We study the Soret coefficient of binary molecular mixtures with dispersion forces. Relying on standard transport theory for liquids, we derive explicit expressions for the thermophoretic mobility and the Soret coefficient. Their sign depends on composition, the size ratio of the two species, and the ratio of Hamaker constants. Our results account for several features observed in experiment, such as a linear variation with the composition; they confirm the general rule that small molecules migrate to the warm, and large ones to the cold.
The drift-diffusion equation on a finite interval with reflecting boundary conditions is solved by Laplace transformation. The Green function is obtained as a series in powers of e(-hu/D), where u is the drift velocity, D the diffusion coefficient and h the width of the interval. In the drift-dominated regime hu/D >> 1, the first terms provide an exact solution in the limit of short and long times, and a good approximation in the intermediate regime. As a possible application, we discuss confined colloidal suspensions subjected to an external field.
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