# Cantera/Diffusion

### From charlesreid1

Cantera treats diffusion using either a multicomponent, species-by-species diffusion rate, or using a mixture-averaged diffusion rate for each species.

More information and context is available at http://public.ca.sandia.gov/chemkin/docs/oppdif.pdf

# Diffusitivites

Notation for some diffusivities should be defined before describing models for multicomponent or mixture-averaged diffusive fluxes. Three diffusivities are defined:

- - multicomponent species diffusivity
- - mixture-averaged diffusivity
- - binary diffusivity

The diffusive flux is modeled as being proportional to species gradients. The diffusivities are the proportionality constants of that relationship.

# Multicomponent

The multicomponent diffusive flux model assumes the diffusive flux is proportional to every species gradient. This means that each species has a distinct contribution to the diffusive flux from the gradient of each species in the mixture:

(Assuming domain/diffusion is one-dimensional)

where is the diffusive flux velocity for species k.

There are two contributions to the diffusion velocity : the multicomponent diffusion velocity, and a contribution to diffusion velocity via thermal gradients:

These are defined (assuming the one dimension is denoted ) as:

or more generally,

and the thermal diffusion term is:

or,

# Mixture-Averaged

The mixture-averaged diffusive flux model assumes the diffusive flux for species k, , depends only on the gradient of species k:

and the thermal diffusion term is:

The mixture-averaged diffusivities are computed from the binary diffusivities as follows: