Electrorheological (ER) fluids have been an important offset of smart materials. The calculated results of the effective dielectric constants are usually used to analysis the mechanical properties of ER fluids Within the Maxwell-Wagner model, Rayleigh identity is used to calculate the effective dielectric constants of a simple cubic lattice of conducting sphere in ER fluids. The problem is formulated explicitly in terms of an infinite matrix equation that is solved by iteration. A general analytical formula for the effective dielectric constants is derived as a series expansion in powers of the volume fraction of spheres. The results of sample numerical calculation are presented. Based on our numerical results, implications for the design of high performance ER fluids are discussed briefly.
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