On the notion of thermophoretic velocity

Abstract

The phenomenology of thermal diffusion of a particle in a solvent involves the Soret coefficient of the particle/solvent mixture. It is usually considered that the migration velocity of the particle in the solvent is proportional to the Soret coefficient. I show here that this view is wrong because ordinary diffusion contributes to migration if the solvent is not homogeneous. I examine several examples (NaCl in water, polystyrene in ethylbenzene, maghemite nanoparticles) to show that this contribution can be sufficiently strong to change the sign of the migration velocity and vitiate the interpretation of experimental data, measurement of the Soret coefficient, the comparison of experiment with theory and inter-experimental comparisons.

Acknowledgments

I am indebted to Alain Bourdon for insightful criticism of the first version of the manuscript. I have benefited from stimulating conversations with S. Nader Rasuli and Ramin Golestanian.

Notes

† The converse effect is also found, experimentally and theoretically, namely the change in the diffusivity due to an inhomogeneous drift velocity, in charge-carrier transport in a gas or a semiconductor subjected to a high electric field. Because the leading edge drifts at a slower velocity than the trailing edge, the carrier packet is squeezed along the direction of motion, and the longitudinal diffusivity is smaller than the transverse diffusivity. See 23 and references therein.

† Unpublished data of G. Demouchy and A. Bourdon on ionic-coated maghemite nanoparticles show a D(T) dependence larger than expected from the temperature dependence of the solvent viscosity in the Stokes–Einstein formula with a T-independent radius R. The thermally activated nature of the weak acid–base equilibrium of the citrate ions coating the nanoparticle surface is suspected to alter the hydrodynamic radius.

† An activity correction to D/kTμ is due in a non-ideal solution. See 10, p. 774 or 27, pp. 450–452.