Flocculation reaction control

Flocculation processes are complicated phenomena because of the varieties of both particle morphology and chemical reactions they encompass.34 A few concepts of a general nature have emerged, however, and they will be the focus of this chapter. From the perspective of kinetics, perhaps the most important of these broad generalizations is the distinction that can be made between transport-controlled and reaction-controlled flocculation, parallel to the classification of adsorption processes described in Section 4.5. Flocculation kinetics are said to exhibit transport control if the rate-limiting step is the movement of two (or more) particles toward one another prior to their close encounter and subsequent combination into a larger particle. Reaction control occurs if it is particle combination instead of particle movement (toward collision) that limits the rate of flocculation. 

Fig. 6.5. Comparison between floccules formed by transport-controlled ( DLCA ) or reaction-controlled ("RLCA") flocculation and the results of computer simulations of these two processes (bottom row). (Adapted, with permission, from P. Meakin.6 Copyright by the American Geophysical Union.)...

A more mechanistic approach to reaction controlled flocculation entails representing the sticking probability" in terms of a Boltzmann factor (hat... 

Given that Eq. 6.1 (with D 2) applies to reaction-controlled flocculation kinetics, Eq. 6.54 implies that MM(t) [or MN(t)] must also exhibit an exponential growth with time. Therefore, by contrast with transport-controlled flocculation kinetics, a uniform value of the rate constant kmn cannot be introduced into the von Smoluchowski rate law, as in Eq. 6.17, to derive a mathematical model of the number density p,(t). Equations 6.22 and 6.24 indicate clearly that a uniform kinil leads to a linear time dependence in the... 

The scaling exponent 6 = 1 for the model rate constant in Eq. 6.56, as compared to 6 - 0 for the model expressed in Eq. 6.27. Thus kmn is not scale invariant for reaction-controlled flocculation described by Eqs. 6.59 and 6.63. Moreover, the value of 6 is not consistent with finite z in Eq. 6.48, indicating at once that a power-law time dependence of M0(t) at large time does not exist. This fact does not preclude the applicability of the generic scaling form of pq(t) in Eq. 6.49, however, since no explicit time dependence appears in the latter equation. To examine this possibility, Eq. 6.60 is transformed with the help of Eq. 6.64b ... 

Light-scattering experiments on flocculating suspensions of silica colloids provided the data in the following table. (R is the average cluster radius.) Estimate the fractal dimension of the clusters formed and indicate whether the flocculation process is transport or reaction controlled. Hint Apply Eq. 6.1 and the concepts in Section 6.1.)... 

Direct particle counting of an initially monodisperse suspension was used to measure the time dependence of the q-moment M0, as given in the following table. Examine these data for conformity to either transport- or reaction-controlled flocculation kinetics and estimate the characteristic time scale, 2/kn p0, wherekn = kmn for m n 1. (Answer k n= 3.05 x 10 22 m3 s"1 = 2KD/Wmn, corresponding to Wmn = 4.07 X 104 for all m, n.)... 

Experimentally, it is observed that for sufficiently long flocculation times, semilog plots of (M2Mpq/p0) versus q/MM are approximately linear if flocculation is transport controlled, whereas log-log plots of (M2Mpq/p0) versus q/M M are approximately linear if flocculation is reaction controlled. Develop a theoretical basis for these two observations. (Hint Review Sections 6.3 and 6.4.)... 

The asymptotic scaling expression for pq(t) in Eq. 6.49 appears to be accurate for models of both transport and reaction controlled flocculation... 

Automated controls for flocciJating reagents can use a feedforward mode based on feed turbidity and feed volumetric rate, or a feed-back mode incorporating a streaming current detector on the flocculated feed. Attempts to control coagulant addition on the basis of overflow turbidity generally have been less successful. Control for pH has been accomplished by feed-forward modes on the feed pH and by feed-back modes on the basis of clarifier feedwell or external reaction tank pH. Control loops based on measurement of feedwell pH are useful for control in apphcations in which flocculated sohds are internaUy recirculated within the clarifier feedwell. 

The proposed mechanism of effect of surfactant and ultrasound is reported in Fig. 7.5. The long chain surfactant molecules attach to surface of nanoparticles due to physical adsorption. Only thin layer is adsorbed onto the CaC03 nanoparticles. Due to presence of ultrasound and use of surfactant will control the nucleation. Surfactant keeps the particles away from each other by preventing flocculation due to change in surface tension of reaction mass. The concentration of additives was changed from 0.2 to 1.0 g/L. Addition of 0.2 g/L tripolyphosphate shows the increase in the rate of precipitation which is determined from the Ca(OH)2 consumption. Polyacrylic acid shows the least rate of precipitation (0.115 mol/1), which... 

The stability ratio usually is measured by determining the initial rate of flocculation under reaction or transport control, with these two conditions... 

The functional requirements of practical food emulsions are not complete stability, but rather controlled instability. Destabilizing reactions of food emulsions involve creaming, flocculation, and coalescence. An emulsion would cream or sediment if the dispersed phase is sufficiently different in density from the continuous phase. Creaming can be reduced by increasing the viscosity of the aqueous phase or be enhanced by increasing the particle size of oil droplets or lowering the density of the oil phase. 

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