Flocculation spherical particle

Because most shear-thinning fluids, particularly polymer solutions and flocculated suspensions, have high apparent viscosities, even relatively coarse particles may have velocities in the creeping-flow of Stokes law regime. Chhabra(35,36) has proposed that both theoretical and experimental results for the drag force F on an isolated spherical particle of diameter d moving at a velocity u may be expressed as a modified form of Stokes law ... 

Assume that to a dispersion of spherical particles in water a given amount of a linear dextran (see Table 6.1) is added to increase the viscosity. However, the addition of the polymer also tends to cause depletion flocculation, which is undesirable. What would be the best value of the molar mass M of the polymer—large, small, or indifferent—if flocculation is to be prevented, while the viscosity becomes as high as possible ... 

In the nuclear industry one of the main applications of colloid technology is in the handling and reprocessing of radioactive waste, where the problems are mainly concerned with the flocculation and separation of particulate radioactive materials. A second application is that of the sol-gel process to the preparation of nuclear fuel in the form of spherical particles of uniform size. 

Flocculation rates. Stability ratios for spherical particles dispersed in polymer solution were calculated numerically by Feigin and Napper (1980b) from... 

We must now relate the energetics to the kinetics. The theory of rapid flocculation was first proposed by Smoluchowski , who treated the problem as one of diffusion (Brownian motion) of the spherical particles of an initially monodisperse dispersion, with every collision, in the absence of a repulsive force, leading to a permanent contact. In general, we may express the rate of flocculation, i.e. the rate of decrease of the total number of particles, as... 

The structure of the suspension and the compression rheological properties determine much of the consolidation behaviour. Colloidally stable, dilute suspensions of monodisperse spherical particles are well described by the relationships described above. The effect of the shape of the particles and the particle concentration can be accounted for by multiplying the expression given in equation (9.22) by suitable factors. For flocculated suspensions, the situation is much more complex. The attractive interparticle forces can produce a cohesive network of particles, which will resist consolidation depending on its strength. Because flocculation generally affects the suspension microstructure, the permeability will change. 

In order to offer a same surface of interaction more nearly spherical particles would have to be large, i.e. in the range of very coarse colloidal systems or even of suspensions. For such particles the effects of gravity and of slight motions in the Hquid are much larger than for elongated particles and would tend to destroy any structure based upon the flocculation in the secondary minimum. It is, however, worth while to apply refined techniques of observation to suspensions of nearly spherical particles in order to detect phenomena connected with the existence of this minimum of energy. 

Part I deals with the single double layer. Part II with the interaction of two flat plates, and here most of the fundamental results of the theory already come to the fore. Part III gives a treatment of the, interaction of spherical particles, which serves to clarify various details, especially the influence of particle dimensions and of the kinetics of flocculation. 

The basic theory of gel formation from colloidal particles has been formulated by Thomas and McCorkle (228), who show that the Verwey-Overbeek theory for the interaction of two spherical double layers around adjacent spherical colloidal particles leads to isotropic flocculation. New particles can be attached more readily to the ends of a chainlike floe where the repulsion energy barrier is at a minimum. It is this type of aggregation that converts a sol to a gel at a certain point by forming an infinite network of chains of particles throughout the sol volume. (See also Chapter 3.)... 

As Silicate before Neutralization. In a typical process, invented by Moyer (434), sodium silicate solution was poured into methanol to produce a suspension of finely divided spherical particles of sodium silicate. These were then neutralized by reaction with acid. In this way, globular particles of silica gel about 1-2 microns in diameter, free from sharp edges, were obtained. In another approach to making small particles of silica gel, Kanhofer (435) mixed an alkylene polyamine with the sodium silicate before reaction with acid. Silica gel particles from 5 to 20 microns of unusually low density were obtained. It is probable that the polyamine acted as a flocculating agent and minimized gel shrinkage. 

IPEC formation between (strong) polyelectrolytes results in highly aggregated and/or macroscopic flocculated systems. Nevertheless, the aggregation can be stopped at a colloidal level in extremely dilute solutions, and a polydisperse colloidally stable system of nearly spherical particles can usually be achieved [47]. 

The adhesive forces may also vary with the roughness of the particle. Thus, the adhesive force between the particles of coke shape [152] possessing microscopic surface roughness and a plane surface is smaller than that of smooth spherical particles of the same material. This is because contact between the coke-shaped particles and the plane is effected at individual points, which reduces the contact area and hence the adhesive force. Coke-shaped powders include coal and silica gel particles [153] as well as particles of dust and ashes formed in nuclear explosions in carbonate soils (coral reefs), when the soil particles are decarburized and acquire a flocculent shape [157] similar to that of coke. In general, powders of coke shape may be obtained by combustion of the volatile components from the particle surface. 

These three pictures are characteristic of the entire study of the structure of the various compounds. They show clearly that below the region of 4>c carbon black is present in the form of isolated spherical particles. At the critical volume concentration one can see networks of long drawn-out and branching chains (flocculates) consisting of spherical particles, plus some dispersed particles that continue to exist in isolation. An analysis of the carbon black concentration found at the fracture surface revealed that in all the samples examined this was considerably larger than was to be expected on the basis of the quantity of carbon black incorporated. 

In DLVO the total potential energy is expressed as simply the sum of the repulsive and the attractive energy (Equation 10.3) and in Equation 10.4 DLVO is written for simple equal-sized spherical particles. According to the DLVO theory, prevention (or promotion) of flocculation can be achieved through the control of the balance of attractive and repulsive... 

Figure 10.3 DLVO theory gives the potential energy as the sum of the electrostatic (repulsive) and the van der Waals (attractive) forces. The equation shown here is for equal-sized spherical particles (H R). If the particles Interact over a (liquid) medium (as opposed to vacuum), the Hamaker constant (A) becomes an effective Hamaker constant. The secondary shallow minimum (of a few kaTj at rather high separations indicates reversible flocculation. The aggregates are rather loose (weak) and are called floes. This secondary minimum has been confirmed experimentally and often can disappear with a small energy input, e.g. gentle stirring...

Problem 11.6 Kinetics of coagulation of a hydrosol Negatively charged spherical particles with radius R flocculate at 25 °C in an aqueous Na2S04 solution, with a concentration equal to 0.93 x 10 mol L The viscosity of the solution is 8.9 x 10 kg m s The following results were obtained by particle counting during the flocculation of this colloidal system as a function of time ... 

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