The free energy density can have a contribution from the thermal energy. Therefore, the chemical potential in Equation 3-293 can have the contribution

where R is the universal gas constant, T is the temperature, and ST is Soret coefficient. The flux from thermophoresis is then defined as a function of the chemical potential,

For linear mobility, M is related to the diffusion coefficient D as

It s also possible to define the thermal diffusion coefficient DT = DST, in which case the thermophoresis flux reads