Connection between thermophoresis and thermodiffusion in a liquid binary mixture

Abstract

In a liquid suspension, thermophoresis is the motion of a suspended particle under a temperature gradient. In a liquid binary mixture, thermodiffusion is the generation of a composition gradient upon application of a temperature gradient. A quantitative connection is established between the two phenomena without making assumptions about their mechanisms. It is shown that Galilean invariance and the choice of a Galilean reference frame play a key role in that connection. The results are not restricted to very dilute suspensions or mixtures.

Keywords:

• thermophoresis
• suspension
• thermodiffusion
• binary mixture
• Galilean invariance

Notes

Notes

1. Ryskin 16 remarks that the label ‘Fokker–Planck equation’ has often been given to an equation having the same pattern but with a wrong definition of D(x ₀), not consistent with Galilean invariance.

2. If the medium were anisotropic, D would actually be a second-order tensor D ^ij instead of D δ^ij in the isotropic case (δ^ij is the Kronecker symbol).

3. Actually in their equation (1) w is replaced by w − d, where d is the diameter of a particle as it can be a significant fraction of w.