Brownian agglomeration

To protect an aqueous alumina suspension with a volume fraction of 0.2 and a particle radius of 100 nm from Brownian agglomeration in water, for a period of 2 weeks, AG should be larger than 20 kT. 

Sampson, K. J. and D. Ramkrishna, Particle Size Correlations in Brownian Agglomeration. Closure Hypotheses for Product Density Equations, J. Colloid Inter/ Sci. 110, 410-423 (1986). 

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). 

The particles in a disperse system with a liquid or gas being the dispersion medium are thermally mobile and occasionally collide as a result of the Brownian motion. As the particles approach one another, both attractive and repulsive forces are operative. If the attractive forces prevail, agglomerates result indicating an instability of the system. If repulsive forces dominate, a homogeneously dispersed or stable dispersion remains. 

If colloids are sufficiently large or the fluid shear rate high, the relative motion from velocity gradients exceeds that caused by Brownian (thermal) effects (orthokinetic agglomeration). 

Heterodisperse Suspensions. The rate laws given above apply to monodisperse colloids. In polydisperse systems the particle size and the distribution of particle sizes have pronounced effects on the kinetics of agglomeration (O Melia, 1978). For the various transport mechanisms (Brownian diffusion, fluid shear, and differential settling), the rates at which particles come into contact are given in Table 7.2. 

Agglomeration of Pt crystallites due to Brownian motion can really be observed and it can also be shown that, indeed, the interaction between the Pt particles and the supporting soot in the presence of the electrolyte, phosphoric acid, is weak enough to allow for relatively free movement of the Pt particles. This fast process obviously is also the reason for the nonobservability of slower surface diffusion-induced Ostwald ripening. Fortunately alloy catalysts composed of platinum and nonnoble metals seem to show a reduced tendency to agglomeration as their deterioration and activity loss is much slower than that of the pure platinum catalyst. 

TJhe aggregation of particles in a colloidal dispersion proceeds in two distinct reaction steps. Particle transport leads to collisions between suspended colloids, and particle destabilization causes permanent contact between particles upon collision. Consequently, the rate of agglomeration is the product of the collision frequency as determined by conditions of the transport and the collision efficiency factor, the fraction of collisions leading to permanent contact, which is determined by conditions of the destabilization step (2). Particle transport occurs either by Brownian motion (perikinetic) or because of velocity gradients in the suspending medium (orthokinetic). Transport is characterized by physical parame-... 

The equation derived by Troelstra and Kruyt is only valid for coagulating dispersions of colloids smaller than a certain maximum diameter given by the Rayleigh condition, d 0.10 A0. Equation 4 applies in cases where particles are transported solely by Brownian motion. Furthermore, the kinetic model (Equations 2 and 3) has been derived under the assumption that the collision efficiency factor does not change with time. In the case of some partially destabilized dispersions one observes a decrease in the collision efficiency factor with time which presumably results from the increase of a certain energy barrier as the size of the agglomerates becomes larger. 

The Fundamentals of Acoustic Agglomeration of Small Particulates. Let us consider a polydisperse aerosol consisting of submicrometer and micron sized particles. The mean separation distance between particles would typically be about 100 micrometers. Brownian movement of the particles is caused by the collision of the thermally agitated air molecules with the particles. Also any convection currents or turbulence in the carrier gas will of course cause the particles to be partially entrained and moved in the air. If we next impose an acoustic field of acoustic pressure p, the acoustic velocity u will be given by... 

Once particles are present in a volume of gas, they collide and agglomerate by different processes. The coagulation process leads to substantial changes in particle size distribution with time. Coagulation may be induced by any mechanism that involves a relative velocity between particles. Such processes include Brownian motion, shearing flow of fluid, turbulent motion, and differential particle motion associated with external force fields. The theory of particle collisions is quite complicated even if each of these mechanisms is isolated and treated separately. 

The second method for aerosol coagulation in turbulent flows arises because of inertial differences between particles of different sizes. The particles accelerate to different velocities by the turbulence depending on their size, and they may then collide with each other. This mechanism is unimportant for a monodisperse aerosol. For a polydisperse aerosol of unspecified size distribution, Levich (1962) has shown that the agglomeration rate is proportional to the basic velocity of the turbulent flow raised to the 9/4 power, indicating that the agglomeration rate increases very rapidly with the turbulent velocity. Since very small particles are rapidly accelerated, this mechanism also decreases in importance as the particle size becomes very small, being most important for particles whose sizes exceed 10-6 to 10"4 cm in diameter. In all cases brownian diffusion predominates when particles are less than 10-6 cm in diameter. 

The collection of the pyrolysis oils is difficult due to their tendency to form aerosols and also due to the volatile nature of many of the oil constituents. As the aerosols agglomerate into larger droplets, they can be removed by cyclonic separators. However, the submicron aerosols cannot be efficiently collected by cyclonic or inertial techniques, and collection by impact of the aerosols due to their Brownian or random motion must be utilized. A coalescing filter is relatively porous, but it contains a large surface area for the aerosol particles to impact by Brownian motion as they are swept through by the pyrolysis gases. Once the aerosol droplets impact the filter fibers, they are captured and coalesce into large drops that can flow down the fibers and be collected. 

Example 14.3. Estimating Agglomeration Rates (a) Estimate the time necessary to halve the particle concentration of a turbid water of 10 uniform dx = d2) particles per cm that are completely destabilized (a = 1). Assume that the Brownian motion alone (d 1 /zm) is responsible for the collision. According to equation 4 in Table 14.4, for 20 C is of the order of 5 x 10" 2 cm s . 

Individual colloidal particles are so small that they are not retained by ordinary filters. Moreover, Brownian motion prevents their settling out of solution under the influence of gravity. Fortunately, however, we can coagulate, or agglomerate, the individual particles of most colloids to give a filterable, amorphous mass that will settle out of solution. 

---