Volume fractions, emulsions, effect droplets

In a subsequent theoretical analysis, Princen [26] initially used a model of infinitely long cylindrical drops to relate the geometric and thermodynamic properties of monodisperse HIPEs to the volume fraction of the dispersed phase. Thus the analysis could be restricted to a two-dimensional cross-section of the emulsion. Two principle emulsion parameters were considered the film thickness between adjacent drops (h) and the contact angle (0) [27-29]. The effects of these variables on the volume fraction, , both in the presence and absence of a compressive force on the emulsion, were considered. The results indicated that if both h and 0 are kept at zero, the maximum volume fraction () of the uncompressed emulsion is 0.9069, which is equivalent to = 0.7405 in real emulsions with spherical droplets (cf. Lissant s work). If 0 is zero (or constant) and h is increased, the maximum value of decreases on the other hand, increasing 0 with zero or constant h causes to increase above the value 0.9069, again at zero compression. This implies that, in the presence of an appreciable contact angle, without any applied compressive force, values of <(> in excess of the maximum value for undeformed droplets can occur. Thus, the dispersed phase... 

Pons et al. have studied the effects of temperature, volume fraction, oil-to-surfactant ratio and salt concentration of the aqueous phase of w/o HIPEs on a number of rheological properties. The yield stress [10] was found to increase with increasing NaCl concentration, at room temperature. This was attributed to an increase in rigidity of films between adjacent droplets. For salt-free emulsions, the yield stress increases with increasing temperature, due to the increase in interfacial tension. However, for emulsions containing salt, the yield stress more or less reaches a plateau at higher temperatures, after addition of only 1.5% NaCl. 

An important quantity, which characterizes a macroemulsion, is the volume fraction of the disperse phase 4>a (inner phase volume fraction). Intuitively one would assume that the volume fraction should be significantly below 50%. In reality much higher volume fractions are reached. If the inner phase consists of spherical drops all of the same size, then the maximal volume fraction is that of closed packed spheres (fa = 0.74). It is possible to prepare macroemulsions with even higher volume fractions volume fractions of more than 99% have been achieved. Such emulsions are also called high internal phase emulsions (HIPE). Two effects can occur. First, the droplet size distribution is usually inhomogeneous, so that small drops fill the free volume between large drops (see Fig. 12.9). Second, the drops can deform, so that in the end only a thin film of the continuous phase remains between neighboring droplets. 

Colloidal interactions between emulsion droplets play a primary role in determining emulsion rheology. If attractions predominate over repulsive forces, flocculation can occur, which leads to an increase in the effective volume fraction of the dispersed phase and thus increases viscosity (McCle-ments, 1999). Clustering of milk fat globules due to cold agglutination increases the effective volume fraction of the milk fat globules, thereby increasing viscosity (Prentice, 1992). 

Consider first the effect of a dispersed phase, of volume fraction continuous phase of viscosity D0 and dispersed particles (droplets) which do not attract. At low volume fractions the Einstein equation should apply to a suspension of solid particles at constant temperature,... 

Effect of Emulsion Characteristics. As discussed in Chapter 4, the rheology of emulsions is affected by several factors, including the dis-persed-phase volume fraction, droplet size distribution, viscosity of the continuous and dispersed phases, and the nature and amount of emulsifying surfactant present. All of these parameters would be expected to have some effect on flow behavior of the emulsion in porous media. However, the relationship between bulk rheological properties of an emulsion and its flow behavior in porous media is feeble at best because, in most cases, the volume... 

Effect of Aging. With increasing volume fraction of the dispersed phase, increasing droplet diameter and wider diameter distribution, the viscosity of a dispersed system increases (36). Unstable emulsions show droplet coalescence by extending the diameter distribution, accompanied by viscosity increasing, an effect, which is called "aging" (36-38). ... 

At lower Na+ concentration, the high negative charge (zeta potentials of salt-free emulsion droplets are 115 mv and above (5)) immobilizes a water layer around the droplets, thus effectively increasing the apparent volume fraction. Addition of Na+ reduces the net charge and some of the immobilized water is released giving a lower apparent volume fraction and lower apparent viscosity. 

Assuming that the W/O emulsion behaves as a near hard-sphere dispersion, it is possible to apply the Dougherty-Krieger equation [7, 8] to obtain the effective volume fraction, 4>. The assumption that the W/O emulsion behaves as a near hard sphere dispersion is reasonable as the water droplets are stabihsed with a block copolymer with relatively short PHS chains (of the order of lOnm and less). Any lateral displacement of the polymer will be opposed by the high Gibbs elasticity of the adsorbed polymer layer, and the droplets will maintain their spherical shape up to high volume fractions. 

No. The fact that y decreases with time for surfactant B implies that the latter must contain some component(s) in small concentrations that decrease y to a lower value than the main component(s) can. Application of Eq. (10.6) with tads = 120 s and D — 3 10 10 m2 s 1 leads to a thickness of the layer 5 that provides the minor surfactant of about 60 pm in other words, the effective surface-to-volume ratio would be 1/ 60 Hf 6 = 17 I03m In the emulsion, however, the ratio of O-W surface area to the volume of the surfactant solution may be far greater. It would be given by 6 q>/ di2( 1 — (p) for an assumed oil volume fraction

droplet size d32 = 1 pm, this leads to a value of 2 106 m 1, i.e., more than 100 times that during the macroscopic measurement of y. This implies that the concentration of the minor components at the droplet interface would be very small, probably having a negligible effect on y. 

FIGURE 17.20 The effect of filler particles on gel properties, (a) Relative modulus (Gm/G0) as a function of particle volume fraction (broken lines are calculated for various values of the ratio Gp/Go, indicated near the curves. The drawn lines are average experimental values for acid casein gels (C) and polymer gels (polyvinyl alcohol, P), with emulsion droplets that are either bonded (B) or nonbonded (N) to the gel matrix, (b) Highly schematic pictures of the gel structure. Shaded area denotes primary gel. Particles are nonbonded (1) bonded (2) bonded but with intermediate layer (3) bonded and aggregated (4). (Adapted from T. van Vliet. Colloid Polymer Sci. 266 (1988) 518.)... 

Liquid droplets cannot be treated the same as solid particles in their codispersed systems. This behavior has been indicated by equation 66 or 68, in which the Einstein constant increases with increasing viscosity ratio of the dispersed phase to the continuous phase. As is shown by Yan et al. (195, 197, 198), liquid droplet and solid particle effects are additive only when the solid concentration is low, say s < 0.05, and when both solid particles and liquid droplets have comparable sizes. However, when the particle-to-droplet size ratio is large, the particles and the droplets become additive (192) for a wider solid concentration range (Figures 34 and 35). The apparent viscosity of the system may be added in terms of the two distinct model systems pure emulsion characterized by solid-free dispersed phase volume fraction and pure suspension characterized by the volume fraction of the solids. The additive rule for the ternary systems is similar to the rule for bimodal solid particle suspensions due to Farris (139) ... 

The latter form is a good approximation for any 0> Oq and h/R 1. In most foams, the effect is expected to be minimal, as the bubbles tend to be relatively large. For emulsions of small drop size, however, the effect may be considerable and the peculiar properties resulting from extreme crowding may commence at an apparent volume fraction that is considerably smaller than one would expect for zero film thickness. For example, in an emulsion with droplets of 2/ - 1 um and A = 50 nm, the effective volume fraction already reaches a value of 0.74 at an apparent volume fraction of only about 0.64 The finite film thickness... 

Figure 12 Water droplets in model oils with asphaltene and resin fractions extracted from a crade oil normalized cumulative volume showing the effect of asphaltene and resin content. Key emulsion 1 - high asphaltene, no resin 2 -lowasph., no resin 3 - high asph., high resin 4 - high asph., low resin.

A similar transformation occms in dilute suspensions of uniformly charged spheres in a medium of low ionic strength. The solid phase, which can form at volume fractions as low as 0.001, is iridescent and reverts to liquid phase on dilution or addition of electrolyte (Hachisu et al., 1973 Hiltner and Krieger, 1969). Since each sphere is smrounded by a thick electrical double layer and since repulsion prevents significant overlap of double layers of adjacent particles, the spheres can be considered to have a much larger effective radius and hence a much larger volume fraction than the nominal values. The iridescent phase forms when the effective volume fraction reaches approximately 0.5. The fractionation of emulsion droplets into a phase containing monodispersed droplets, discussed at the end of Section 4 (Bibette, 1991), is also based on these principles of phase separation. 

Polysaccharides increase the viscosity of the continuous phase of the emulsion. One of the main functions of polysaccharides in emulsions is to thicken the continuous hquid. The intended effect is usually to impart a desired texture (increase viscosity or stiffness to the system and reduce buoyancy-driven creaming or sedimentation of the emulsion droplets and other particles in the system). Because of their highly swollen molecular structure in solutions, leading to a high effective volume fraction at low concentrations, most polysaccharides are very effective in providing a high viscosity at low concentration. 

The third factor that affects emulsion rheology is the droplet size distribution. This is particularly the case at high-volume fractions. When ( ) > 0.6, T) is inversely proportional to the reciprocal of the mean droplet diameter (18). The above equations do not show any dependence on droplet size and an account should be made for this effect by considering the average distance between the droplets in an emulsion. At high shear rate, the droplets... 

The effect of droplet size and its distribution on the adsorbed layer thickness may be inferred from a comparison of the results obtained with the o/w emulsions with those recently obtained using polystyrene latex dispersions containing grafted PEO chains of (molecular weight 2000) (49). As discussed earlier, the viscoelastic behavior of the system (which reflects the steric interaction) is determined by the ratio of the adsorbed layer thickness to the particle radius (8/R). The larger this ratio, the lower the volume fraction at which the system changes from predominantly viscous to predominantly elastic response. With relatively polydisperse systems, ( )cr shifts to higher values when compared to monodisperse systems with the same mean size. 

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