Fractal structure of aggregates induced by shear motion.

Abstract

Aggregates formed by Brownian motion, shear motion, and differential sedimentation are found to be fractals. To characterize the structure and properties of these aggregates, a set of equations was derived to describe the relationship between aggregate size and solid volume, porosity, density, settling velocity and collision efficiency. By extending concepts developed by Friedlander and Hunt for the analysis of nonfractal particle coagulation at steady state, a steady-state size distribution model for fractal aggregates was developed for size intervals dominated by Brownian motion, shear, or differential sedimentation. A non-steady-state size distribution (two-slope) method was proposed for determining three dimensional fractal dimensions. Using size distributions in terms of both aggregate length and solid volume, a method was also developed to obtain the relationship between solid volume and aggregate size for examining the variation of fractal dimensions over a given size range. Coagulation experiments with latex microspheres in salt solutions were conducted to test predictions of the steady-state model and to study the effects of salt concentration and shear rates on the fractal structure of aggregates in both laminar shear and turbulent shear devices. The prediction of the steady-state model over the subrange dominated by shear motion was verified by the results of the experiments at 0.15 M NaCl and a shear rate of 3.4 s⁻¹, and the experiment at 0.6 M NaCl and a shear rate of 0.5 s⁻¹. In turbulent flow, fractal dimensions were not a function of salt concentration. In laminar shear, at NaCl concentration ≤ 0.3 M fractal dimensions were 1.9 to 2.1 with a collision efficiency of 10⁻³. High NaCl concentrations (0.45 to 0.6M) resulted in lower fractal dimensions of 1.4 to 1.7 with a collision efficiency of 10⁻¹. Laminar shear rates of 0.5 to 15 s⁻¹ had little effect on fractal dimensions. Boundary fractal dimensions of aggregates were not sensitive to changes in NaCl concentrations in both laminar and turbulent flow but they were a function of laminar shear rate.