Void size distribution in simulated fractal aggregates

Abstract

The size-distribution of voids, −dV dL where V( L) is the total volume occupied by holes of size larger than L, is numerically calculated for aggregates of various fractal dimensions built according to various realistic aggregation processes. To calculate the volume of voids, the aggregates are disposed inside a box, which is either a natural box, in the case of aggregation models done in a box (with a finite concentration of particles), or an artificial box, which matches the edges of the aggregate in the case where a single aggregate is built according to a hierarchical scheme (which corresponds to the zero-concentration limit). It is shown that the scaling relation −dV dL ∝ L 2−D , where D is the fractal dimension of the aggregates, is only followed in a restricted regime of small L-values, just above the lower cut-off L s = 1 for D < 2, and after a maximum for D > 2. After this regime and for D < 2, −dV dL goes through a maximum. In the case where an artificial box is considered, another scaling regime −dV dL ∝ L −D is observed above the maximum L max and below an upper cut-off L a. It is shown that the fractal dimension cannot be simply extracted from the void size distribution directly. However, the cut-off effects are considerably attenuated by plotting y = [V(L s ) − V(L)] [V(L) − V(L a )] as a function of x = (L − L s ) (L a − L) . The scaling relation y ∝ x 3− D is then verified in a large regime and allows the fractal dimension to be measured.