Fractal dimensions of aggregates formed in different fluid mechanical environments

The fractal properties of aggregates formed under two different fluid mechanical environments, a paddle mixer and a rolling cylinder, were measured using three different techniques: a non-steady state method requiring both volume and length size distributions, a steady state size distribution method, and an aggregate property scaling method. Based on cumulative size distributions and the non-steady state method, aggregates produced in the rolling cylinder had a fractal dimension of D3(l,v) = 1.59 ± 0.16, while aggregates produced in the paddle mixer had a higher fractal dimension of D3(l,v) = 1.92 ± 0.04. Fractal dimensions calculated assuming steady state size distributions based on aggregate volume were substantially different than those based on aggregate length indicating that size distributions in both devices were not at steady state during the experiment. Although fractal dimension based on cumulative size distributions were similar in magnitude to those calculated using discrete and data-averaged size distributions, the cumulative size distributions produced fractal dimensions with the lowest errors. When D3 < 2, three dimensional and two dimensional fractal dimensions should be equal. Power law equations for two dimensional fractal dimensions based on aggregate properties (length and area) were in good agreement with three dimensional fractal dimensions. Rolling cylinder and paddle mixer aggregates had two dimensional fractal dimensions of D2 = 1.68 ± 0.02 and D2 = 1.89 ± 0.02. These experiments demonstrate that aggregate properties are a function of the fluid mechanical environment used to coagulate particles.