论文信息 - The conductivity of lattices of spheres - II. The body centred and face centred cubic lattices

The conductivity of lattices of spheres - II. The body centred and face centred cubic lattices

The conductivities of body-centred (b. c. c.) and face-centred (f. c. c.) cubic lattices of spheres of a conducting material in a conducting matrix are calculated by using a method originally devised by Lord Rayleigh. Measurements of the conductivity of the b. c. c. lattice of perfectly conducting spheres are presented. Good agreement between theory and experiment is obtained. Our results are shown to be in agreement with asymptotic equations derived by other authors. A formula is given for the case of a disordered array.

[1] G. Batchelor,et al. Transport Properties of Two-Phase Materials with Random Structure , 1974 .

[2] J. D. Bernal,et al. The Bakerian Lecture, 1962 The structure of liquids , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3] D. R. McKenzie,et al. The conductivity of lattices of spheres I. The simple cubic lattice , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4] L. Rayleigh,et al. LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium , 1892 .

[5] Charles W. Tobias,et al. Resistance to Potential Flow through a Cubical Array of Spheres , 1959 .

[6] D. A. Dunnett. Classical Electrodynamics , 2020, Nature.

[7] D. Mckenzie,et al. Exact modelling of cubic lattice permittivity and conductivity , 1977, Nature.

[8] G. Batchelor,et al. Thermal or electrical conduction through a granular material , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[9] J. Maxwell. A Treatise on Electricity and Magnetism , 1873, Nature.

[10] Joseph B. Keller,et al. Conductivity of a Medium Containing a Dense Array of Perfectly Conducting Spheres or Cylinders or Nonconducting Cylinders , 1963 .