Temperature induced migration of interacting charged colloidal particles: an irreversible thermodynamics approach

The migration of particles induced by spatial gradients in temperature is commonly referred to as thermophoresis, thermodiffusion, thermal diffusion, or the (Ludwig-)Soret effect. The force on colloidal particles that drives such a migration depends on the response to variations in temperature, both of single particles and of interactions between particles. A distinction can thus be made between single-particle and collective contributions to the thermophoretic force experienced by a colloidal particle. There is as yet no systematic theory for thermophoresis of charged colloids that accounts for the collective contribution due to interactions between charged colloids. In a previous study, we developed an irreversible thermodynamics approach for uncharged colloids [J. K. G. Dhont and W. J. Briels, J. Colloid Interface Sci., 2024, 666, 457]. In the present study we extend this approach to account for interactions between charged colloids, which includes additional fluxes of ions. Enslavement of ion fluxes to the relatively slowly evolving concentration profile of the colloids, and an approximate evaluation of the heat-of-transfer, leads to microscopic, particle-based expressions for the thermodiffusion coefficient and the Soret coefficient. In addition, an explicit expression for the macroscopic thermoelectric field is derived, which gives rise to a thermoelectrophoretic force. A comparison to existing experimental thermophoresis experiments is presented.