Fluid shear flocculation

Camp and Stein (1943) originally proposed for flocculation that the mean fluid shear rate is proportional to the square root of the mean energy dissipation... 

Particle concentration and size distribution in raw water have extensive and complex effects on the performance of individual treatment units (flocculator, sedimentation tank, and filter) and on the overall performance of water treatment plants. Mathematical models of each treatment unit were developed to evaluate the effects of various raw water characteristics and design parameters on plant performance. The flocculation and sedimentation models allow wide particle size distributions to be considered. The filtration model is restricted to homogeneous suspensions but does permit evaluation of filter ripening. The flocculation model is formulated to include simultaneous flocculation by Brownian diffusion and fluid shear, and the sedimentation model is constructed to consider simultaneous contacts by Brownian diffusion and differential settling. The predictions of the model are consistent with results in water treatment practice. 

Friedlander (11) has examined the effects of flocculation by Brownian diffusion and removal by sedimentation on the shape of the particle size distribution function as expressed by Equation 9. The examination is conceptual the predictions are consistent with some observations of atmospheric aerosols. For small particles, where flocculation by Brownian diffusion is predominant, p is predicted to be 2.5. For larger particles, where removal by settling occurs, p is predicted to be 4.75. Hunt (JO) has extended this analysis to include flocculation by fluid shear (velocity gradients) and by differential settling. For these processes, p is predicted to be 4 for flocculation by fluid shear and 4.5 when flocculation by differential settling predominates. These theoretical predictions are consistent with the range of values for p observed in aquatic systems. 

For the flocculation tank, the significant transport mechanisms leading to interparticle collisions are assumed to be Brownian diffusion and fluid shear. Expressions for the collision frequency functions for these mechanisms were derived by Smoluchowski and are as follows ... 

Assumptions made in modeling the flocculation tank include (1) ideal or plug flow exists throughout the tank (2) the velocity gradient is identical everywhere in the tank (3) flocculation occurs simultaneously by Brownian diffusion and fluid shear, and the collision frequency functions are simply additive (4) the particles are distributed uniformly... 

Plant performance in the absence of flocculation by fluid shear (G == 0 sec ) is examined in Figure 18. Some particle growth occurs by Brownian diffusion in the flocculator and by differential settling and Brownian diffusion in the settling tank. Removal efficiency by sedimentation is smaller than in the standard case (74% compared with 85% ), and filter runs are reduced from 28 to 16 hr. Filtrate quality is good throughout the run. 

This equation is based on the assumption that pseudoplastic (shear-thinning) behaviour is associated with the formation and rupture of structural linkages. It is based on an experimental study of a wide range of fluids-including aqueous suspensions of flocculated inorganic particles, aqueous polymer solutions and non-aqueous suspensions and solutions-over a wide range of shear rates (y) ( 10 to 104 s 1). 

A highly concentrated suspension of flocculated kaolin in water behaves as a pseudo-homogeneous fluid with shear-thinning characteristics which can be represented approximately by the Ostwald-de Waele power law, with an index of 0.15. It is found that, if air is injected into the suspension when in laminar flow, the pressure gradient may be reduced even though the flowrate of suspension is kept constant, Explain how this is possible in slug flow and estimate the possible reduction in pressure gradient for equal volumetric flowrates of suspension and air. 

Plastic fluids are Newtonian or pseudoplastic liquids that exhibit a yield value (Fig. 3a and b, curves C). At rest they behave like a solid due to their interparticle association. The external force has to overcome these attractive forces between the particles and disrupt the structure. Beyond this point, the material changes its behavior from that of a solid to that of a liquid. The viscosity can then either be a constant (ideal Bingham liquid) or a function of the shear rate. In the latter case, the viscosity can initially decrease and then become a constant (real Bingham liquid) or continuously decrease, as in the case of a pseudoplastic liquid (Casson liquid). Plastic flow is often observed in flocculated suspensions. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

Because most shear-thinning fluids, particularly polymer solutions and flocculated suspensions, have high apparent viscosities, even relatively coarse particles may have velocities in the creeping-flow of Stokes law regime. Chhabra(35,36) has proposed that both theoretical and experimental results for the drag force F on an isolated spherical particle of diameter d moving at a velocity u may be expressed as a modified form of Stokes law ... 

Figure 24 illustrates possible flocculation and chaining of particles in flow conditions. Larger particles close to the walls of the vessels experience greater shearing forces because of the nature of the flow patterns shown. Particles that adhere to er5dhrocytes move with them until detachment, often prolonging their own circulation times. Adhesion, seen as a prerequisite to cellular uptake from blood and interstitial fluids is not a foregone conclusion. The probability of adhesion, Padheaon can be written phenomenologically as in Figure 24. The factors include particle diameter, flow rate, the density of receptors, and the force of attraction between particle and receptor.

Although this picture is remarkably generic, the mechanisms responsible for the formation of a particle-lean layer adjacent to the wall depend on the properties of the material under consideration. For the case of solid particle dispersions, wall depletion, particle migration, and solid-liquid separation are the most frequent sources of solvent layer lubrication. Wall depletion occurs whenever dispersions are brought into contact with smooth and solid surfaces because the suspended particles cannot penetrate rigid boundaries [147]. Particle migration is due to various forces arising from fluid inertia, fluid elasticity, and shear-induced diffusivity effects [165]. Solid-liquid separation, which frequently occurs in flocculated suspensions like... 

In some colloidal dispersions, the shear rate (flow) remains at zero until a threshold shear stress is reached, termed the yield stress (ry), and then Newtonian or pseudoplastic flow begins. A common cause of such behaviour is the existence of an inter-particle or inter-molecular network, which initially acts like a solid and offers resistance to any positional changes of the volume elements. In this case, flow only occurs when the applied stress exceeds the strength of the network and what was a solid becomes a fluid. Examples include oil well drilling muds, greases, lipstick, toothpaste and natural rubber polymers. An illustration is provided in Figure 6.13. Here, the flocculated structures are responsible for the existence of a yield stress. Once disrupted, the nature of the floe break-up process determines the extent of shear-thinning behaviour as shear rate increases. 

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