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Paper IPM / P / 8765  


Abstract:  
The Soret effect for a single charged colloidal particle, has been studied by different experimental
groups in recent years [1, 2] and still seems a challenging topic. We know two distinct
theoretical approaches to this phenomenon. The First, motivated by Ruckenstein in 1981 [3],
is based on solving hydrodynamics equations for the charged fluid around colloid. This approach
is restricted to weakly charged colloids with thin doublelayer around them [3?5], and
was verified with Piazza and Guarino in 2002 [1]. The second approach however, uses Gibbs
enthalpy [2, 6] to predict the density profile of a colloid in a temperature field. It is seemed
that this approach has been tested successfully for Polystyrene beads by Duhr and Braun [2].
Recently, Astumian [7] suggested that, we can interpret the Ruckenstein?s approach as the deterministic
motion of a charged colloid in a temperature field, while attribute the second approach
to colloid stochastic Langevin motion in the temperature field [7]. Accepting his suggestion,
two mentioned approaches, may come together in a unified theory which addresses both kinds
of motion simultaneously.
Here, we extend the Ruckenstein?s hydrodynamics approach to a colloid with arbitrary doublelayer
around it. We consider the dielectrophoretic force in our formalism, and since the Boltzmann
weight is hardly reliable in the presence of a temperature gradient, we solve the diffusion
equation to find ions densities. In the diffusion equation, we consider both the convective motion
and ions Soret motion [8].
For a weakly charged colloid, our equations are explicitly solved. Our result has the Ruckenstein?s
formula, as its limiting case. For a colloid with high surface potential also, we solve
the equations numerically. We confront our results with existing experimental data [1, 2] and
possible agreements and/or disagreements are discussed [8, 9].
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