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

Abstract

Abstract:In flocculation processes, particulates randomly collide and coagulate with each other, leading to the formation and sedimention of aggregates exhibiting fractal characteristics. The diffusion-limited aggregation (DLA) model is extensively employed to describe and study flocculation processes. To more accurately simulate flocculation processes with the DLA model, the effects of particle number (denoting flocculation time), motion step length (denoting water temperature), launch radius (representing initial particulate concentration), and finite motion step (representing the motion energy of the particles) on the morphology and structure of the two-dimensional (2D) as well as three-dimensional (3D) DLA aggregates are studied. The results show that the 2D DLA aggregates possess conspicuous fractal features when the particle number is above 1000, motion step length is 1.5-3.5, launch radius is 1-10, and finite motion step is more than 3000; the 3D DLA aggregates present clear fractal characteristics when the particle number is above 500, the motion step length is 1.5-3.5, the launch radius is 1-10, and the finite motion step exceeds 200. The fractal dimensions of 3D DLA aggregates are appreciably higher than those of 2D DLA aggregates.

Reversible pH-Driven Flocculation of Amphiphilic Polyelectrolyte-Coated Nanoparticles for Rapid Filtration and Concentration

“…NPs flocculated in 10% THF exhibit a fractal dimension of 1.95 ± 0.07. All these values fall within the range expected of solids assembled by diffusion-limited aggregation. − …”

Rheology of a Dilute Suspension of Aggregates in Shear-Thinning Fluids

“…In this section we present results by varying the fractal dimension, the flow index, and the number of primary particles. Specifically, we consider three values for each parameter, that is, D f = [1.5, 2.0, 2.5], n = [1.0, 0.7, 0.4], and N p = [10,20,50]. Notice that, since the intrinsic viscosity is normalized with respect to the aggregate volume, the number of primary particles defines the structure resolution (finer for many particles) and, for low fractal dimension, it is also connected to the aggregate aspect ratio.…”

“…In many processes, however, the suspended particles have a complex and irregular shape, without symmetry axes or planes. This is, for instance, the case when primary spherical particles undergo an aggregation process and form clusters with fractal-like morphology [8][9][10]. As for the spheroidal particle case, the prediction of the intrinsic viscosity requires the calculation of the orientational dynamics of the particles subjected to an external shear flow.…”

The growth simulation of pine-needle like structure with diffusion-limited aggregation and oriented attachment

“…This is different from that with specific motion parameters of the early DLA model. 14,58–60 At every step, the displaced coordinate ( x n , y n , z n ) is calculated with the previous place ( x n −1 , y n −1 , z n −1 ) using the equations below: 70 x n = x n −1 + r cos θ cos ϕ y n = y n −1 + r sin θ cos ϕ z n = z n −1 + r sin ϕ …”