Emulsion Laplace pressure

The first theoretical considerations concerning n (p) and G (p) of concentrated 3-D emulsions and foams were based on perfectly ordered crystals of droplets [4,5,15-18]. In such models, at a given volume fraction and applied shear strain, all droplets are assumed to be equally compressed, that is, to deform affinely under the applied shear thus all of them should have the same shape. Princen [15,16] initially analyzed an ordered monodisperse 2-D array of deformable cylinders and concluded that G = Qiox(p < (/), and that G jumps to nearly the 2-D Laplace pressure of the cylinders at the approach of ( > = 100%, following a ( — dependence. 

Further division of droplets leads to an increase in Ap as r r decreases. In order to disrupt such a small droplet, the pressure gradient of the magnitude of 2- must be applied externally. The viscous forces exerted by the continuous phase can also deform the emulsion droplets. The viscous stress (Gr ) should be of the same magnitude as the Laplace pressure to deform the droplets (9), where G is the velocity gradient and r is the viscosity of continuous phase. In any case, the pressure gradient or velocity gradient required for emulsion formation are mostly supplied to the system by agitation. 

For a curved interface the effect of the radius of curvature should be considered. Fortunately, y for a curved interface is estimated to be very dose to that of a planer surface, unless the droplets are very small (<10nm). Curved interfaces produce some other important physical phenomena which affect emulsion properties, such as the Laplace pressure Ap, which is determined by the radii of curvature of the droplets. 

To make an emulsion (foam), one needs oil (a gas), water, energy, and surfactant. The energy is needed because the interfacial area between the two phases is enlarged, hence the interfacial free energy of the system increases. The surfactant provides mechanisms to prevent the coalescence of the newly formed drops or bubbles. Moreover it lowers interfacial tension, and hence Laplace pressure [Eq. (10.7)], thereby facilitating breakup of drops or bubbles into smaller ones. 

For coalescence of emulsion droplets, an important variable is whether a flattened film between the droplets is formed. This is governed by the ratio of the external stress over the Laplace pressure. The external stress can be due to colloidal attraction (e.g., van der Waals forces), a shear stress, or gravitational forces in a sediment layer. Small protein-stabilized droplets will not deform, except in a sediment layer in a centrifuge, and they are very stable to coalescence. If the drops are large, the interfacial tension is low, and the external stress is high, droplets will deform and coalescence can readily occur. Water-in-oil emulsions cannot be made with protein as the surfactant, and it is often difficult to stabilize them against coalescence, except by a layer of small hydrophobic particles (Pickering stabilization). 

FIGURE 17.27 Concentrated foams or emulsions. Values of (a) the modulus G and (b) the yield stress oy, each divided by the apparent Laplace pressure of the particles pLa, as a function of the particle volume fraction Food Colloids. Roy. Soc. Chem., Cambridge, 1989, p. 14.)... 

Polyhedral foams and emulsions if they are not very polydisperse, theory for the modulus and the yield stress is available the only variables are particle volume fraction and Laplace pressure. 

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. 

An additional factor affecting the stability of the bubble is the size of the bubble. We foxmd that PFC gases enabled us to prepare smaller, stable bubbles than using air or nitrogen. This is predominantly due to the very low surface tension at the gas water interface. LaPlace pressures, which describe the pressure at both the inside and outside of the shell surface, increase inversely as the decrease of the bubble diameter. As the diameter of the bubble decreases, the pressure increases xmtil the microbubble either collapses, or the surface area to volume increases so much that proportionately more surface area allows diffusion of the gas across the bubble into the circulation. Perfluoropentane (C5F12) is a liquid at room temperature and boils at 28.5 degrees C. We have found that perfluoropentane emulsion can be stabilized as an emulsion with mean diameter of about 200 nm at room temperature. The material can be activated by heat or other energy to form microbubbles. 

The high energy required to form nano-emulsions can be understood in terms of the Laplace pressure p (the difference in pressure between inside and outside the droplet),... 

The role of surfactant in emulsion formation is crucial and is described in detail in Chapter 6. It reduces the oil-water interfacial tension, yow adsorption at the interface. The droplet size R is directly proportional to yow It enhances deformation and break-up of the droplets by reducing the Laplace pressure p,... 

Schulman emphasized that micellar emulsions are systems in true equilibrium, it being proposed that the components of the surface films in these systems produce a negative interfacial tension at the hydrocarbon-water interface [172]. On mixing, a spontaneous interfacial area increase occurs until zero interfacial tension is attained. In Adamson s [173] model for micellar W/O emulsions, stability is accounted for by a balance of the Laplace pressure AP, related to the micellar radius r and interfacial tension y by... 

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