Interaction bubble/particle

Interaction of Solids With Flotation Reagents. For flotation to occur with the aid of reagents, such compounds must adsorb at the sohd—hquid interface unless the soHd to be floated is naturally hydrophobic. In this latter case only depression can be attempted by the use of additional ions or depressants that hinder bubble—particle adhesion. Frothers (typically long-chain alcohols) and/or modifying agents such as hydrocarbon oils can, however, be used to enhance the collection of naturally hydrophobic soflds such as M0S2, talc, or plastics. 

Temperature and pressure also interact with particle size to affect bubble size and frequency in fluidized beds. Information on the effect of temperature on bubble size in the literature is somewhat inconsistent. However, the information that does exist suggests that bubble size decreases slightly with temperature for Group A materials (Geldart and... 

M.L. Fielden, R.A. Hayes, and J. Ralston Surface and Capillary Forces Affecting Air Bubble-Particle Interactions in Aqueous Electrolyte. Langmuir 12, 3721 (1996). 

Fig. 4.16. Effect of interaction between particles and bubbles in three-phase fluidised beds.

The description of dynamic adsorption layers under the condition of bubble/bubble or bubble/particle interaction is much more complex than the consideration of dynamic adsorption layers of individual bubbles discussed in the present chapter. It is still more difficult to control dynamic adsorption layers experimentally under conditions of the above-mentioned interactions. Because of these experimental difficulties, the role of mathematical modelling is extremely important in studying coagulation and heterocoagulation processes in foams and emulsions. 

Fig. 10.5. Characteristic curves of the total contribution of molecular attraction forces and electrostatic forces conditioned by the overlap of the diffuse parts of the double layers into the energy W of bubble particle interaction at various distances and the surface charges of the same sign (a) and in the case of recharging the bubble (b) (curve I). in (b) dotted lines characterise the contribution to the energy of interaction of non electrostatic repulsion forces when their effective radius is smaller (curve 2) or greater (curve 3) than the thickness of the double layer.

At St > St the inertial impact of a particle deforms the bubble surface, creates a thin water layer between the particle and bubble and makes the particle jump back from the bubble surface. This decreases the collision efficiency which otherwise rises with the particles size. For particles of subcritical diameter the collision efficiency increases with particle diameter. The proposed theory of inelastic collision unlike other theories describes the coupling of inertial bubble-particle interaction and water drainage from the liquid interlayer. 

Recently Xu Yoon (1989, 1990) used the existence of hydrophobic interaction to explain the spontaneous coagulation of hydrophobic particles. Yoon (1991) used a similar approach for weak bubble-particle interactions and emphasises a possible role of hydrophobic interaction in particle-bubble attachment. The investigation underestimates the possible role of the electrostatic interaction stressed by Churaev (1993). Without any ground, Yoon asserts that "bubble-particle adhesion occurs only when the particles are sufficiently hydrophobic". 

Dynamic adsorption layers (DAL) influence practically all sub-processes which manifest themselves in particle attachment to bubble surfaces by collision or sliding. Surface retardation by DAL affects the bubble velocity and the hydrodynamic field and consequently the bubble-particle inertial hydrodynamic interaction. It also affects the drainage and thereby the minimum thickness of the liquid interlayer achieved during a first or second collision or sliding. Thus elementary acts of microflotation and flotation is systematically considered in this book for the first time with accoimt of the role of DAL. Extreme cases of weakly and strongly retarded bubble surfaces are discussed which assists to clarify the influence of bubble and particles sizes on flotation processes. 

For example, when there are electrostatically or sterically interacting bubbles in a foam, the viscosity will be higher when bubbles are smaller (for a given foam quality defined by its gas volume) because the increased interfacial area and thinner films increase the resistance to flow. The viscosity of all dispersions will tend to be higher when the dispersed species sizes are relatively homogeneous, that is, when the particle size distribution is narrow rather than wide [28]. 

The discrete phase simulation method described in Secs. 4.1 through 4.4 is capable of predicting the flow behavior in gas-liquid-solid three-phase flows. In this section, several simulation examples are given to demonstrate the capability of the computational model. First, the behavior of a bubble rising in a liquid-solid suspension at ambient pressure is simulated and compared to experimental observations. Then the effect of pressure on the bubble rise behavior is discussed, along with the bubble-particle interaction. Finally, a more complicated case, that is, multibubble formation dynamics with bubble bubble interactions, is illustrated. 

The simulation also provides some information about the bubble particle interaction as shown in Fig. 25. As the bubble rises in the liquid-solid fluidized bed, an interaction between the bubble and particles takes place. In the simulation model, the bubble-particle interaction is accounted for by adding a surface-tension-induced force to the particle motion equation. This force is also added to the source term of the liquid momentum equation for the liquid elements in the interfacial area to account for the particle effect on the interface. The particle movement is determined from the resulting total force acting on the particle. From the simulation results, it is seen that most particles contacting the bubble do not penetrate the bubble only one or two particles penetrate. Instead, they pass around the bubble surface. When the particles penetrate the bubble, they fall through quickly to the bubble base because of the low viscosity and density of the gas phase. 

It is weU known that the selective adsorption of surfactants at the solid-water interface imparts hydrophobicity to the surface of the solid. The relative hydrophobicity of the solid surface is responsible for various macroscopic properties observed experimentally. For example, in mineral separation, the hydrophobicity of the solid surface leads to selective bubble-particle attachment, which accounts for the selective flotation of minerals in large scale industrial plants. The relative measure of mineral surface hydrophobicity is usually quantified in terms of contact angle measurements and flotation experiments (Fuerstenau 1957, 1970, 2000 Fuerstenau and Herrera-Urbina 1989 Fuerstenau and Pradip 2005 Pradip 1988). Molecular-modeling tools can be successfully employed to compute the interaction energies and contact angle on both virgin and surfactant-covered mineral surfaces. The relative flotation efficacy of different surfactants can thus be related to their molecular structure and properties. 

Maxey and Riley [47] derived an equation of motion for a small rigid sphere of radius R in a nonuniform flow. If one considers small bubbles moving in a polar liquid, this equation might be appropriate because surfactants would tend to immobilize the surface of a bubble and make it behave like a rigid sphere. Maxey and Riley assumed that the Reynolds number based on the difference between the sphere velocity and the undisturbed fluid velocity was small compared to unity. In addition, they assumed that the spatial nonuni-formity of the undisturbed flow was sufficiently small that the modified drag due to particle rotation and the Saffman [48] lift force could be neglected. Finally, they ignored interactions between particles. 

Fielden, M. L., Hayes, R. A. and Ralston, J., Surface and capillary forces affecting air bubble-particle interactions in aqueous electrolyte, Langmuir, 12, 3721-3727 (1996). 

The situation is more complicated if the sphere approaching a planar surface is deformable, such as a bubble in a liquid or an oil drop in water. We can also think of the inverse situation a solid particle interacting with liquid surface such as a bubble or drop. A particle approaching a liquid-fluid interface will lead to a deformation of the interface. Then, there are three possibilities The particle is repelled by the interface and remains in the first liquid, it goes into the interface and forms a stable three-phase contact, or it crosses the interface and enters the fluid phase completely. The second fluid can be a gas. An example, is interaction of particles with bubbles in a liquid [685]. This interaction is of fundamental importance for flotation [591]. Another example is bubble interacting in a liquid. The hydrodynamic interaction between fluid interfaces is more complicated than between rigid interfaces because we have to take a deformation into account. 

In addition to two fluid interfaces interacting with each other, the interaction of fluid interfaces with solid-liquid interfaces is important [686, 695]. One example is the interaction of particles with bubbles or drops (Figure 7.1c). The interaction of particles with bubbles in aqueous liquid is the key process in flotation [591]. The interaction with drops is essential in oil recovery. Direct particle bubble force measurements have been carried out with the AFM [739—741, 1216] (reviewed in Ref. [742]). Also, the force between individual particles and oil drops in water has been measured by atomic force microscopy [743, 744]. 

Fig. 9. Bubble-wake interactions in a gas—Hquid-soHd reactor (a) soHds concentration profile within bubble-wake domain, where A—A and B—B represent planes through the bubble, vortex, and wake (b) projected impact of interactions on reaction rate as function of particle si2e and Hquid velocity, where (—)...

The modeling of fluidized beds remains a difficult problem since the usual assumptions made for the heat and mass transfer processes in coal combustion in stagnant air are no longer vaUd. Furthermore, the prediction of bubble behavior, generation, growth, coalescence, stabiUty, and interaction with heat exchange tubes, as well as attrition and elutriation of particles, are not well understood and much more research needs to be done. Good reviews on various aspects of fluidized-bed combustion appear in References 121 and 122 (Table 2). 

Flotation is a physical process involving relative interaction of three phases solid, water, and air. An understanding of the wettability of the solid surface, physical surface, and chemical phenomena by which the flotation reagents act and the mechanical factors that determine particle-bubble attachment and removal of particle-laden bubbles, is helpful in designing and operating flotation systems successfully. 

In view of the importance of the particle/bubble contact, it may be assumed that the stress acting on the particles during gas sparging is determined by electrostatic interactions as well as by hydrophobic and hydrophilic interactions, which are determined by the nature of the liquid/solid system. The use of Pluronic as additive leads to the reduction of destruction process [44,47] possibly due to less bubble/floc contact which is also described by Meier et. al. [67]. 

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