Percolation occurs when the sheet finally falls apart due to the solid backbone losing connectivity. This section shows how the percolation threshold can be made approximately universal by expressing it in terms of the critical number per unit area at percolation, weighted by an area quantity that comes from an electrical analysis of the effect of one hole on the conductivity of the sheet. This section discusses percolation in 3-D, using the model of randomly overlapping ellipsoidal shapes. The starting point is empty space, which is then randomly filled with overlapping ellipsoidal shapes. These shapes are ellipsoids of revolution, but of arbitrary aspect ratio, ranging from very thin disks to very narrow needles.
Percolation occurs when the solid shapes become continuous.
The effect of aspect ratio on this percolation threshold is studied. Go to Part II Chapter 4. Microstructure development and probes Go back to Part II Chapter 2.