Thermoelectric effect on charged colloids in the Hückel limit

We study the thermophoretic coefficient DT of a charged colloid. The non-uniform electrolyte is characterized in terms of densities and diffusion currents of mobile ions. The hydrodynamic treatment in the vicinity of a solute particle relies on the Hückel approximation, which is valid for particles smaller than the Debye length, a ≪ $ \lambda$ . To leading order in the parameter a/$ \lambda$ , we find that the coefficient DT consists of two contributions, a dielectrophoretic term proportional to the permittivity derivative d$ \varepsilon$/dT , and a Seebeck term, i.e., the macroscopic electric field induced by the thermal gradient in the electrolyte solution. Depending on the particle valency, these terms may take opposite signs, and their temperature dependence may result in a change of sign of thermophoresis, as observed in several recent experiments