A simple mass balance around species gives the following advection-diffusion equation:

(19–3)

Here, is the mass flux of species , is the net mass rate of creation or depletion of species , and represents the contribution of any user-defined rate to the mass creation or depletion rate. The mass flux of species is a vector quantity denoting the mass of species that passes through a unit area per unit time. It corresponds to the sum of the mass flux of species resulting from the bulk motion of the fluid together with a superimposed diffusion:

(19–4)

Hence, the conservation equation for a chemical species takes the following general form:

(19–5)

where is the mass fraction () of the chemical species . In an -component mixture, there are independent species concentration equations of the form of Equation 19–5, since the mass fractions sum to .

Diffusion is limited to situations where the diffusive flux is due to concentration gradients only (the Fickian effect):

(19–6)

where is the diffusion coefficient for species in the mixture. In nondilute mixtures, the variation of with the local mixture composition may adopt far more complicated forms that are not handled in Ansys Polyflow. Temperature gradients, pressure gradients, and external forces may also contribute to the diffusion flux, although their effects are usually minor.

It is usually quite difficult to measure diffusion coefficients for the transport of chemical species. It is also difficult to find those values in the literature. However, in practical situations, the role of diffusion is frequently smaller than that of advection, which is always present, and it is not unusual to neglect the diffusion mechanism.

To close the system of equations, an equation of state relating density to the state of the mixture is required. For dilute liquid solutions, an acceptable equation of state is "constant density".

For gases at low pressure and high temperature, it is customary to make use of the ideal gas law, which relates density to pressure and temperature. More generally, however, equations of state are nonlinear algebraic relationships relating density to the field variables (such as temperature, pressure, and composition).