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2 results

  • 8 - Electric Resistivity

  • Nikolai Bagdassarov, Goethe-Universität Frankfurt Am Main
  • Book:
    Fundamentals of Rock Physics
    Published online:
    19 November 2021
    Print publication:
    09 December 2021, pp 292-360

  • Summary

    Electrical conductivity and resistance obey Ohm’s law. Specific resistance may be measured in two- or four-electrode schemes. Mechanisms of electrical conductivity in rocks are ionic, electronic, anionic and protonic. Some mantle minerals, i.e. olivine, possess polaron conductivity. Conduction bands and density of states are considered for some minerals. Effective conductivity in heterogeneous rocks can be estimated from Wiener or Hashin–Shtrikman bounds, effective medium approximation (EMA) and resistor network models. The electrical conductivity of mineral aggregates can be effectively described by brick and percolation models. Diluted electrolytes and Kohlrausch’s law of independent movement of ions are considered in fluid-bearing rocks, whose electric conductivity obeys Archie’s law. Formation factor and cementation exponent are analyzed for sedimentary rocks. The relationship between rock conductivity and pore saturation is described by the Waxman–Smith model. Focus Box 8.1: Calculations of density of states (Fermi gas model). Focus Box 8.2: Reciprocal lattice and band gaps. Focus Box 8.3: Olivine structure.

  • 11 - Thermodynamics of Irreversible Processes

  • from Part III - Continuous Media
  • Jean-Philippe Ansermet, École Polytechnique Fédérale de Lausanne, Sylvain D. Brechet, École Polytechnique Fédérale de Lausanne
  • Book:
    Principles of Thermodynamics
    Published online:
    14 December 2018
    Print publication:
    03 January 2019, pp 308-360

  • Summary

    The thermodynamics of irreversible processes is based on the expression of the entropy source density derived in the previous chapter. From it, phenomenological laws of transport can be presented in a unified way. Heat transport is given by Fourier’s law that leads to a heat equation in which Joule and Thomson effects can be included. It can explain thermal dephasing, heat exchangers and effusivity. Matter transport leads to the Dufour and Soret effects, which imply Fick’s law and the diffusion equation, which can be used to discuss Turing patterns and ultramicroelectrode. Transport of two types of charge carrier leads to the notion of diffusion length, giant magnetoresistance and planar Ettingshausen effect. Transport can be perpendicular to the generalised force, as in the Hall, Righi-Leduc and Nernst effects. The formalism accounts also for thermoelectric effects such as the Seebeck and Peltier effects, with which to analyse thermocouples, a Seebeck loop, adiabatic thermoelectric junctions, the Harman method of determing the ZT coefficient of a thermoelectric material and the principle of a Peltier generator.