First passage calculation of the conductivity of particle aggregate-laden suspensions and composites

There is considerable interest in transport via conduction through particle laden suspensions (e.g. nanofluids) and composite materials. Frequently, such multiphase systems display enhanced conductivities beyond what is expected from the effective medium approximation. While the origin of this enhancement is often a source of controversy, the most common explanation for anomalous conductivity enhancements is the aggregation of particles. In this work, we employ a first passage simulation technique to investigate the influence of particle aggregation on the resulting conductivity of particle-laden suspensions and composites. Aggregates are modeled as quasifractal objects, and a sequential algorithm is used to computationally generate aggregates of prescribed fractal dimension, pre-exponential factor, number of primary particles, and degree of overlap (coalescence) between primary particles. Four model types of aggregates (highly linear structures with little coalescence, highly linear structures with substantial coalescence, dense structures with little coalescence, and dense structures with substantial coalescence) are examined via the first passage technique, enabling determination of the conductivity of a suspension/composite containing aggregates at a known volume fraction. It is found that for a given type of aggregate, the number of primary particles per aggregate has little-to-no influence on suspension/composite conductivity under any circumstances. For low conductivity particles (particle conductivity/host material conductivity = 10), aggregate formation and aggregate morphology have little influence on suspension/composite conductivity, except at particle volume fractions > 0.10 where slight enhancements beyond the effective medium approximation are observable. However, for high conductivity aggregates (particle conductivity/host matrix conductivity = 100), the influence of aggregation is substantial, and all morphological descriptors of the aggregate influence suspension/composite conductivity. In this instance, the resulting enhancement in conductivity can be equivalent to the enhancement expected if well dispersed spherical particles were incorporated into the suspension/composite at a volume fraction 3-5 times higher than the actual aggregate volume fraction.