Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-21T12:24:34.448Z Has data issue: false hasContentIssue false
  • English
  • Français

Plane potential flows past doubly periodic arrays and their connection with effective transport properties

Published online by Cambridge University Press:  21 April 2006

F. K. Lehner
F. K. Lehner
Affiliation:
Koninklijke/Shell Exploratie en Produktie Laboratorium, 2288 GD Rijswijk ZH, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

A method of constructing plane potential flows past doubly periodic arrays of cylindrical obstacles is described. It is based on Rankine's well-known technique of determining by simple superposition the shape of an oval-shaped obstacle simultaneously with the flow round the obstacle. This paper deals with the use of such potentials in calculating effective medium conductivities for a class of doubly periodic two-phase materials which contain either non-conducting or perfectly conducting cylindrical inclusions embedded within a conducting matrix phase.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 35 - 51
Copyright
© 1986 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions. Dover Publications.
Batchelor, G. K. 1974 Transport properties of two-phase materials with random structure. Ann. Rev. Fluid Mech. 6, 227.Google Scholar
Batchblor, G. K. & O'Brien, R. W.1977 Thermal or electrical conduction through a granular material. Proc. R. Soc. Lond. A 355, 313.Google Scholar
Keller, J. B. 1963 Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders. J. Appl. Phys. 34, 991.Google Scholar
Keller, J. B. 1964 A theorem on the conductivity of a composite medium. J. Math. Phys. 5, 548.Google Scholar
Keller, H. B. & Sachs, D. 1964 Calculations of the conductivity of a medium containing cylindrical inclusions. J. Appl. Phys. 35, 537.Google Scholar
Mcpheedran, R. C., Mckenzie, D. R. & Phan-THIEN, N. 1983 Transport properties of two-phase composite materials. In Advances in the Mechanics and the Flow of Granular Materials ed. M. Shahinpoor, vol. 1, pp. 415. Gulf Publishing Co.
Mendelson, K. S. 1975 Effective conductivity of a two-phase material with cylindrical phase boundaries. J. Appl. Phys. 46, 917.Google Scholar
Nicholson, C. & Phillips, J. M. 1981 Ion diffusion modified by tortuosity and volume fraction in the extracellular microenvironment of the rat cerebellum. J. Physiol. (London), 321, 225.Google Scholar
Obenhettinger, F. & Magnus, W. 1949 Anwendung der Elliptischen Funktionen in Physik und Technik. Springer-Verlag.
Rayleigh, Lord 1982 On the influence of obstacles arranged in rectangular order on the properties of the medium. Phil. Mag. 34, 481.Google Scholar