Aggregation perikinetic

These kernels are valid for inertialess particles (i.e. Stp = 0) and can be extended to finite Stokes numbers only by employing ad hoc corrections. For example, Ammar Reeks (2009) derived for the kernel proposed by Salfman Turner (1956) a correction that is based on the local Stokes number. The relative importance of perikinetic aggregation versus orthokinetic aggregation is quantified by a Peclet number ... 

In fact, when Pe < 0.001 only perikinetic aggregation need be considered, whereas when Pe > 10 the perikinetic contribution is negligible. 

FIGURE 13.2 Perikinetic aggregation. The relative particle number concentration as a function of the time t after aggregation has started over the halving time t0 5. N refers to number, N0 to initial total number, and the subscripts 1, 2, 3, etc. to the numbers of particle monomers, dimers, trimers, etc. The equation for the number of /c-mers is also given. 

Figure 13.3 Basic data needed to calculate capture efficiency in perikinetic aggregation. As an example, part of the colloidal interaction potential V as a function of interparticle distance h is given it is calculated from DLVO theory [Eqs. (12.1) and (12.7)] for d=0.5pm, A =. 25kBT, i o=15mV, and 7=10mM (1/ K = 3nm). y is the integrand of Eq. (13.5), y that of Eq. (13.7) note the different scales.

FIGURE 13.4 Idealized curves of the stability factor W in perikinetic aggregation for small particles stabilized by electrostatic repulsion, as a function of the salt concentration m. Numbers near the curves denote the valence of the ions in the solution. The dotted lines indicate the critical coagulation concentrations mCI. 

Capture Efficiency. The value of the capture efficiency a is nearly always smaller than unity, for a variety of reasons. In many cases the magnitude of a can be reasonably predicted, although the theory is complicated. Hydrodynamic effects are in principle like those in perikinetic aggregation they impede close encounter of the particles. Moreover, the velocity gradient exerts a shear stress, order of magnitude rj , onto the... 

Other Complications. At high volume fractions, the encounter rate will be more than proportional to cp, because the effective volume available for the particles is decreased owing to geometric exclusion. This also applies to perikinetic aggregation. For orthokinetic aggregation a high volume fraction will, moreover, affect the capture efficiency, because the stress sensed by the particles will be greater than f/f see Section 5.1.2. 

When perikinetic aggregation occurs and the particles that become bonded to each other stay in the same relative position as during bond formation,... 

A sample calculation may be enlightening. Assume aggregation of spherical particles in water at room temperature W 1 (rapid perikinetic aggregation), a = 0.2 pm,

[Pg.520]

It is very difficult to avoid convection currents with a velocity gradient of the order of 0.1 s 1 to occur. As soon as the particles have grown to a size for which Eq. (13.10) equals unity, orthokinetic aggregation will take over, which soon proceeds very much faster than perikinetic aggregation. 

Consider the situation given in Figure 17.19 at the moment that a gel is formed, (a) What would be the size of the particles making the fractal gel, i.e., what is the value of aeff (b) Assuming that unhindered perikinetic aggregation occurs (i.e., W — 1), what would be the aggregation time needed to form a gel (c) Is the latter value a reasonable one ... 

Orthokinetic Aggregation The process of aggregation induced by hydrodynamic motions such as stirring, sedimentation, or convection. Orthokinetic aggregation is distinguished from perikinetic aggregation, the latter being caused by Brownian motions. 

The perikinetic aggregation is controlled by diffusiort, and the aggregation kernel of collisions in a monodisperse suspertsion of particles with the size L is... 

The rate constant k is determined by the interaction between the particles. Let us first consider the simple case of particles that do not interact except at zero separation where they form a permanent bond. The aggregation rate of such indifferent sticky particles is governed by the rate of transport toward each other. The transport may be dominated by an imposed external force field or it may be the result of only diffusion. In the former case, the aggregation process is called orthokinetic and in the latter perikinetic. Here, we focus on perikinetic aggregation. 

When the dispersion is stirred or when it flows, diffusion is not the only mechanism determining the collision probability. Under such conditions, the shear rate, that is, the velocity gradient, normal to the particle surface, dv(x)/dx (see Section 17.1.3) enhances the collision frequency, so that the orthokinetic aggregation rate is faster than the perikinetic aggregation rate. Under conditions of rapid aggregation, it can be derived that... 

E. Barouch, Heterocoagulation. VI. Interactions of monodispersed hydrous aluminum oxide sol with polystyrene latex, /. Colloid Interf. Sci. 1980, 76,319-329 (c) K. Csoban, E. PefFerkorn, Perikinetic aggregation induced by chromium hydrolytic polymer and sol,/. Colloid Interf. Sci. 1998, 205,516-527. 

Perikinetic Aggregation. The process of aggregation when induced by Brownian motions. Perikinetic aggregation is distinguished from... 

The process of aggregation is seen to require a low charge on each particle and a collision event. Assuming that electrical repulsion is absent, as a result of pretreatment with electrolyte, then the rate of aggregation depends on Brownian motion. In the assumed absence of velocity gradients, induced by e.g. stirring, we have the case of perikinetic aggregation or flocculation when Brownian motion alone dictates the rate. 

Figure 6.6 (a) Perikinetic aggregation, (b) Orthokinetic aggregation (schematic)... 

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