Velocity gradient flocculation,

Among the primary collision mechanisms is Brownian flocculation, also termed perikinetic flocculation, which dominates for submicrometer particles at relatively high number densities. The second principal collision mechanism is that of velocity gradient flocculation, also termed orthokinetic flocculation, which dominates for particles of micrometer size and larger. Evidently, the presence of any stabilizer in the solution will reduce the number of particle encounters and subsequent floccing, as discussed in the last section, resulting in slow flocculation. In our discussion we shall separate the transport and stability problems by assuming that the suspension is completely destabilized, so flocculation occurs on encounter rapid flocculation). Our concern here is with the effect of the particle motion alone on the number of encounters between the suspended particles. 

The natural process of bringing particles and polyelectrolytes together by Brownian motion, ie, perikinetic flocculation, often is assisted by orthokinetic flocculation which increases particle coUisions through the motion of the fluid and velocity gradients in the flow. This is the idea behind the use of in-line mixers or paddle-type flocculators in front of some separation equipment like gravity clarifiers. The rate of flocculation in clarifiers is also increased by recycling the floes to increase the rate of particle—particle coUisions through the increase in soUds concentration. 

MUNICIPAL WATER treatment). Scale-up of orthokinetic flocculators, generally in the form of paddle devices, is based on the product of mean velocity gradient and time, for a constant volume concentration of the flocculating particles. 

The parameter used to design rapid mix and flocculation systems is the root mean square velocity gradient G, which is defined by equation... 

Equipment typically consists of concentric circular compartments for mixing, flocculation and settling. Velocity gradients in the mixing and flocculation compartments are developed by turbine pumping within the unit and by velocity dissipation at baffles. For ideal flexibihty it is desirable to independently control the intensity of mixing and sludge scraper drive speed in the different compartments. 

The water is actually touching the blade, so the velocity that it attains on contact must be equal to that of the blade. Of course, as it departs, its velocity will be dilferent, but this is not the critical point of power transfer. The blade transfers power to the water while still in contact. Upon detachment, the water parcel that got the power being transferred will then commence expending the power to overcome fluid friction imposed upon it by neighboring parcels this process produces the velocity gradient required for flocculation to occur. 

Also, excessive velocity gradients can simply break the floes to pieces. To prevent excessive velocity gradients between paddle tips, a minimum distance of 0.3 m should be provided between them. Also, a minimum clearance of 0.3 m should be provided between paddles and any structure inside the flocculator. Paddle tip velocity should be less than 1.0 m/s (Peavy et al., 1985). 

Here, the characteristic flocculation time is seen to be inversely proportional to the velocity gradient and the solids volume fraction. 

Flocculation experiments were conducted under steady-state conditions in a reactor with four mixed-flow tanks of equal volume in series. Mixing in each tank was provided by a motor-driven mixer with a horizontal paddle impeller. The intensity of mixing was characterized by the root mean square velocity gradient G. 

In the experimental phase, 900 ML of stationary-phase E. coli cells were removed from the chemostat and placed in a stirrer-reactor assembly, which provided both rapid-mix and flocculation velocity gradients. A 100-mL aliquot of a specified PEI concentration was then added to the E. coli suspension during a 2-min rapid mix (G = 190 sec ). The suspension was flocculated for 60 min at G = 20 sec with turbidities and particle size distributions recorded before flocculant addition and after flocculation. The initial suspension had a pH = 7.0 ( 0.1), ionic strength I = 0.06M NaCl, T = 25°C, and a cell concentration of 2.5 ( 0.5) X 10" cells/mL before flocculation. The flocculation velocity gradient (G = 20 sec ) was set by regulating the angular velocity of a two-pronged stirrer to yield the desired torque. 

Once the optical constant was known, the turbidity of the flocculated suspension calculated from Equation 11, using the known particle size distribution, could be compared with the experimentally measured turbidity. Correlations were made between particle size distributions and turbidity readings as the PEI molecular weight and dose were varied. The velocity gradient in the stirrer-reactor was held constant at G = 20 sec Other experiments indicate that the influence of varying the velocity gradient in the range G = 20 to 60 sec" on either turbidity or particle size distribution was minor. 

Figure 11. Differential turbidity distribution—initially, 90% of turbidity is produced by particles smaller than 2.0 pm following flocculation, 80% of turbidity is produced by aggregates larger than 2.0 pm (mol wt— 1800 polymer dose—5.00 mgjL velocity gradient—20f sec initial particle count—2.350E 07/ML reaction time—(Dj 0 min (O) 60 min)...

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. 

Here k is Boltzmann s constant, T is the absolute temperature, /x is the fluid viscosity, Vi and Vj are the volumes of particles with sizes i and /, respectively, and G is the velocity gradient of the fluid. Equations 14 and 15 often are written in terms of the diameters of the particles rather than in terms of their volumes. However, when two particles collide, it is useful to consider that their total volume is conserved (coalesced-sphere assumption) therefore, the equations for flocculation kinetics are expressed in terms of particle volumes throughout this work. 

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... 

A hydraulic detention time of 1 hr was assumed for all cases examined here this is representative of actual treatment practice. The velocity gradient was varied, with values of 0, 10, and 50 sec" selected for examination. Ten sec" was used for the standard case the range from 10 to 50 sec" represents most cases in practice. A zero velocity gradient does not occur in real systems, but this assumption allows only the effects of Brownian diffusion on flocculation to be determined. Some treatment plants have shorter flocculation times than 1 hr, and higher velocity gradients than 10 sec" the reference or standard case chosen here has a Gt product of 36,000 which is consistent with water treatment practice. 

Increasing the velocity gradient in the flocculation tank improves the performance of subsequent settling and filtration facilities. This effect is as expected. The integral analysis presented here describes the causes of these improvements and relates improved solid-liquid separation to... 

Figure 19. Velocity gradient effects of flocculation and settling on particle size distribution function ((A) G = 50 sec (B) G = 0 sec )...

An important effect in Equation (3.34) is that the collision radius enters as Rl and since we have approximated Rc = 2R it becomes 8R consequently this indicates that shearing is very sensitive to particle size. For this reason small particles are rather insensitive to shearing forces, whereas larger particles, for instance with R > 0.5 pm, can often be flocculated by stirring or shaking particularly at electrolyte concentrations close to the ccc. The sensitized coagulation which occurs in the presence of a velocity gradient is known as orthokinetic flocculation. 

It was anticipated by von Smoluchowski that Brownian diffusion is not the only mechanism by which one particle can come into contact with another. There can be convection in the system as well. Convection aids flocculation when it enhances the relative velocity between nearby particles, making it easier for them to surmount the maximum in the potential energy curve and reach the primary minimum corresponding to flocculation. Application of a velocity gradient (shear) is especially effective in the flocculation of relatively large particles (Hiemenz and Rajagopalan, 1977 Zeichner and Schowalter, 1977, 1979). It can also break up floes associated with the secondary minimum of the particle interaction curve (Zeichner and Schowalter, 1977, 1979). 

The process of aggregation is seen to require a low charge on each particle and a collision event. Assuming that electrical repulsion is absent, as a result of pretreatment with electrolyte, then the rate of aggregation depends on Brownian motion. In the assumed absence of velocity gradients, induced by e.g. stirring, we have the case of perikinetic aggregation or flocculation when Brownian motion alone dictates the rate. 

It is commonly observed that gentle stirring promotes flocculation of particles which have been destablized and which may have commenced to aggregate by Brownian motion (see Part I of this chapter). This is due to the velocity gradients which are induced in the liquid causing relative motion and therefore collisions between the particles which are present. Such flocculation caused by fluid motion is called orthokinetic , to differentiate it from that caused by Brownian motion, called perikinetic . 

This is the simple Smoluchowski equation of orthokinetic flocculation, and shows that the rate of flocculation is second-order with respect to concentration, depends linearly on the velocity gradient and is proportional to the third power of the collision radius. Consequently, in these simple terms theory states that the rate of flocculation can be increased by ... 

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