Effective Media Theory Using Nearest Neighbor Pair Distributions
The behavior of heterogeneous materials is interesting on several levels. First, such materials are common in nature and our technological society. Their behavior is difficult to predict, to understand, and to explain. On a theoretical level, the nature of these materials leads naturally to questions of repeatability and averaging. The microscale problem is often describable by classical dynamical equations (Navier-Stokes, Fourier heat conduction, etc.), but using this information to obtain constitutive equations is difficult, and has led to the development of two theoretical techniques (viz., renormalization and effective media theory).
KeywordsConstitutive Equation Effective Viscosity Space Point Effective Conductivity Rigid Sphere
Unable to display preview. Download preview PDF.
- J.C. Maxwell, Electricity and Magnetism, Clarendon Press, Oxford (1873).Google Scholar
- D.K. Ross, The Potential due to Two Point Charges Each at the Centre of a Spherical Cavity and Embedded in a Dielectric Medium Aust. J. Phys., 21, 817–822 (1968).Google Scholar
- T.S. Lundgren, Slow Flow Through Stationary Random Beds and Suspensions of Spheres, J. Fluid Mech., 238, 579–598, (1972).Google Scholar
- J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics, Noordhoff, Leyden (1973).Google Scholar
- H. Lamb, Hydrodynamics, Cambridge University Press (1932).Google Scholar
- G.B. Stokes, On the Effect of the Internal Friction of Fluids on the Motion of Pendulums, Trans. Cambridge Phil. Soc., 9, p8; also in Mathematical and Physical Papers, Vol. 3, Johnson Reprint Corporation, New York, (1966).Google Scholar
- M.F. Hurwitz, Hydrodynamic Interactions of Many Rigid Particles, Ph. D. Thesis, Cornell University, Ithaca, NY (1996).Google Scholar
- H.C. Brinkman, A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles, Applied Scientific Research, Al, 27–34 (1947).Google Scholar