Coagulation orthokinetic

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. 

The coagulation, flocculation, and adsorption processes were modeled mathematically using classical coagulation theory as a starting point. The Smoluchowski equation for orthokinetic coagulation in laminar flow is written (18)... 

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... 

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... 

The ratio of the probability of a collision induced by a fluid velocity gradient (dv/dx) (i.e., orthokinetic coagulation) to the collision probability under the influence of Brownian motion (perikinetic coagulation—what we have considered so far) has been shown to be (Probstein 1994)... 

The relative decrease in the total concentration of particles because of orthokinetic coagulation was determined from microscopic observation. The rate constant k is obtained from the slope of the semiloga-rithmic plot (Equation 9) (Min-U-Sil 30 = 2 gram/liter Al = 4.6 X 10r M pH = 5.5 (du/dz) = 110 seer )... 

The rate constant k0 for orthokinetic coagulation is determined by physical parameters (velocity gradient du/dz, floe volume ratio of the dispersed phase, = sum over the product of particle number and volume), and the collision efficiency factor a0 observed under orthokinetic transport conditions ... 

The overall rate of agglomeration of any suspension, that is prepared experimentally and consists of small and large colloids, is obtained by adding the expressions derived for perikinetic and orthokinetic coagulation (Equations 2 and 5) ... 

Conceptually similar results were demonstrated by Krutzer et al. [14], who measured the orthokinetic coagulation rate under laminar Couette flow and isotropic turbulent flow (as well as other flow conditions). Despite equal particle collision rates, significance differences were observed in the overall rates indicating different collision efficiencies (higher collision efficiencies were found under a turbulent flow regime). Thus, identical chemical properties of a dispersion do not determine a single collision efficiency the collision efficiency is indeed dependent upon the physical transport occurring in the system. 

Kramer, T. A. Clark, M. M. 1999 Incorporation of aggregate breakup in the simulation of orthokinetic coagulation. Journal of Colloid and Interface Science 216, 116-126. 

In the case of orthokinetic coagulation of liquid drops driven by the thermocapillary migration, the particle velocity v is given by the expression (see Young et al. ) ... 

In contrast, V is not a linear fnnction of time for orthokinetic coagulation. When the floccn-lation is driven by a body force, i.e., in case of sedimentation or centrifugation, we obtain ... 

Orthokinetic coagulation and differential sedimentation play an important role in such processes as flotation, water treatment, dust entrapment and natural precipitation from the atmosphere. 

If the orthokinetic coagulation is driven by thermocapillary migration, the counterpart of Eq. (Ill) reads (181) ... 

In a floe blanket clarifier as used in the treatment of potable water with ahimmium sulphate, a fluidised bed of aluminium hydroxide floes is formed in the body of the vessel and the chemically treated feed water is led directly into this bed fi om below [Ives, 1968], The effect of the floe blanket is twofold. First, the presence of a high concentration of floes rapidly increases the rate of coagulation of the particles in the feed stream by orthokinetic coagulation and second there is a particle capture mechanism operating in which the smaller floes, which might otherwise pass throu the clarifier, collect on the larger ones. 

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