On the Force Acting on Particles in an Inhomogeneously Heated Polarizing Liquid

The formulation of the problem and the method of its solution for determining the force acting on particles in a non-uniformly heated polarizable liquid, both from the side of the liquid itself and from the applied external electric field, are considered. It is assumed that the dielectric constant of a liquid depends on temperature, the coefficients of thermal diffusivity of particles and liquid are different, and the temperature distribution does not depend on the motion of the liquid, which corresponds to small Peclet numbers. The dynamics of a fluid is considered in the approximation of small Reynolds numbers, taking into account the volume force acting on it from the side of the electric field in the presence of a temperature gradient. The solution to the problem is sought in the linear approximation with the specified temperature gradients and the applied external electric field. A general expression for the force acting on particles in such a liquid is obtained and a qualitative analysis of their dynamics as a result of the cross action of the temperature gradient and the electric field is carried out.

Keywords

temperature gradient; polarizable liquid; particles; electric field; interaction force.

References

1. De Groot S.R., Marur P. Nonequilibrium Thermodynamics. Amsterdam, NorthHolland, 1962.
2. Bakanov S.P., Deryagin B.V. [Theory of Thermophoresis of Large Solid Aerosol Particles]. Doklady Akademii Nauk SSSR, 1962, vol. 147, no. 1, pp. 139-142. (in Russian)
3. Volker T., Blumsb E., Odenbacha S. Thermodiffusion in Magnetic Fluids. Journal of Magnetism and Magnetic Materials, 2002, no. 252, pp. 218-220. DOI: 10.1016/S0304-8853(02)00728-X
4. Volker T., Odenbach S. The Influence of a Uniform Magnetic Field on the Soret Coefficient of Magnetic Nanoparticles. Physics of Fluids, 2003, no. 15, p. 2198. DOI: 10.1063/1.1584435
5. Lange A. Magnetic Soret Effect: Application of the Ferrofluid Dynamics Theory. Physical Review Journals, 2004, no. 70, p. 046308, 14 p. DOI: 10.1103/PhysRevE.70.046308
6. Sprenger L., Lange A., Odenbach S. Thermodiffusion in Ferrofluids Regarding Thermomagnetic Convection. Comptes Rendus Mecanique, 2013, no. 341, pp. 429-437. DOI: 10.1016/j.crme.2013.02.005
7. Bloom E.Ya. On the Thermophoresis of Particles in Magnetizable Suspensions. Magnetohydrodynamics, 1979, no. 1, pp. 23-27. DOI: 10.1017/S006869050000338X
8. Martynov S.I., Naletova V.A., Timinin G.A. Particle Movement in a Nonuniformly Heated Magnetized or Polarized Liquid. Modern Problems of Electrohydrodynamics. Moscow, Moscow State University, 1984, pp. 133-144.
9. Baryshnikov A.A. Research and Development of Technology for Enhanced Oil Recovery Through Displacement using an Electromagnetic Field. PhD Thesis, Tyumen, 2014. (in Russian)
10. Vissers T., van Blaaderen A., Imhof A. Band Formation in Mixtures of Oppositely Charged Colloids Driven by an ac Electric Field. Physical Review Letters, 2011, no. 106, article ID: 228303, 4 p. DOI: 10.1103/PhysRevLett.106.228303.
11. Xiang-Zhong Chen, Hoop M., Mushtaq F., Siringil E., Chengzhi Hu, Nelson B.J., Pane S. Recent Developments in Magnetically Driven Micro- and Nanorobots. Applied Materials Today, 2017, vol. 9, pp. 37-48. DOI: 10.1016/j.apmt.2017.04.006
12. Martynov S.I. Hydrodynamic Interaction of Particles. Fluid Dynamic, 1998, no. 33, pp. 245-251. DOI: 10.1007/BF02698709.
13. Konovalova N.I., Martynov S.I. Simulation of Particle Dynamics in a Rapidly Varying Viscous Flow. Computational Mathematics and Mathematical Physics, 2012, vol. 52, no. 12, pp. 2247-2259. DOI: 10.1016/j.apmt.2017.04.006