Adding Transport Through Migration
Note: Migration is only available in a limited set of add-on products. For a detailed overview of which features are available in each product, visit
https://www.comsol.com/products/specifications/
In addition to transport due to convection and diffusion, the Transport of Diluted Species interface supports ionic species transport by migration. This is done by selecting the Migration in Electric Field check box under the Transport Mechanisms section for the physics interface. The mass balance then becomes:
(4-12)
where
•
ci (SI unit: mol/ m3) denotes the concentration of species i
•
Di (SI unit: m2/s) is the diffusion coefficient of species i
•
u (SI unit: m/s) is the fluid velocity
•
F (SI unit: A·s/mol) refers to Faraday’s constant
•
V (SI unit: V) denotes the electric potential
•
zi (dimensionless) is the charge number of the ionic species, and
•
um,i (SI unit: mol·s/kg) is its ionic mobility
In this case the diffusive flux vector is
The velocity, u, can be a computed fluid velocity field from a Fluid Flow interface or a specified function of the spatial variables x, y, and z. The potential can be provided by an expression or by coupling the system of equations to a current balance, such as the Electrostatics interface. Sometimes it is assumed to be a supporting electrolyte present, which simplifies the transport equations. In that case, the modeled charged species concentration is very low compared to other ions dissolved in the solution. Thus, the species concentration does not influence the solution’s conductivity and the net charge within the fluid.
The Nernst-Einstein relation can in many cases be used for relating the species mobility to the species diffusivity according to
where R (SI unit: J/(mol·K)) is the molar gas constant and T (SI unit: K) is the temperature.
Note: In the Nernst-Planck Equations interface, the ionic species contribute to the charge transfer in the solution. It includes an electroneutrality condition and also computes the electric potential field in the electrolyte. For more information, see Theory for the Nernst-Planck Equations Interface. This interface is included in the Chemical Reaction Engineering Module.