(Updated 13-March-2000)
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Particle
Dynamics & Fractal Coagulation Processes
(Updated 13-March-2000) |
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Particles are extremely important in
the natural environment and in engineered systems. Particles contribute to
water turbidity and many engineered systems are designed to treat water
through particle removal. Particles can also enhance the transport of
relatively insoluble chemicals sorbed on their surfaces. My research over
the past 18 years has examined particle transport dynamics, including the
transport of chemicals to particles, and the formation of larger, fractal
particles through aggregation processes.
Particles produced through aggregation are highly amorphous, non-spherical and fractal, and have three-dimensional fractal dimensions that span a range of ~1.1 to the maximum of 3. Previous methods for calculating fractal dimensions of inorganic aggregates have been based on the analysis of a single particle, but most systems of interest consist of a spectrum of particle sizes. In order to analyze average properties of aggregates in real coagulating suspensions with broad size distributions, we developed new spectral techniques to estimate fractal dimensions. Using these techniques, we demonstrated that there was no universality of the fractal dimension for aggregates formed from fluid shear and differential sedimentation processes. Fractal dimensions of microspheres formed in three different mixing environments, for example, were: 1.9, in a paddle mixer; 1.59 in a rolling cylinder; and 1.43 to 1.74 in a laminar shear device (depending on shear rate and salt concentration). The fractal nature of these particles has been found to have important implications for calculations of particle properties such as their settling velocities and collision efficiencies. Fractal aggregates of inorganic microspheres, for example, settle an average of eight times faster than spheres of identical size and mass. Collision frequencies between large bacterial aggregates (100 um) and small microspheres (~ 1 um) were five orders-of-magnitude higher than predicted using sphere-based (curvilinear) coagulation models. Similarly high but slightly larger collision frequencies were obtained for aggregates made from microspheres. These results demonstrate that fractal aggregates of particles can collide much more frequently than expected based on spherical-particle coagulation models. They suggest that coagulation rates in natural and engineered systems are much more rapid than predicted by coagulation models based on impermeable spheres. Use the links provided through this web page to see examples of fractals and to see a list of publications associated with this topic. |