The vectors and and the second-order tensors are all functions of , and are given as solutions of integrodifferential equations . The general diffusional driving forces, , include the concentration (or activity) driving force, the pressure gradient driving force, and the external driving force (BSL, p. 766):
(although for ideal gases, a somewat simpler expression can be used: BSL, p. 860).
1e. The fluxes in terms of the transport properties
When the Boltzmann equation has been solved, then one can express the fluxes in terms of the transport properties:
Species mass flux:(1.14)