Flotation force

To distinguish between the capillary forces in the case of floating particles and in the case of partially immersed particles on a substrate, the former are called lateral flotation forces and the latter, lateral immersion forces. - " These two kinds of force exhibit similar dependence on the interparticle separation but very different dependencies on the particle radius and the surface tension of the liquid (see References 35 and 212 for comprehensive reviews). The flotation and immersion forces can be both attractive (Figures 5.17a and b) and repulsive (Figures 5.17c and d). This is... 

Hence, the flotation force decreases, while the immersion force increases, when the interfacial tension a increases. Besides, the flotation force decreases much more strongly with the decrease of R than the immersion force. Thus, F(,o tion is negligible for F < 10 pm, whereas can be... 

Since both expressions contain the angle %, it is convenient for one to use it further as a variable, replacing t. The flotation force, F, is given by... 

The maximum value of the flotation force can be found by taking a derivative of above expression and setting it equal to zero ... 

If we place a second particle on the interface, it will notice the deformed liquid surface (Figure 5.16c) and vice versa [588, 589]. As a result, the three-phase contact line is not radially symmetric anymore. The asymmetry of the contact line leads to a lateral force between the two floating particles. It is called lateral flotation force (reviewed in Ref [590]). 

Figure 5.17 Capillary flotation forces between two particles at a liquid surface can be attractive or repulsive depending on the meniscus slopes di and 2-...

The flotation force for spherical particles can be quantified by applying the superposition principle. In this case, the deformation caused by two particles is assumed to be equal to the sum of the deformations caused by the isolated individual particles. For two spheres of radius J i and J 2 with slope angles bi and b2, the lateral force is [590, 598, 599]... 

Here, p and 5 are the densities of the particles and liquid, respectively. With — VyUoiS we see that the lateral flotation force is proportional to RIrI/Yi-... 

Calculate the flotation force between two hydrophobized silica particles with a contactangleof80°, Rp = 20 pm, and Qp = 2500 kg in a water surface for a... 

Immersion forces can also be calculated with Eq. (5.43). They can be attractive or repulsive, depending on the meniscus angles and 112 The same rule applies as for flotation forces attraction for sin sin 2 > 0 and repulsion for sin sin 2 < 0. Usually, the particles attract each other since the contact angles are low if the particles were not wetted by the liquid it would be difficult to keep them dispersed in solution. One example of a force versus distance measurement for two immersed spheres is shown in Figure 5.20. 

The flotation of mica has been correlated to the adhesion force measured from surface force (SFA—see Section VI-4) experiments although, to these authors, it is clear that dynamic effects prevent an absolute comparison [69, 70],... 

The examples in the preceding section, of the flotation of lead and copper ores by xanthates, was one in which chemical forces predominated in the adsorption of the collector. Flotation processes have been applied to a number of other minerals that are either ionic in type, such as potassium chloride, or are insoluble oxides such as quartz and iron oxide, or ink pigments [needed to be removed in waste paper processing [92]]. In the case of quartz, surfactants such as alkyl amines are used, and the situation is complicated by micelle formation (see next section), which can also occur in the adsorbed layer [93, 94]. 

An attempt has been made to develop the hot-water process for the Utah sands (Fig. 10) (20). With od-wet Utah sands, this process differs significantly from that used for the water-wet Canadian sands, necessitating disengagement by hot-water digestion in a high shear force field under appropriate conditions of pulp density and alkalinity. The dispersed bitumen droplets can also be recovered by aeration and froth flotation (21). 

Particle-Bubble Attachment. In the above, principles leading to creation of desired hydrophobicity/hydrophihcity of the particles has been discussed. The next step is to create conditions for particle-bubble contact, attachment, and their removal, which is simply described as a combination of three stochastic events with which are associated the probability of particle-bubble colhsion, probabihty of attachment, and probability of retention of attachment. The first term is controlled by the hydrodynamic conditions prevaihng in the flotation unit. The second is determined by the surface forces. The third is dependent on the s irvival of the laden bubble by liq ud t irbulence and impacts by the other suspended particles. A detailed description of the hydrodynamic and other physical aspects of flotation is found in the monograph by Schulze (19 ). 

Flotation is another method to remove solid (cells) from fermentation broth, using air bubbles to float protein. We may use different kinds of high shear-force devices to make homogeneous solutions for liberating intracellular enzymes. Figure 7.8 shows several types of impeller for homogenisation. 

In flotation it is clear by now that there are three phases air, mineral, and water. The three are shown in Figure 2.23 (A) to meet at a common boundary. In this condition there will be a balance of interfacial tension forces. These can be resolved so that, for equilibrium at the point of intersection ... 

This is a unit operation process where air bubbles, as gas, are used to remove solid or liquid particles from the liquid wastewater. The air bubbles are often trapped in the morphology of the suspended particles and as a result of buoyant forces, the particles move up and float on the surface where they are skimmed out. The common flotation methods include dissolved air, air flotation, vacuum flotation, and chemical additives.3... 

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