## Physical effects upon the collision of chemically completely destabilized colloids

Collision of colloids can be effected by Brownian motion, by velocity gradients resulting from laminar and turbulent flow and also by differential movement in the sedimentation of such particulates. If coagulation is used as technical process for the improvement of solid separation through aggregation, then velocity gradient induced collisions predominate.

PER UNIT TIME A VOLUME AV IS FILLED:

AV=2(Rij2-z2) [(du/dz)z] dz through integration from -Rijto +Rij:

(with a concentration of n j particles per unit volume)

COLLISIONS PER UNIT TIME WITH CENTRAL PARTICLE

Fig. 5 Smoluchowski's model for the collision between colloids in shear flow systems (after [1])

Von Smoluchowski [1] has developed a readily understandable and practically useful mathematical model for the rate of collisions in a locally linear shear flow system (cf. Fig. 5). He assumes that all particulates collide if they move within a sphere of a diameter that corresponds to the sum of the diameters of the potentially colliding solids. The calculation of the flux through such a sphere of influence leads to the (potential) number of collisions of all particles "i" transported into that sphere with a particle "j" located in the center.

This collision number (see Fig. 5) describes the rate of collisions as directly dependent on the number n, of particles "i", i.e., the ones that are moving into the sphere of collision. The total number of collisions is obtained by multiplying it with the concentration ns of the central particle "j". Furthermore, the collision rate is directly proportional to the linear velocity gradient. In most practical applications such linear velocity gradients will exist only locally. Camp et al. [5] have shown the relationship between such conceptual linear velocity gradients and the energy input per unit volume of reactor space. This parameter is used widely in the description of collision rates in practical applications. The expression for the collision rate can be rewritten as a rate of particle aggregation or as a rate of disapperance of primary or total particles (see for instance [6]). The resulting rate law for coagulation still contains the linear dependence on the volume related energy input. This has been the basis of most quantitative assessments of coagulation processes: it is postulated that the energy input or the torque at the shaft of the stirrer in the coagulation chamber is the physical variable that exclusively describes the control of

PER UNIT TIME A VOLUME AV IS FILLED:

AV=2(Rij2-z2) [(du/dz)z] dz the process rate. The type of stirrer, for instance, should be of no effect.

One may assume, however, that the energy dissipation in stirred real reactors leads to a non-homogeneous distribution in terms of the absolute size of the (locally linear) velocity gradient. There will therefore be locally differing aggregation conditions. This will be superimposed by the characteristics of the coagulating chemicals, i.e., the ability to form stronger or less strong floes. The possible consequences of such non-uniform boundary conditions for the aggregation process are shown in Fig. 6 (where the first column depicts schematically the various alternatives for particles to aggregate, the second column indicates the effect of such aggregation for the selection of a separation process, and the third column in-dentifies quantitative measures to assess this specific reaction progress). The indications given in Fig. 6 as to the effects of these aggregate properties upon the liquid-solid-separation process and how to assess these characteristics are significant for the operator. Measuring, for instance, the djdw, i.e., the diameter of the 60-percentile in the particle distribution curve, relative to the diameter of the 10-percentile, furnishes quantitative information on the heterodispersity of the system. The products of the coagulation reaction will differ in terms of:

IDEAL

respectively

REAL

GOOD FOR SKDIMENTING

GOOD FOR FILTRATION

VOLUMINOUS DIFFICULT TO SEPARATE

STRUCTURE

HETERODISP. A /A

SUSPENSION

Fig. 6 Schematic depiction of the consequences for colloid aggregation if energy dissipation (and chemicals distribution) is non-homogeneous respectively

GOOD FOR SKDIMENTING

GOOD FOR FILTRATION

VOLUMINOUS DIFFICULT TO SEPARATE

STRUCTURE

SIZE DENSITY SHAPE

SIZE DENSITY SHAPE

SIZE DENSITY

SIZE POROSITY

SIZE SHAPE FACTOR

HETERODISP. A /A

SUSPENSION

GATES

FRAGILE AGGRE- /T

1) absolute size of the aggregates formed;

2) the degree of heterodispersity of the aggregated sol;

3) the shape of the agglomerates;

4) the porosity of the aggregates;

5) the destruction of the aggregates formed under changed shear conditions if the adherence is a weak one.

These aggregate characteristics have been investigated to a lesser degree, yet, they are of great significance for the practical or technical application of the process.

Such deviation of the reaction progress from the course described by the collision term developed by [1] can be observed if particle counting devices are used to follow the reaction. Figure 7 (after [7]) describes such reactions in stirred cylindrical batch reactors where for identical stirrer speed the reaction progress should be the same in all systems. The observed reaction progress, however, is different in each system. One would conclude that the so-called turbine-type stirrer is the most effective in generating a reaction-favorable environment, while the reaction progress as —In (ri(/n0)

GATES

erit reaction progress as —In (ri(/n0)

MontmoriUonite (SS.2 rrtg/1} Calcium (0.01 Mol/I rot. speed 34 rpm turbine stirrer

stirrer anchor stirrer

B 12. 16 . 20 . 24 28 reaction time in mm anchor stirrer

MontmoriUonite (SS.2 rrtg/1} Calcium (0.01 Mol/I rot. speed 34 rpm turbine stirrer stirrer reaction progress as -In (ni/n0)

Montmorillonite (S8.S me/l) O B h Calcium (0.01 Mol/'!

rot. speed rpm propeller stirrer

SIZE SHAPE FACTOR

erit

reaction time in min

anchor stirrer

Fig. 7 Observations on the different rate of coagulation in stirred systems under identical conditions of energy input for differently designed stirrers (after [7])

reaction time in min reaction progress as -In (ni/n0)

Montmorillonite (S8.S me/l) O B h Calcium (0.01 Mol/'!

rot. speed rpm propeller stirrer

anchor stirrer

Fig. 6 Schematic depiction of the consequences for colloid aggregation if energy dissipation (and chemicals distribution) is non-homogeneous

Fig. 7 Observations on the different rate of coagulation in stirred systems under identical conditions of energy input for differently designed stirrers (after [7])

reaction PROGRESS

(assessed for instance by par-icle number reduction in 30 min)

reaction PROGRESS

(assessed for instance by par-icle number reduction in 30 min)

Fig. 8 The effect of heterogeneous energy dissipation on the progress of the coagulation reaction: in geometrically similar systems of different scale the reaction progress is different even if the (microscopically determined) overall energy dissipation is identical (after [8]). There are no numbers given since they depend exclusively on the experimental boundary conditions diss. ENERGY

(for instance as diss, energy per volume as a )

SCALE of reactors

(here illustrated by reducing cylinder stirrer systems by factor 2)

Fig. 8 The effect of heterogeneous energy dissipation on the progress of the coagulation reaction: in geometrically similar systems of different scale the reaction progress is different even if the (microscopically determined) overall energy dissipation is identical (after [8]). There are no numbers given since they depend exclusively on the experimental boundary conditions propeller stirrer is less effective. For higher rotational speed the stirrer characteristics appear to change, the propeller stirrer generates at higher rotational speeds the most favorable flow regime while the turbine stirrer is less favorable. In all instances the ancho-type of stirrer is least effective for this type of destabilized suspension. If other chemicals are used, for instance, organic polymers instead of Ca2+ then the sequence of effectivity of stirrers is a different one again (compare [7]).

These observations suggest that there are in-homogeneous patterns of energy dissipation in stirred coagulating systems. This might lead to a reaction progress of differing magnitude if different stirrers are employed. More recent investigations on the fluid structure in stirred coagulation chambers [8] and its effects upon the coagulation rate confirm this notion. In these studies the fluid regime was analyzed by Laser-Dop-pler-Anemometry techniques, permitting an instantaneous recording of all three components of the convec-tive and turbulent fluid motion. The reaction progress itself was also analyzed in a microscopic and close to instantaneous way by using a most detailed particle-counting technique, based on the blockage of a rotating laser beam (see [9]). Figure 8 shows first results in a generalized form: the dimensionless plotted reaction progress grows nearly linearly with increasing energy dissipation (calculated in this instance with the help of the observed and detailed fluid motion parameters). Yet, if the reactor-stirrer system is enlarged, i.e., only the scale changed, then the same observed overall energy dissipation (however, with locally differing flow patterns) will yield a different overall reaction progress.

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