Calculation of Effective Dielectric Constants of a Simple Cubic Lattice of Conducting Spheres

Based on the Maxwell-Wagner model, an analytical formula for effective dielectric constants is derived as a series expansion in powers of the volume fraction of spheres. Effective dielectric constants of simple cubic lattices of conducting particles suspended in dielectric or conducting fluids are calculated. The numerical results show that effective dielectric constants depend upon the ratios of the permeability of conducting spheres to that of the suspending fluids under high frequency (0.1-1 kHz) applied fields, whereas, it is determined by the ratios of the conductivities of spheres to that of fluids under low frequency or dc electric fields. The imaginary parts of effective dielectric constants can be very big sometimes. This means that the resistive losses of electrorheological fluids can be very strong at times. The effect of conduction in a system cannot be neglected in the design of high performance electrorheological fluids.