偶极子模型在介质混合体中的适用范围

Limits for Validity of Dipole Approximation in a Dielectric Mixture

对于颗粒相互靠近、两相介电系数比较大的介质混合体来说,采用偶极子模型(Dipoleapproximation)计算局部场强将会引起很大误差。为此,分别采用有限元方法和偶极子模型计算混合体中颗粒球表面的电场分布,由此计算出在球面各点偶极子模型与有限元结果之间的相对误差。结果表明,最大误差总是发生在沿电场方向颗粒球的顶点或非常靠近该点的某处。在此基础上,本文提出以这个最大误差不超过容许误差作为评判偶极子模型是否成立的标准,由此确定其适用范围,并绘制出对应于三种不同容许误差的计算曲线。与前人研究结果的对比表明,这种确定偶极子模型适用范围的方法是可行的,由其计算所得的曲线是可信的。

The dipole approximation seriously compromises the accuracy in the calculations of the local electrical field strengths for a dielectric mixture with a great dielectric mismatch when the particles approach closely. It investigates the limits for validity of the dipole approximation in a dielectric mixture with spherical inclusions through electric field analysis. The electric field distributions on an arbitrarily selected sphere surface are computed by the finite element model （FEM） and the dipole approximation respectively. The relative errors between the dipole approximations and the FEM results are obtained for two type mixtures. It is found that the maximum relative error always happened at or very near the pole of the spherical particle along the direction of the external electric field. Based on which, a new criterion of valid limits of the dipole approximation, is presented. Three calculated curves of the valid limits for the dipole approximation corresponding to three different allowable errors are drawn. The comparison between these curves and the previously published results by other researchers highlights that this criterion is feasible and these curves are credible.