Aggregation kinetics of small particles in agitated vessels

Abstract

Abstract--Rapid coagulation by turbulence in stirred tanks was studied for particles and aggregates smaller than the Kolmogorov microscale. The coagulation kinetics are determined by the floc structure and by the hydrodynamic and colloidal interactions between the colliding particles. The collision efficiency for doublet formation in the heterogeneous shear field of a stirred tank follows from particle trajectory analysis of solid particles in simple shear flow, provided the simple shear rate is made to correspond to the residence time weighted turbulent shear rate. Experimentally, the resulting aggregates proved to be fractal-like with their porosity increasing with aggregate size. Porosity within the aggregates results in penetration of the floc surface by the fluid flow, giving rise to enhanced collision efficiencies compared to solid particles. The collision efficiencies between porous flocs may be estimated by a model that pictures a porous floc as consisting of an impermeable core and a completely permeable shell. With the collision efficiencies from this shell-core model the aggregate growth could be described adequately.

Modelling the breakup of solid aggregates in turbulent flows

“…independent of the aggregate size, results in a ∼ τ −1/2 f ∼ ε −1/4 . This latter exponent (p = 1/4) is the typical value found in experiments for the scaling of a mean aggregate size at steady state (Selomulya et al 2002;Coufort, Bouyer & Liné 2005;Kusters, Wijers & Thoenes 1997). Computer simulations of non-rigid aggregates confirm this result, e.g.…”

“…The exponent n is a parameter depending on the number of contacts among the primary particles in the aggregate. From (4.2), the local solid volume fraction is estimated as ϕ(r) ∼ r d f −3 , where r = |r|, from which the aggregate strength follows as τ a ∼ a n(d f −3) (Kusters 1991;Ba ldyga & Bourne 1995). Balancing τ a with τ f results in (Potanin 1993) where a cr is the critical aggregate size above which breakup occurs.…”

Light-Scattering Cross Section of Hydrophilic and Hydrophobic Silica Aggregates

“…Most recent experiments of aggregation in turbulent medium tend to prove that the aggregates have a fractal structure (Kusters et al, 1997;Gruy, 2001;Cugniet, 2003). An aggregate containing i identical primary particles of radius a 1 is characterised by its fractal dimension D f and outer radius a i which are linked by the relation:…”

“…Given an aggregation model (Kusters et al 1997), the variation with time of the aggregate population density can be calculated, thus the turbidity change over the aggregation process. By comparison between predicted and measured turbidity plots versus time, the different models can be validated and the unknown parameters calculated.…”

Computer simulation of the aggregates formation during flocculation process

“…Destabilization of particles can be achieved by chemical coagulation which is a very complex process due to the influence of many physical and chemical factors as: pH of water, ζ-potential of the particle, dosage of the reagent and its type, reaction time and mixing speed, temperature, etc. Existing basic theories, based mainly on Smoluchowski's rapid coagulation principle, allow to examine the kinetics of the coagulation process and to predict effect of aggregation expressed as the particles number reduction [3]. Further development of basic theories allow to create mathematical models of flocculation, which consider the process in greater details, namely: characterize size, strength, density of resulting flocs [4].…”