偶极子模型计算混合体局部场强的误差分析

Error Analyses in the Calculations of the Local Electric Field Strengths in a Mixture by the Dipole Approximation

针对偶极子模型近似计算较高占空比混合体局部场强时误差较大的问题,以有限元法的数值计算结果作为电场的真实值,得到了偶极子模型在近似计算混合体中球形颗粒表面各点场强时的相对误差。结果表明,若占空比<20%,则对于所有介质颗粒,最大误差总是出现在最大场强点;若占空比>20%,则颗粒与环境介电常数差异达到一定值时,最大相对误差将会转移到球面上另外一点,并随介电常数差异增大而逐渐靠近最小场强点。对不同占空比的混合体,考察了最大误差点随介电常数差异的变化而移动的规律,并据此绘制出了一条计算曲线。

The dipole approximation seriously compromises the accuracy in the calculations of the local electric field strengths for a mixture with a high volume fraction of particles. In this paper, the relative errors in the calculations of the electric field strengths on the surface of one spherical particle using the dipole approximation were obtained on the basis of the assumption that the results by the finite element method were exact. It was clear that, for any mixture, the maximum errors always present at the points with the maximum electric field strengths when the volume fractions of particles exceed 20%. However, if the volume fractions of particles were less than 20% and the dielectric mismatch between the particles and the environment were greater than a threshold, the maximum relative errors would present to the other points which are close to the points with the minimum electric field strengths. For the various mixtures with different volume fractions of particles, the rules of the moving of the maximum relative errors with the dielectric mismatch were studied, and a curve was drawn.