NASA - National Aeronautics and Space Administration

In the past two decades, several experimental and simulation studies have proposed simple empirical relations between projected two-dimensional (2-D) and three-dimensional (3-D) structural properties of fractal-like aggregates in the cluster–dilute regime. These empirical relations have found extensive use in inferring the 3-D structural properties of aggregates from their projected (i.e., 2-D) properties—measurable from aggregate electron microscopy images. This study probes the limitations and nongeneralizability of these simple and straightforward empirical relationships and proposes replacing them with new empirical formulas. A straightforward empirical relationship for directly determining the 3-D fractal dimension (Df ) of an aggregate from the knowledge of its 2-D aspect ratio is also identified. These new relationships were derived by comparing the ratios of several 2-D and 3-D structural properties of a statistically significant number of simulated aggregates with point-contacting monomers as a function of their 3-D Df ranging from 1.0 to 3.0 in increments of 0.1.