Convection-diffusion equation

From Chemepedia

The convection-diffusion equation can be written on a mass or mole basis, and it describes density or concentration field of a component in a multicomponent flowing fluid.

Mass basis

If is the total mass flux of species in a multicomponent mixture, the convection-diffusion equation is

            (1)

where

  • is the local change in the density of species A.
  • is the difference in the mass influx and outflux of species A.
  • is the rate of generation or consumption per unit volume of species due to a homogenous reaction.

For a fluid of constant mass density and with constant diffusivities, Eq. (1) can be expressed as

            (2)

This can also be expressed in the compact, material derivative form:

            (3)

Mole basis

If is the total mole flux of species in a multicomponent mixture, the convection-diffusion equation is

            (4)

where

  • is the local change in the concentration of species A.
  • is the difference in the molar influx and outflux of species A.
  • is the molar rate of generation or consumption per unit volume of species due to a homogenous reaction.

For a fluid of constant concentration and with constant diffusivities, Eq. (4) can be expressed as

            (5)