Volume 235, February 2013, Pages 540–549

Effect of shear rate on aggregate size and structure in the process of aggregation and at steady state

  • Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, Pod Patankou 5, 166 12 Prague 6, Czech Republic

Abstract

The paper deals with the dependence of aggregate properties on the shear rate (G) in the aggregation process and at steady state. Natural raw water and ferric sulphate were aggregated in a Taylor–Couette reactor. The methods of image and fractal analysis were used to determine the aggregate size and structure. It was observed that at the early phase of aggregation, the aggregate growth rate is higher for lower shear rates. At G ≤ 150 s− 1, the time aggregation curve contains the local maximum before reaching the steady state. Moreover, the different extent of break-up and restructuring was proved for different values of shear rate. At G ≥ 200 s− 1, the aggregation curve misses the local extreme completely. It was found that with increasing shear rate (G = 21.2–347.9 s− 1), the aggregates are smaller (d = 1504–56 μm), more compact (D2 = 1.54–1.91) and more regular (Dpf = 1.37–1.10). A relationship for the description of dependence of fractal dimension on the shear rate was also suggested.


Graphical abstract

The paper deals with the dependence of aggregate properties on the shear rate during aggregation and at steady state. At lower shear rates, the time aggregation curve contains the local maximum before reaching the steady state. With increasing shear rate, the aggregates are smaller, more compact and more regular.

Highlights

► Effect of shear rate on properties of aggregates formed in water treatment ► At G ≤ 150 s− 1 aggregation curve contains local maximum before attaining steady state ► At G ≥ 200 s− 1, aggregation curve misses local maximum before attaining steady state ► With increasing shear rate, aggregates are smaller, more compact and more regular ► Relationship describing dependence of fractal dimension on shear rate was proposed

Keywords

  • Aggregation;
  • Aggregate size;
  • Fractal dimension;
  • Shear rate;
  • Steady state;
  • Time evolution

1. Introduction

The processes of destabilization and aggregation are traditionally used to remove colloidal particles in water treatment. The purpose is to prepare aggregates of such properties (size, structure, shape, density, etc.) that are suitable for reaching the maximum effectiveness of following separation steps, such as sedimentation, filtration or flotation.

The formation of suspension includes the processes of aggregation, break-up and in some cases restructuring [1], [2], [3], [4] and [5]. These processes can (but do not have to) proceed simultaneously and they depend on the balance between the hydrodynamic force F and the cohesive force J. The hydrodynamic force arises from a flow of fluid around a particle and is thus determined by the magnitude of the shear rate G, cross-sectional area of a particle A and dynamic viscosity of fluid μ. The cohesive force is given by the sum of all attractive forces acting between interacting particles (e.g. van der Waals, electrostatic or hydrophobic forces). It depends particularly on the particle (and/or reagent) composition and concentration and determines the strength of formed aggregates [1], [4], [6], [7] and [8]. If the cohesive force prevails (J > F), aggregation occurs. If the hydrodynamic force prevails (F > J), aggregates are not formed at all or a break-up of already existing aggregates takes place. When these forces are approximately in equilibrium, the restructuring occurs.

When chemical conditions (type and concentration of particles and reagents, pH and overall water composition) are kept constant, the cohesive force between two primary particles does not change during the aggregation process. However, the hydrodynamics are influenced by the shear rate in the mixed volume which is not spatially (and temporally) constant at all and which depends on the geometry of the mixing tank and stirrer shape and speed (and temperature as well). This fact allows the already formed aggregates to be broken again when exposed to the regions with higher shear rates [8], [9], [10], [11], [12] and [13]. Nevertheless, the global/mean/average shear rate is still used for the characterization of hydrodynamics for practical reasons.

There are different perspectives on studying aggregate properties. First, it is the development of properties in time as the suspension is being formed (aggregation kinetics) and another, it is the description of aggregate properties at a steady state when they stabilize at some constant values. Both can be studied theoretically and/or experimentally.

The aggregation kinetics is theoretically studied with the use of population balance modelling based on the classical equation developed by Smoluchowski [14] which expresses the change of the number concentration of aggregates in time. This model assumes that only binary collisions between particles occur, the collision efficiency is 100%, colliding particles are spherical and of equal size, and neither aggregate break-up nor restructuring is considered. This expression has been modified by adding terms representing the aggregate break-up [15] and structure changes [3]. Population balances were then used by many other authors [3], [5], [13], [16], [17], [18] and [19]. Experimental results that have been reported so far generally show two different trends of the development of aggregate size in time. In the first case, the aggregate size increases with time quite rapidly in the early stage of aggregation, and the growth slows down gradually until the steady state is reached [2], [5], [20], [21], [22], [23] and [24]. In the other case, the aggregates grow to a maximum and then their size decreases again before a steady state is reached [3], [9], [11], [12], [18], [25] and [26]. The reason for the appearance of such a peak in a size-time profile has not yet been satisfactorily explained, although there are some suggestions that it might be the result of restructuring (break-up and re-aggregation) [11].