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 NonUniform 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).