion coefficients is 0.

Specify the molecular and thermal diffusivities of the present species based on the selected .

The Knudsen diffusion transport mechanism accounts for the interaction of the species with the surroundings (interspecies collisions excluded) — for example, the pore wall when a species passes through porous media.

Depending on which is selected, either the or the diffusion coefficient

is corrected with the coefficient

in the following way

For gases, the is often valid and requires the λpath (SI unit: m). Typically, for transport in porous media, the pore diameter can be entered here. For other cases, choose .

This section is available when the check box is selected for the Transport of Concentrated Species interface.

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If required, select an electric potential defined by an AC/DC interface that is present in the model (if any). For example, select to use the electric field defined by the Current Conservation node cucn1 in an Electric Currents interface ec.

Settings for the mobilities are used for the and transport models. By default the mobility is set to be calculated based on the species diffusivities and the temperature using the . To manually specify the mobilities, select for the mobility um,c (SI unit: s·mol/kg) and enter one value for each species.