A simple multiscale model of the Soret effect (thermal diffusion) in liquids

Howard Brenner

Department of Chemical Engineering

MIT Cambridge, MA 02139

hbrenner@mit.edu

The Soret effect [1] refers to the resulting inhomogeneity in composition created in an otherwise homogeneous binary liquid solution confined between parallel walls by the imposition of a steadystate temperature gradient across the walls. The Soret effect is a special case of the general phenomenon of thermal diffusion. While the mechanism by which the separation occurs in gases has been well understood for almost a century as a result of the work of Chapman and Enskog based on solving the Boltzmann equation [2], no comparable explanation has existed in the case of liquids owing to the greater complexity of the molecular forces existing in liquids. Our presentation outlines a simple multiscale model [1,3] of the phenomenon in liquids whereby the separation is explained in terms of thermo-osmotic forces [3] acting on a dilute suspension of Brownian particles (the solute, species 1) dispersed in a liquid (the solvent, species 2). The analysis uses these temperature gradient-induced forces acting on individual colloidal particles (i.e., solute molecules) to model the overall macroscale Soret effect. The analysis parallels Einsteins (1905) classical analysis of Brownian diffusion in isothermal binary liquids. Despite the models simplicity, the results of the Soret model are shown to compare well with experimental data [4] over a wide range of solutes and solvents.

References

[1] J. R. Bielenberg and H, Brenner, A hydrodynamic/Brownian motion model of thermal diffusion in liquids, Physica A 356, 279-293 (2005).

[2] S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, rd. ed. (Cambridge University Press, Cambridge, 1970).

[3] H. Brenner, Nonisothermal Brownian motion: Thermophoresis as the macroscopic manifestation of thermally biased molecular motion, Phys. Rev. E 72, 061201-1 to 16 2005).

[4] S. Iacaponi, R. Rusconi and R. Pizza,The macromolecular tourist: Universal temperature dependence of thermal diffusion in aqueous colloidal suspensions, Eur. hys. J. E 19. 59-67 (2006).