Also known as the Soret effect.

https://en.wikipedia.org/wiki/Thermophoresis

See Self-thermophoresis and Collective behaviour of thermally active colloids

Soret - Sur l'etat d'équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homogène dont deux parties sont portées a des

Thermodiffusion of interacting colloids. I. A statistical thermodynamics approach

Thermophoresis of DNA determined by microfluidic fluorescence