# Diffusion Coefficients for Multicomponent Gases

Diffusion Coefficients for Multicomponent Gases

In the analysis of combustion problems and other multicomponent reacting systems, it is important to account for the relevant transport properties of the reacting mixture. This Demonstration is concerned with computing the ordinary diffusion coefficients of a mixture. The thermal diffusion coefficients, which describe the Soret effect, are not considered.

For an ideal gas mixture, the general expression for the ordinary diffusion flux of species in a mixture of species is:

i

N

J

i

Mw

i

Mw

mix

N

∑

j=1

Mw

i

D

ij

x

i

where is the molecular weight of species , = is the mixture molecular weight, are the ordinary diffusion coefficients for the mixture, and are the species mole fractions. The ordinary diffusion coefficients for the mixture can be determined from the kinetic theory of gases ([1] and [2]), and are given by

Mw

i

i

Mw

mix

∑

i=1

x

i

Mw

i

D

ij

x

i

D

ij

x

i

Mw

mix

Mw

i

F

ij

F

ii

where the components are elements of the matrix . The components of the matrix are given by

F

ij

-1

L

ij

L

L

ij

N

∑

k=1

x

k

Mw

i

ik

Mw

j

x

j

δ

ik

Mw

i

x

i

δ

ij

δ

jk

where are the binary diffusion coefficients. These coefficients can be predicted from the kinetic theory of gases, using the Chapman–Enskog theory with a Lennard–Jones (6-12) potential [2] and [3].

ij

In this Demonstration you can select a gas mixture of up to molecular species. You can specify the molar composition of the mixture (moles of each species) as well as the mixture temperature and pressure . From the species popup menus you can select distinct molecular species for the mixture. The Demonstration then computes the multicomponent diffusion coefficients, which are displayed in tabular form. The diagonal terms are not computed, as these components (known as the mutual diffusion coefficients) require a separate calculation beyond the scope of this Demonstration [2].

N=6

m

i

T

P

N

n

i

From the pull-down menu, you can also view the species molecular parameters and the binary diffusion coefficients used in the computation. If the molecular species chosen are not distinct, the inverse of is not defined, and you need to update the selected molecular species.

n

i

L

ij