Applicability of Fractals to the Analysis of the Projection of Small Flocs

Fractal Simulation of Flocculation Processes Using a Diffusion-Limited Aggregation Model

“…For the 3D DLA model, the simulation with too few particles (<500), too big a motion step length (>4), too large a launch radius (>10), and too small a finite motion step (<200) cannot produce 3D DLA aggregates with clear fractal features, either. The 3D DLA simulation with the particle number of >500, motion step length of 1.5-3.5, launch radius of 1-10, and finite motion step of >200 can form 3D DLA aggregates having apparent fractal features with fractal dimensions of around 2.20, which agrees well with the experimental values of 1.8-2.20 reported in [30] and is considerably higher than that of the 2D DLA aggregates, probably due to the excluded volume effect [7] which means that the centers of the primary particles in three-dimensional space cannot approach each other more closely than the length of the diameter of the primary particle. As reported, the diffusion-limited cluster-cluster aggregation model (DLCA) with fractal dimension of 1.75-1.85 [31][32][33] can reveal the real flocculation processes better than the DLA model; we intend to conduct further research on fractal simulations of the flocculation processes by using the DLCA model as well.…”

“…The "seed" particle and other free particles are considered to have circular shapes (or spherical shapes) and their radius is fixed at 0.5. The fractal dimensions of the DLA aggregates are obtained by using the gyration calculation method [7,28,29]. Particularly, the number of primary particles is a function of the gyration radius of the aggregates (depicted in Figure 1b), which obeys the following scaling form:…”

“…Oles [5] found that the fractal dimensions increased from 2.1 to 2.5, resulting from the compaction of the aggregate structure which was attributed to the selective breakup that removed the weaker (and more porous) parts of the colloidal aggregates. Adachi et al [6,7] conducted many valuable works on the structure properties of colloidal flocs, such as effect of ionic strength on the initial flocculation dynamics [8], shear viscosity of coagulated suspensions [9], effect of floc structure on the rate of shear coagulation [10], and the restructuring behavior of small flocs [11].…”

Modeling particle‐size distribution dynamics in a flocculation system

“…4 to 7, 23, and 50 m Figure 3b . Therefore, consistent with Ž many previous studies Kuster et al, 1993;Jackson, 1998;. Adachi et al, 1998 , the present simulations further exhibited the important role of the fractal dimension in regulating the flocculation dynamics and steady-state particle-size distribu-Ž .…”

Comparison of Agglomeration Behavior of Fine Particles in Liquid among Various Mixing Operations

“…Many experimental and theoretical studies have been done on the agglomeration behavior of fine particles in liquid: agglomeration structure by using a fractal dimension, [6][7][8][9][10][11] wettability of particles, 12,13) heterogeneous agglomeration with a different surface electrification and size, [14][15][16][17][18] particle collision frequency in turbulent flow, 19,20) particle-size grouping.…”