Flocculation Brownian

There are three processes by which the number of oil drops in an emulsion is decreased. These are Brownian flocculation, sedimentation flocculation and creaming. But it should be noted that if the absorbed film strength is quite high, flocculation may not necessarily result in coalescence. It is also important to note that flocculation which may be due to any of above three reasons is reversible, but coalescence which follows flocculation is irreversible. 

He have presented a simple procedure whereby one can estimate the stability of a colloidal system undergoing simultaneous creaming and gravity-induced flocculation. This procedure is by no means restricted to only this case. One can easily take into account other particle loss mechanisms, such as shear-induced flocculation or Brownian flocculation. What is required in these cases are the appropriate particle/particle collision kernels, which can be computed by solving the governing convective-diffusion equation. 

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. 

For a simple calculation of the number concentration evolution in a batch experiment due to Brownian flocculation of a destabilized suspension, we may suppose that the particles grow with uniformly equal size, which is determined by constant total volume distributed over all the particles. Dropping the subscript on n, we then have from Eq. (8.2.7) that the rate of decrease of the initial number density distribution is described by second-order kinetics that is. 

In the Brownian flocculation example the effect of particle collisions due to fluid mixing was not considered. The simplest example one might consider is that of... 

We note that in contrast to Brownian flocculation, which was described by second-order kinetics, shear flocculation follows first-order kinetics. 

In the case, when the van der Waals force is negligible. Equation 4.277 rednces to = F 0 + O2)/ (4n0i02) [240,656]. Danov et al. [665] have shown that in the case of Brownian flocculation of identical small droplets, hi obeys the following transcendental equation ... 

Schowalter WR, Eidsath AB (2001) Brownian flocculation of polymer colloids in the presence of a secondary minimum. Proc Natl Acad Sci USA 98 3644—3651. doi 10.1073/ pnas.061028498... 

Reddy et al. [4] developed a general equation describing the behavior of a polydis-persed emulsion in which Brownian flocculation, sedimentation, and creaming take place simultaneously. The observation is made at various abscissas of the sample. 

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. 

In other words, the lower the mass of the particle, the higher its velocity, because the average energy of any particle at a given temperature is constant, kT. A dispersed particle is always in random thermal motion (Brownian motion) due to coUisions with other particles and with the walls of the container (4). If the particles coUide with enough energy and are not well dispersed, they will coagulate or flocculate. 

Diffusion filtration is another contributor to the process of sand filtration. Diffusion in this case is that of Brownian motion obtained by thermal agitation forces. This compliments the mechanism in sand filtration. Diffusion increases the contact probability between the particles themselves as well as between the latter and the filter mass. This effect occurs both in water in motion and in stagnant water, and is quite important in the mechanisms of agglomeration of particles (e.g., flocculation). 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

Particle collision frequency due to Brownian motion was estimated to be less than 1% of the collision frequency due to shear. The effects of Brownian motion could therefore be neglected in the flocculation rate calculations. However, for the smallest molecular size, radius of gyration 14 nm (see Table I), the effect of Brownian motion on the particle-polymer collision efficiency was of the same order of magnitude as the effect of shear. These two contributions were assumed to be additive in the adsorption rate calculations. Additivity is not fundamentally justified (23) but can be used as an interpolating... 

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... 

Because polymer adsorption is effectively irreversible, and because adsorption and floe growth occur simultaneously, flocculation is a non-equilibrium process. As a result, performance is largely determined by the kinetics of adsorption and aggregation. Both of these can be regarded as collision processes involving solid particles and polymer molecules. In each case, collisions can arise due to either Brownian motion or agitation of the suspension. The collision frequency v between particles and polymer molecules can be estimated from °... 

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