Flocculation perikinetic

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. 

Perikinetic flocculation is the first stage of flocculation, induced by the Brownian motion. It is a second-order process that quickly diminishes with time and therefore is largely completed in a few seconds. The higher the initial concentration of the soflds, the faster is the flocculation. 

It is reasonable to assume, at least for oppositely charged polymers and particles, that aA > ag, which means that the adsorption time is always expected to be shorter than the coagulation time under perikinetic conditions. Consequently, perikinetic flocculation rates are very likely not to be adsorption rate limited. The ratio of orthokinetic adsorption time to orthokinetic coagulation time is... 

Perikinetic flocculation, 22 55 Perindopril, molecular formula and structure, 5 15 It Perinone Orange... 

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 term perikinetic flocculation is used to describe a process where after addition of a polyelectrolyte the degree and the rate of flocculation are governed by Brownian motion alone. No shear forces are used to help promote flocculation. If it is assumed that every contact between particles leads to adhesion, then the rate of perikinetic flocculation is given by... 

Perikinetic and Orthokinetic Flocculation. Particles in a dispersion are subjected under any circumstances to Brownian motion (the average velocity is distributed according to the Boltzmann exponential law) and hence, it is the absolute barrier height compared to the thermal energy kpT) that determines stability. This means that larger particles are more stable against thermal motion (perikinetic flocculation) than smaller particles. However, of practical importance during heterophase polymerization is the behavior of particles in dependence on the stirrer speed (orthokinetic flocculation), where their velocity depends on the... 

According to the theory of von Smoluchowski the most rapid aggregation will occur when every contact leads to the adherence of one particle to another. So the rate of perikinetic flocculation or aggregation is given by... 

The simple orthokinetic rate equation 4.42 has an analogous equation for perikinetic flocculation, due to Brownian-motion collisions of particles (see Part I of this chapter, which deduces the half life of particles from such flocculation). The perikinetic rate equation is ... 

For dujdz = 1 sec and a particle diameter of 10 cm, the ratio Jjlis of the order of and completely negligible but when the diameter of at least one of the particles is larger than 1 (x the ratio Jbccomes larger than unity and for particles of 10 jx the orthokinetic flocculation is far more important than the normal perikinetic flocculation The enhanced flocculation velocity under the influence of agitation is thus seen to be present irrespective of the fact whether the system is monodispersed or poly-dispersed. 

Although reduction or elimination of the repulsion barrier is a necessary prerequisite of successful flocculation, the actual flocculation in such a destabilized suspension is effected by particle—particle collisions. Depending on the mechanism that induces the collisions, the flocculation process may be either perikinetic or orthokinetic. 

In summary, polymeric flocculants generally increase peri-kinetic flocculation rates compared with perikinetic coagulation rates. This is not necessarily true for orthokinetic flocculation, and experimental results in the literature are seemingly in conflict. Collision rate theory predicts that the polymer adsorption step may become rate limiting in orthokinetic flocculation. The present study was designed to elucidate the relationship between polymer adsorption rates and particle flocculation rates under orthokinetic conditions. 

The polymer radius has to be larger than 80% of the particle radius to avoid adsorption limitation under orthokinetic conditions. As a rule of thumb a particle diameter of about 1 pm marks the transition between perikinetic and orthokinetic coagulation (and flocculation). The effective size of a polymeric flocculant must clearly be very large to avoid adsorption limitation. However, if the polymer is sufficiently small, the Brownian diffusion rate may be fast enough to prevent adsorption limitation. For example, if the particle radius is 0.535 pm and the shear rate is 1800 s-, then tAp due to Brownian motion will be shorter than t 0 for r < 0.001, i.e., for a polymer with a... 

Considering that the mechanism of flocculation or agglomeration of a pond is perikinetic in nature (see Eq. 9.17), using the data given below, graphically estimate kp and the time needed for half of the particles to flocculate. ... 

In conventional technologies of purification featuring sedimentation or clarification as tjie first separation stage, perikinetic coagulation is usually only the first step of aggregation reactions. If chemical requirements to maximize flp of raw water are not entirely met, higher flocculation intensity or time is needed. 

Another process of flocculation that occurs under shearing conditions is referred to as orthokinetic, to distinguish it from the diffusion-controlled perikinetic process. In this case, the rate of flocculation is related to the shear rate by the expression ... 

Coagulation filtration is recommended for the treatment of raw water with a relatively low content of suspended particulate matter. The coagulant supply is connected to the piping in front of the filter water inlet. The perikinetic stage of coagulation takes place in the piping and in the upper part of the filter the orthokinetic stages take place in the filtration bed where floccules of hydroxide are trapped. 

Transport—movement of the particles into adhesive contacts via perikinetic (Brownian) or orthokinetic motion resulting in aggregate growth (flocculation). 

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 . 

Equation 4.52 can be used to calculate the collision radii of particles when perikinetic and orthokinetic rates of flocculation are equal, and flocculation is in transition from Brownian-motion (diffusion) dominated kinetics to fluid-motion kinetics. For example ... 

So for most cases of fluid motion caused by stirring or baffled flow the perikinetic rate dominates for particles less than 1 pm diameter, and the orthokinetic rate dominates for particles larger than 1 pm. For example, at G = 10 s when the particle radius has increased to 5 pm (diameter 10 pm) orthokinetic flocculation will proceed 1000 times faster than perikinetic (equation 4.50). 

Even when the particles are completely destabilized, with no repulsion energy barrier, there is evidence" that orthokinetic collisions will be reduced by particles rolling around one another without aggregating. This will multiply the orthokinetic rate (equation 4.42) by a factor of less than one, which will make the sizes of particles undergoing equal effective rates of perikinetic and orthokinetic flocculation smaller than those hsted above (which assumed that all collisions were permanent and effective). 

The equations cannot be treated exactly like other orthokinetic equations because of the limitation i j. If i = j there would be no differential settlement and, therefore, no collisions and aggregation. Similarly, it cannot be applied to an initially monodisperse suspension because aU particles would settle at the same rate. If the suspension were subject initially to significant perikinetic (Brownian diffusion) flocculation then it would become hetero-disperse and flocculation by differential settling would follow. 

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