含椭球包体多相复合介质电导率的有效介质理论

本文应用有效介质理论(EMT),研究含椭球包体的多相复合介质中的导电性。建议用各向异性因子m估计非均匀系统的局域各向异性,并给出一个计算此情况下有效电导率张量的公式。对于椭球包体取向完全无序的介质,建议以介质的几何结构因子I_i(i=χ,y,z)估计组成包体的颗粒之间的近场效应。研究表明,结构因子I_i与包体的退极化因子n_i(i=χ,y,z)之间存在简单的关系。EMT的计算结果表明,抻长的椭球包体(b/α≈0.2)和压扁的椭球包体((b/α≈7—8)是导致渗流阈值对c₁^*=0.17的两种主要几何结构。初步的理论分析表明,由这两种几何形状产生渗流的共同机制是在介质中形成“无穷”长的链状集团。

EFFECTIVE-MEDIUM THEORY FOR ELECTRICAL CONDUC-TANCE OF A TWO-PHASE COMPOSITE MEDIUM WITH ELLIPSOIDAL-INCLUSIONS

In this paper the electrical conductance of a two-phase composite medium with ellipsoidal inclusions has been investigated by using the effective-medium theory(EMT). An anisotropic factor m is suggusted TO take account of the local anisotropy of an inhomogeneous system. A formula for calculating the effective electrical conductivity tensor in such case has been proposed. A geometrical structure factor I_i(i = x,y,z) is introduced to estimate the near field effect between the particles aggregated in the inclusions. It has been shown that there is a simple relation between the structure factor I_i and the depolarization factor n_i. The calculated results based on the EMT show that prolate ellipsoid (b/a = 0.2) and oblate ellipsoid (b/a=7.5) are the two principle geometrical configurations leading to the percolation threshold c₁^* =0.17. A preliminary theoretical analysis informs that the common mechanism leading to the percolation by these two configurations is the formation of an 'infinite' chain-shaped cluster.