A numerical study of the ζ2 parameter for random suspensions of disks

The effective conductivity of two‐component composites can be tightly bounded through the knowledge of structural parameters. While the first‐ and second‐order parameters are known analytically for isotropic materials, the third and higher order parameters are generally not. Their evaluation has, therefore, become the subject of much research. In particular, the third‐order structural parameter ζ2 has been computed many times. Interface methods, beginning with Rayleigh, have proven successful for periodic composites with simple unit cells. Statistical methods, involving three‐point correlation functions, work well for dilute random suspensions. Composites consisting of complicated, dense suspensions have been much more difficult to treat. In this article, we illustrate how one can greatly accelerate the computation of structural parameters with interface methods, so that these methods can be applied to dense suspensions with tens of thousands of randomly placed inclusions per unit cell. We implement a num...

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