Brownian motion flocculation

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 °... 

Adequate dispersion must be obtained for the measurement to be successful because the technique is based upon the Brownian motion of the particles in a liquid medium. If the particles should flocculate in the liquid, gravitational settling will occur, thereby removing the particles from the measurement zone in the sample cell. For this measurement to be successful, the refractive index of the material, both the real and the imaginary component, must be known. In the particle size regime where PCS can be employed, the refractive index has a very significant effect on the measured average particle size. 

Transport control of flocculation is realized in an especially direct way in the process known as diffusion-limited cluster-cluster aggregation5 (aggregation as used in this term means flocculation in the present chapter). In this process, which is straightforward to simulate and visualize on a computer, particles undergo Brownian motion (i.e., diffusion) until they come together in close proximity, after which they coalesce instantaneously and irreversibly to form floccules (or clusters ). The clusters then diffuse until they contact one another and combine to form larger clusters, and so on, until gravitational... 

Under the assumption that the target and incoming floccules engage in Brownian motion independently,18 D = Dm + Dn, and the rate coefficient becomes... 

Droplet aggregation is said to occur when droplets stay together for a time much longer than they would in the absence of colloidal interactions, (i.e., than can be accounted for by collisions due to Brownian motion) (Walstra, 2003). Mechanisms responsible for the physical instability of droplets through aggregation are flocculation, coalescence or partial coalescence. 

These are suspensions with a size range of 20 to 200 nm. Like suspensions, they are kinetically stable but, due to the small size of the particles, they have much longer physical stability (i) an absence of sedimentation, as the Brownian motion is sufficient to prevent separation by gravity and (ii) an absence of flocculation, as the repulsive forces (electrostatic and/or steric) are much larger than the weak van der Waals attraction. 

It can be observed that with an increase in solvent polarity the dispersion stability displays a maximum, which corresponds to a minimum in the normalized setthng rate the normalization is done to account for differences in the density and the viscosity of the solvents. The normalized setthng rate equals the observed settling rate times the solvent viscosity/(particle density minus the solvent density). The maximum stabihty in this case is observed in moderately polar solvents (20 < e < 45). Bare particles suspended in a hquid medium are in constant Brownian motion and can flocculate rapidly on colhsion if the 1 is larger than about 15 kT. Stabilization can usually be achieved by decreasing the van der Waals attractive forces. The potential energy due to the van... 

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