导电球简立方格子有效介电常数的计算

基于MaxwellWagner模型,推导出有效介电常数关于颗粒体积比的一系列正幂项解析表达式,计算导电球颗粒悬浮于介质或导电液体中构成的简立方格子结构的有效介电常数.数值计算结果表明:在高频条件下(0.1～1.0kHz),有效介电常数主要由导电球颗粒与液体的介电常数比决定,而在低频或直流条件下,导电球颗粒与液体电导率比则起主要作用;有效介电常数的虚数部分有时会很大,即电流变液中的电致损耗有时会相当强,在设计高性能的电流变液时,体系的电导率效应不能忽略.

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.