Coalescences

Coalescence occurs when the film between the droplets or bubbles ruptures. Subsequently, the Laplace pressure is responsible for fusing of the particles, forming a larger single particle, and so on. This process eventually results in the disappearance of the dispersion, that is, in a complete segregation into two bulk phases. Coalescence requires that the film separating the particles is thin and therefore, it is much more likely to happen when the emulsion or foam is creamed (or sedimented) or drained and, even more so, when it is aggregated. 

FIGURE 18.7 Liquid film between gas bubbles or emulsion droplets in which a hole is created, for example, by thermal fluctuations. 

When a monolayer of stabilizer is present in the interface, the situation is much more complicated. First, when a wave develops, the liquid in the film moves but the monolayer prevents the interface from moving along (cf. Section 17.4.2, Equation 17.22, and Section 18.3.2). Second, in thin films, colloidal interaction forces are effective, together resulting in a total Gibbs energy of interaction Ai ,G between the dispersed particles that varies with particle separation h. This subject has been discussed in some detail in Sections 16.2 and 16.3. When the perturbation is so severe that across the thin region of the film the interparticle separation is such that dAi tG(/t)/d/t 0, the film thins until rupture. 

The use of polymeric and/or proteinaceous stabilizers that form intermolecular bonds provides the interface with a high dilation modulus, that is, a high resistance against film thickness fluctuation. 

The method of dynamic gas disengagement (Sriram and Mann, 1977 Patel et al., 1989) to obtain an estimate of bubble size distribution is worthy of mention since it is convenient to use, sometimes even in real systems, especially for lower gas fractions. The impeller is stopped and the trend in the level measured against time. This trend indicates the bubble size distribution if terminal rise velocities are known and if coalescence is negligible. 

The best test of whether a system is coalescing or noncoalescing is to set it up in a vessel of standard configuration and impeller speed, in which overall gas 

Several more fundamental measurements of quasi-static two-bubble coalescence times are reported Machon et al. (1997) give a summary. 

The stability of emulsions thus depends on the resistance to film thinning and rupture, which we shall consider in greater detail in Chapter 12. Meanwhile it is clear that practical problems of dc-emulsification will involve the identification of circumstances which will reduce this resistance. 

Processes akin to ripening can of course also contribute to droplet growth in emulsions, although in most cases it is not the dominant mechanism. 

Analogous considerations apply to the destruction of foams in which the film of liquid lies between two gas bubbles rather than between two liquid droplets. 

For the mainly oil-soluble Span 20 siufactant, however, the lifetimes are much less and films rupture prematurely, in line with predictions based on Bancroft s rule. At concentrations well above the CMC where the effective volume fraction of micelles is significant ( 5 vol%), thin liquid films may drain in a stepwise fashion by stratification. This phenomenon, seen initially with foam films, was explained by the formation of periodic colloidal structures inside the film that results in layering of the micelles. At a step-transition, a layer of micelles leaves the film and the film thickness decreases by approximately the effective micellar diameter. It can also occur in emulsion films shown recently for hexadecane-aqueous sodium case-inate-hexadecane systems. The step-height seen of around 20 nm is very close to the measured diameter of the casein micelles of between 20 and 25 nm. The layering ultimately increases the lifetime of a film, but a critical film area exists below which step transitions are inhibited such thick films containing layers of micelles are even more stable. 

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For jet fuels, the elimination of free water using filters and coalescers by purging during storage, and the limit of 5 ppm dissolved water are sufficient to avoid incidents potentially attributable to water contamination formation of micro-crystals of ice at low temperature, increased risk of corrosion, growth of micro-organisms. 

These hazards are reduced drastically by desalting crude oils, a process which consists of coalescing and decanting the fine water droplets in a vessel by using an electric field of 0.7 to 1 kV/cm. 

Impingement demister systems are designed to intercept liquid particles before the gas outlet. They are usually constructed from wire mesh or metal plates and liquid droplets impinge on the internal surfaces of the mist mats or plate labyrinth as the gas weaves through the system. The intercepted droplets coalesce and move downward under gravity into the liquid phase. The plate type devices or vane packs are used where the inlet stream is dirty as they are much less vulnerable to clogging than the mist mat. 

Another type of gravity separator used for small amounts of oily water, the oil interceptor, is widely used both offshore and onshore. These devices work by encouraging oil particles to coalesce on the surface of plates. Once bigger oil droplets are formed they tend to float to the surface of the water faster and can be skimmed off. A corrugated plate interceptor (CPI) is shown below and demonstrates the principle involved. However there are many varieties available. Plate interceptors can typically reduce oil content to 50-150 ppm. 

Hydrocylones have become common on offshore facilities and rely on centrifugal force to separate light oil particles from the heavier water phase. As the inlet stream is centrifuged oil particles move to the centre of the cyclone, coalesce and are drawn off upwards, while the heavier water is taken out at the bottom. 

Although it is hard to draw a sharp distinction, emulsions and foams are somewhat different from systems normally referred to as colloidal. Thus, whereas ordinary cream is an oil-in-water emulsion, the very fine aqueous suspension of oil droplets that results from the condensation of oily steam is essentially colloidal and is called an oil hydrosol. In this case the oil occupies only a small fraction of the volume of the system, and the particles of oil are small enough that their natural sedimentation rate is so slow that even small thermal convection currents suffice to keep them suspended for a cream, on the other hand, as also is the case for foams, the inner phase constitutes a sizable fraction of the total volume, and the system consists of a network of interfaces that are prevented from collapsing or coalescing by virtue of adsorbed films or electrical repulsions. 

It is quite clear, first of all, that since emulsions present a large interfacial area, any reduction in interfacial tension must reduce the driving force toward coalescence and should promote stability. We have here, then, a simple thermodynamic basis for the role of emulsifying agents. Harkins [17] mentions, as an example, the case of the system paraffin oil-water. With pure liquids, the inter-facial tension was 41 dyn/cm, and this was reduced to 31 dyn/cm on making the aqueous phase 0.00 IM in oleic acid, under which conditions a reasonably stable emulsion could be formed. On neutralization by 0.001 M sodium hydroxide, the interfacial tension fell to 7.2 dyn/cm, and if also made O.OOIM in sodium chloride, it became less than 0.01 dyn/cm. With olive oil in place of the paraffin oil, the final interfacial tension was 0.002 dyn/cm. These last systems emulsified spontaneously—that is, on combining the oil and water phases, no agitation was needed for emulsification to occur. 

An important aspect of the stabilization of emulsions by adsorbed films is that of the role played by the film in resisting the coalescence of two droplets of inner phase. Such coalescence involves a local mechanical compression at the point of encounter that would be resisted (much as in the approach of two boundary lubricated surfaces discussed in Section XII-7B) and then, if coalescence is to occur, the discharge from the surface region of some of the surfactant material. 

There appear to be two stages in the collapse of emulsions flocculation, in which some clustering of emulsion droplets takes place, and coalescence, in which the number of distinct droplets decreases (see Refs. 31-33). Coalescence rates very likely depend primarily on the film-film surface chemical repulsion and on the degree of irreversibility of film desorption, as discussed. However, if emulsions are centrifuged, a compressed polyhedral structure similar to that of foams results [32-34]—see Section XIV-8—and coalescence may now take on mechanisms more related to those operative in the thinning of foams. 

The charge on a droplet surface produces a repulsive barrier to coalescence into the London-van der Waals primary attractive minimum (see Section VI-4). If the droplet size is appropriate, a secondary minimum exists outside the repulsive barrier as illustrated by DLVO calculations shown in Fig. XIV-6 (see also Refs. 36-38). Here the influence of pH on the repulsive barrier between n-hexadecane drops is shown in Fig. XIV-6a, while the secondary minimum is enlarged in Fig. XIV-6b [39]. The inset to the figures contains t,. the coalescence time. Emulsion particles may flocculate into the secondary minimum without further coalescence. 

It was pointed out in Section XIII-4A that if the contact angle between a solid particle and two liquid phases is finite, a stable position for the particle is at the liquid-liquid interface. Coalescence is inhibited because it takes work to displace the particle from the interface. In addition, one can account for the type of emulsion that is formed, 0/W or W/O, simply in terms of the contact angle value. As illustrated in Fig. XIV-7, the bulk of the particle will lie in that liquid that most nearly wets it, and by what seems to be a correct application of the early oriented wedge" principle (see Ref. 48), this liquid should then constitute the outer phase. Furthermore, the action of surfactants should be predictable in terms of their effect on the contact angle. This was, indeed, found to be the case in a study by Schulman and Leja [49] on the stabilization of emulsions by barium sulfate. 

The preceding treatment relates primarily to flocculation rates, while the irreversible aging of emulsions involves the coalescence of droplets, the prelude to which is the thinning of the liquid film separating the droplets. Similar theories were developed by Spielman [54] and by Honig and co-workers [55], which added hydrodynamic considerations to basic DLVO theory. A successful experimental test of these equations was made by Bernstein and co-workers [56] (see also Ref. 57). Coalescence leads eventually to separation of bulk oil phase, and a practical measure of emulsion stability is the rate of increase of the volume of this phase, V, as a function of time. A useful equation is... 

The inset in Figure XIV-6 shows the coalescence time tc for the droplets for the pH corresponding to each DLVO curve. Does DLVO theory adequately explain the variation of tc with pH What additional factors may play a role ... 

While, in principle, a tricritical point is one where three phases simultaneously coalesce into one, that is not what would be observed in the laboratory if the temperature of a closed system is increased along a path that passes exactly tlirough a tricritical point. Although such a difficult experiment is yet to be perfomied, it is clear from theory (Kaufman and Griffiths 1982, Pegg et al 1990) and from experiments in the vicinity of tricritical points that below the tricritical temperature only two phases coexist and that the volume of one slirinks precipitously to zero at T. ... 

For a general dimension d, the cluster size distribution fiinction n(R, x) is defined such that n(R, x)dR equals the number of clusters per unit volume with a radius between andi + dR. Assuming no nucleation of new clusters and no coalescence, n(R, x) satisfies a continuity equation... 

Figure B2.4.1. Proton NMR spectra of the -dimethyl groups in 3-dimethylamino-7-methyl-l,2,4-benzotriazine, as a fiinction of temperature. Because of partial double-bond character, there is restricted rotation about the bond between the dunethylammo group and the ring. As the temperature is raised, the rate of rotation around the bond increases and the NMR signals of the two methyl groups broaden and coalesce.

Figure B2.4.3 shows an example of this in the aldehyde proton spectnim of N-labelled fonnamide. Some lines in the spectnim remain sharp, while others broaden and coalesce. There is no frmdamental difference between the lineshapes in figures B2.4.1 and figures B2.4.3—only a difference in the size of the matrices involved. First, the uncoupled case will be discussed, then the extension to coupled spin systems.

Figure B2.4.3. Proton NMR spectrum of the aldehyde proton in N-labelled fonnainide. This proton has couplings of 1.76 Hz and 13.55 Hz to the two amino protons, and a couplmg of 15.0 Hz to the nucleus. The outer lines in die spectrum remain sharp, since they represent the sum of the couplings, which is unaffected by the exchange. The iimer lines of the multiplet broaden and coalesce, as in figure B2.4.1. The other peaks in the 303 K spectrum are due to the NH2 protons, whose chemical shifts are even more temperature dependent than that of the aldehyde proton.

After coalescence, a possible set of eigenvectors is given in equation (B2.4.24). If these are substituted into (B2.4.22), the results are pure real, reflecting the fact that iP - 8 is now positive. 

Flueli M, Buffat P A and Borel J P 1988 Real time observation by high resolution electron microscopy (HREM) of the coalescence of small gold particles in the electron beam Surf. Sc/. 202 343... 

Lewis L J, Jensen P and Barrat J L 1997 Melting, freezing and coalescence of gold nanoclusters Phys. Rev. B 56 2248... 

It sometimes happens that two or more bubbles coalesce to form one that hardly rises at all in the narrow part of the nitrometer tube this may be driven up to the rest of the collected gas at the top of the tube by gently squeezing the rubber pressure tubing connecting the movable reservoir J with the nitrometer proper. 

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