Bubbles repulsion between

Interfacial Forces. Neighboring bubbles in a foam interact through a variety of forces which depend on the composition and thickness of Hquid between them, and on the physical chemistry of their Hquid—vapor interfaces. For a foam to be relatively stable, the net interaction must be sufficiently repulsive at short distances to maintain a significant layer of Hquid in between neighboring bubbles. Otherwise two bubbles could approach so closely as to expel all the Hquid and fuse into one larger bubble. Repulsive interactions typically become important only for bubble separations smaller than a few hundredths of a micrometer, a length small in comparison with typical bubble sizes. Thus attention can be restricted to the vapor—Hquid—vapor film stmcture formed between neighboring bubbles, and this stmcture can be considered essentially flat. 

Berkman and Egloff explain that some additives increase the flexi-bihty or toughness of bubble walls, rather than their viscosity, to render them more durable. They cite as illustrations the addition of small quantities of soap to saponin solutions or of glycerin to soap solution to yield much more stable foam. The increased stability with ionic additives is probably due to elec trostatic repulsion between charged, nearly parallel surfaces of the hquid film, which acts to retard draining and hence rupture. 

Flotation of Naturally Hydrophobic Minerals. Flotation response of naturally hydrophobic minerals correlates very well with elec-trokinetic measurements. Figure 3 shows that the flotation of coal correlates well with zeta potential of demineralized coal (5.). The flotation rate is maximum where the zeta potential is zero and it decreases with increase in the magnitude of the zeta potential. Similar observations were made earlier by Chander and Fuerstenau (6 ) for the flotation of molybdenite. The decrease in flotation rate with increase in zeta potential is because of the electrical double layer repulsion between the charged particle and the air bubble. 

This means that there are no contradictions between the kinetic theory of microflotation by Derjaguin Dukhin, in which the limiting stage is the overcoming of the electrostatic repulsion between bubble and particle, and the capillary theory of flotation by Scheludko in which a special attention is paid to t,p(. and the contact angle. Both models are identical in the... 

The last effect to be described here is film elasticity In case of ionic surfactants the aqueous phase in the double layers contain dissolved counter ions of the surfactants. When the ionic density increases, the repulsive forces of equally charged ions become substantial, see Fig. 11. The repulsive forces are also responsible for a certain elasticity of double layers. The thickness of double layers in the well-known coloured air bubbles lies between 1,000 and 10,000 A. It can be determined by the order of interferential colours The process is very dynamic and fluctuates over the surface area. Under certain conditions the drainage reaches an end at a metastable state (so called black films ) giving the lamella or bubble a limited time of existence ... 

Thus, the internal pressure of the bubbles is just balanced by the interfacial forces acting across the lamellar film. The most important interfacial interactions contributing to n(S) are electrostatic repulsion between charged interfaces and steric interactions due to adsorbed species. Those topics have already been discussed in the context of colloidal stability and will not be treated further here. 

In addition to inducing froth stability, frother specfes can take part in the overall process of adsorption on the mineral surface. Like the collector species, the ftother species also can be expected to migrate to the particle-gas interface during the time of contact and assist in establishing the attachment of the bubble to the particle. Coadsotption of ftother along with the collector species can be favorable for flotation, possibly because the neutral molecules adsorbed between charged collector ions can reduce the repulsion between the latter species and thereby enhance the overall surfactant adsoiption. 

Concerning the stabilization of bubbles by hydrophobic ions in water, Akulichev has hypothetized that ions such as Cl, F, etc. migrate to the bubble surface while others (like OH") cannot.52 The basis of this model is that the repulsion between electrical charges of the same polarity on the bubble surface slows down or prevents its dissolution. Atchley repeated the experiments, extending the range of dissolved ions by 3 orders of magnitude (lO to 10 2 M), and provided the proof that the concentration of dissolved ions is important in the stabilization process. Until now all the experiments have been carried out with water, and the field remains open as far as organic solvents are concerned. 

There are three scenarios for the behavior of two colliding particles in a dispersion (e.g., emulsion) depending on the properties of the films (Fig. 1) (1) When the film formed upon particle collision is stable, floes of attached particles can appear. (2) When the attractive interaction across the film is predominant, the film is unstable and ruptures this leads to a coalescence of the drops in emulsions or of the bubbles in foams. (3) K the repulsive forces are predominant, the two colliding particles will rebound and the colloidal dispersion will be stable. In some cases, by var3ring the electrolyte concentration or pH, it is possible to increase the repulsion between the particles in a flocculated dispersion and to cause the inverse process of peptization [1]. 

While the secondary Bjerknes force is always attractive if the ambient radius is the same between bubbles, it can be repulsive if the ambient radius is different [38]. The magnitude as well as the sign of the secondary Bjerknes force is a strong function of the ambient bubble radii of two bubbles, the acoustic pressure amplitude, and the acoustic frequency. It is calculated by (1.5). 

In this situation, the equilibrium thickness at any given height h is determined by the balance between the hydrostatic pressure in the liquid (hpg) and the repulsive pressure in the film, that is n = hpg. Cyril Isenberg gives many beautiful pictures of soap films of different geometries in his book The Science of Soap Films and Soap Bubbles (1992). Sir Isaac Newton published his observations of the colours of soap bubbles in Opticks (1730). This experimental set-up has been used to measure the interaction force between surfactant surfaces, as a function of separation distance or film thickness. These forces are important in stabilizing surfactant lamellar phases and in cell-cell interactions, as well as in colloidal interactions generally. 

Reay also considered the viscous interaction between a bubble and particle as the particle approaches the bubble. In effect, he allowed the particle to rotate as it gets close to the bubble. This model predicts, as G becomes very small, that particles will attach to bubbles as a result of hydrodynamic forces alone (for small particles and large bubbles). In effect, the vacuum induced in the wake behind a rising bubble can trap particles in spite of mtcrfacial repulsion due to electrostatic effects. This model suggests that for flotation of oily water another mechanism (hydrodynamic capture), in addition to collision, may contribute to the overall removal rate. Evidence is presented in this paper that hydrodynamic capture is an operative mechanism tor the bubble and particle sizes encountered in flotation of oil drops using bubbles from 0.2 to 0.7 mm in diameter. 

An important example of a repulsive van der Waals force is the force between a solid particle interacting in water with an air bubble. This is a typical situation in flotation, where air bubbles are used to extract mineral particles from an aqueous dispersion (see Section 7.6.1). For some materials the van der Waals force between the solid-liquid and the liquid-vapor... 

One of the central questions in the stability of foams is why are liquid films between two adjacent bubbles stable, at least for some time In fact, a film of a pure liquid is not stable at all and will rupture immediately. Formally this can be attributed to the van der Waals attraction between the two gas phases across the liquid. As for emulsions, surfactant has to be added to stabilize a liquid film. The surfactant adsorbs to the two surfaces and reduces the surface tension. The main effect, however, is that the surfactant has to cause a repulsive force between the two parallel gas-liquid interfaces. Different interactions can stabilize foam films [570], For example, if we take an ionic surfactant, the electrostatic double-layer repulsion will have a stabilizing effect. 

Electric double layers can be present at the gas/liquid interfaces between bubbles in foams. In this case, since the interfaces on each side of the thin film are equivalent, any interfacial charge will be equally carried on each side of the film. If a foam film is stabilized by ionic surfactants then their presence at the interfaces will induce a repulsive force opposing the thinning process. The magnitude of the force will depend on the charge density and the film thickness. 

---