I N I T I A L V A L U E S

Enter a value or expression for the initial value of the concentration c, in the

Concentration field. The default value is 0 mol/m3. Enter coordinates for the initial values for Velocity field u (SI unit: m/s) and Pressure p (SI unit: Pa).

Domain Features for the Reacting Flow, Diluted Species Interface

Boundary Conditions for the Reacting Flow, Diluted Species Interface

These boundary conditions are described for The Transport of Diluted Species Interface in the COMSOL Multiphysics Guide.

•Inflow (also pairs menu)

•Outflow

•Concentration (also pairs menu)

•Flux

•No Flux

•Symmetry

•Periodic Condition

•Open Boundary

•Thin Diffusion Barrier

These boundary conditions are described for The Free and Porous Media Flow Interface.

•Wall (also pairs menu)

•Inlet

•Outlet

•Boundary Stress

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•Symmetry

•Periodic Flow Condition

•Microfluidic Wall Conditions (also pairs menu)

Pair and Point Conditions for the Reacting Flow, Diluted Species Interface

These conditions are described for The Free and Porous Media Flow Interface.

•Flow Continuity (pairs menu)

•Pressure Point Constraint (points menu)

These conditions are described for The Transport of Diluted Species Interface in the

COMSOL Multiphysics Guide

•Continuity (pairs menu)

•Pairs Thin Diffusion Barrier

•Microfluidic Wall Conditions (also pairs menu)

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T h e o r y f o r t h e T r a n s p o r t o f

C o n c e n t r a t e d S p e c i e s I n t e r f a c e

The theory relating to The Transport of Concentrated Species Interface is detailed in this section and includes these topics:

•Multicomponent Mass Transport

•Multicomponent Diffusion: Mixture-Average Approximation

•Multispecies Diffusion: Fick’s Law Approximation

•Multicomponent Thermal Diffusion

•References for the Transport of Concentrated Species Interface

Multicomponent Mass Transport

Suppose a reacting flow consists of a mixture where i 1, …, Q species and j = 1, …, N reactions. Equation 3-2 then describes the mass transport for an individual species:

where, denotes the mixture density (SI unit: kg/m3) and u the mass average velocity of the mixture (SI unit: m/s). The remaining variables are specific for the of species, i, which is being described by the mass transfer equation; i is the mass fraction (1), ji is the mass flux relative to the mass average velocity (SI unit: kg/(m2·s)) and Ri is the rate expression describing its production or consumption (SI unit: kg/(m3·s)). The relative mass flux vector ji can include contributions due to molecular diffusion, thermal diffusion, and mass flux due to migration in an electric field.

Summation of the transport equations over all present species gives Equation 3-3 for the conservation of mass

assuming that

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Using the mass conservation equation, the species transport for an individual species, i, is given by:

Q 1 of the species equations are independent and possible to solve for using Equation 3-4. To compute the mass fraction of the last species, COMSOL Multiphysics uses the fact that the sum of the mass fractions is equal to 1:

Multicomponent Diffusion: Mixture-Average Approximation

The mixture-averaged diffusion model assumes that the relative mass flux due to molecular diffusion is governed by a Fick’s law type expression

where i is the density and xi the mole fraction of species i. The diffusion hence depends on a single concentration gradient and is proportional to a diffusion coefficient Dmi . The diffusion coefficient describes the diffusion of species i relative to the remaining mixture and is referred to as the mixture-averaged diffusion coefficient. Equation 3-6 can be expressed in terms of mass fractions as

using the definition of the species density and mole fraction

i = i , xi = ------i M Mi

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