Experimental, numerical, and theoretical investigation on the concentration-dependent Soret effect in magnetic fluids
Authors: Sprenger Lisa , Lange Adrian , Zubarev Andrey Yu. , Odenbach Stefan 
Published: February 2015

Applying a temperature gradient to a layer of a binary fluid establishes a diffusive transport mechanism called thermophoresis or Soret effect which separates the two fluid’s components and is measured by the Soret coefficient. Recent investigations carried out on concentrated magnetic fluids showed that the intensity of the Soret effect depends on the concentration of the nanoparticles transported. The present article, therefore, deals with the concentration-dependence of the Soret coefficient using five equally composed magnetic fluids only varying in the concentration of the particles from 2 vol. % to 10 vol. % of magnetic material. The current investigations point out that the determination of the Soret coefficient and especially its dependence on the particles’ concentration is based on the determination of the thermal and particle diffusion coefficient. The article, therefore, presents a theoretical approach for the determination of the thermal diffusion coefficient and adapts a commonly used Ansatz for the particle diffusion coefficient for the present case of concentrated magnetic fluids. It is thereby possible to determine a theoretical Soret coefficient in dependence on an empirical parameter α. The coefficient is compared with the experimental approaches which have been previously used, these will be referred to as “analytical approach” throughout the text. A second comparison is achieved with a hybrid Soret coefficient which fits the experimentally detected separation curves numerically. Within the investigations, the hydrodynamic concentration of the particles is used, assuming a surfactant layer’s thickness of 2 nm per magnetic particle which leads to concentrations between approximately 11 vol. % and 47 vol. %. The diffusion coefficient ranges from 0.6 × 10−11 m2/s to 2.5 × 10−11 m2/s depending on the analytical model used. The theoretical Soret coefficient decreases with increasing particles’ concentration; the experimental values derived from the analytical approach decrease from 0.06 K−1 to 0.01 K−1 for increasing particles’ concentration. The numerically determined coefficient ranges from 0.11 K−1 to 0.022 K−1. The experimental values are smaller than former experimental results suggest (0.16 K−1), which is due to the fact that in former works, only magnetic concentrations had been considered. All three current investigations prove what could also be partly seen in former experiments that the higher the particles’ concentration the weaker is thermophoresis. The particle diffusion coefficient has to be known for the determination of the Soret coefficient. It is carried out a proof of principle in the article showing that the horizontal thermophoresis cell can also be used to determine the rehomogenisation process which takes place after separating the fluid by applying a homogeneous temperature to the fluid. The diffusion coefficients that could be determined experimentally range from 1 × 10−11 m2/s to 6 × 10−11 m2/s.