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Colloidal Magnetic Fluids pp 83–156Cite as

Thermodynamics, Electrodynamics, and Ferrofluid Dynamics

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Part of the book series: Lecture Notes in Physics ((LNP,volume 763))

Abstract

Applying thermodynamics consistently and in conjunction with other general principles (especially conservation laws and transformation properties) is shown in this review to lead to useful insights and unambiguous results in macroscopic electromagnetism. First, the static Maxwell equations are shown to be equilibrium conditions, expressing that entropy is maximal with respect to variations of the electric and magnetic fields. Then, the full dynamic Maxwell equations, including dissipative fields, are derived from locality, charge conservation, and the second law of thermodynamics.

The Maxwell stress is obtained in a similar fashion, first by considering the energy change when a polarized or magnetized medium is compressed and sheared, then rederived by taking it as the flux of the conserved total momentum (that includes both material and field contributions). Only the second method yields off-equilibrium, dissipative contributions from the fields. All known electromagnetic forces (including the Lorentz force, the Kelvin force, the rotational torque M × H) are shown to be included in the Maxwell stress. The derived expressions remain valid for polydisperse ferrofluids and are well capable of accounting for magneto-viscous effects.

When the larger magnetic particles cluster, or form chains, the relaxation time τ of the associated magnetization M 1 becomes large and may easily exceed the inverse frequency or shear rate, τ ≳ 1/ω, 1/γ, in typical experiments. Then M 1 needs to be included as an independent variable. An equation of motion and the associated modifications of the stress tensor and the energy flux are derived. The enlarged set of equations is shown to account for shear thinning, the fact that the magnetically enhanced shear viscosity is strongly diminished in the high-shear limit, γτ≫1. There is no doubt that it would account for other high-frequency and high-shear effects as well.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany

    M. Liu

  2. Sektion Physik, Universität München, 80539 München, Germany

    K. Stierstadt

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  1. M. Liu
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  2. K. Stierstadt
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Correspondence to M. Liu .

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Editors and Affiliations

  1. Institut für Strömungsmechanik, TU Dresden, Dresden, 01062, Germany

    Stefan Odenbach

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Liu, M., Stierstadt, K. (2009). Thermodynamics, Electrodynamics, and Ferrofluid Dynamics. In: Odenbach, S. (eds) Colloidal Magnetic Fluids. Lecture Notes in Physics, vol 763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85387-9_2

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  • DOI: https://doi.org/10.1007/978-3-540-85387-9_2

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