Flocculation volume fractions dispersions

In a high-volume-fraction dispersion with electrosteric stabilization of the latex and an increasing dispersed-phase surface area, the high viscosity observed at low shear rates with decreasing latex size relates to electroviscous and hydration effects. Lower surface acid concentrations on some of the smaller latices may also result in partial flocculation of the latex and a higher effective volume fraction in the presence of coalescing aids (22, 26). 

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

The stability of these dispersions has been investigated. A strong dependence of critical flocculation conditions (temperature or volume fraction of added non-solvent) on particle concentration was found. Moreover, there seems to be little or no correlation between the critical flocculation conditions and the corresponding theta-conditions for the stabilising polymer chains, as proposed by Napper. Although a detailed explanation is difficult to give a tentative explanation for this unexpected behaviour is suggested in terms of the weak flocculation theory of Vincent et al. 

The stability of the various dispersions was assessed and compared by determining the critical flocculation conditions (temperature or volume fraction of added non-solvent for the grafted polymer), as a function of particle concentration. 

Figure 3. Critical flocculation temperature (T) versus log (particle volume fraction ) for the two Si02 g PDMS dispersions in bromocyclohexane O, S15/PDMS5 x, S15/ PDHS3.

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). 

A similar, and even more dramatic, viscosity enhancement was observed by Buscall et al. (1993) for dispersions of 157-nm acrylate particles in white spirit (a mixture of high-boiling hydrocarbons). These particles were stabilized by an adsorbed polymer layer, and then they were depletion-flocculated by addition of a nonadsorbing polyisobutylene polymer. Figure 7-9 shows curves of the relative viscosity versus shear stress for several concentrations of polymer at a particle volume fraction of 0 = 0.40. Note that a polymer concentration of 0.1 % by weight is too low to produce flocculation, and the viscosity is only modestly elevated from that of the solvent. For weight percentages of 0.4-1.0%, however, there is a 3-6 decade increase in the zero-shear viscosity ... 

Figure 7.12 Shear-stress dependence of the relative viscosity for dispersions in water of charged polystyrene particles of radius a = 115 nm with nonadsorbing Dextran T-500 polymer (synthesized from glucose) added as a depletion flocculant. The polymer molecular weight is 298,(HX), and its radius of gyration Rg is 15.8 nm. Volume fractions and polymer concentrations are

Sherman concluded that in the 0/W systems a small fraction of the continuous phase was immobilized by the dispersed phase either by attractive forces or by flocculation. Therefore, the apparent volume fraction was greater than the actual volume fraction of that component. The equations he used to describe the viscosities of these emulsions further extended the approach of Mooney and took account of the particle diameter. 

The relaxation time may be used as a guide for the state of the dispersion. For a colloidally stable dispersion (at a given particle size distribution), r increases with increase of the volume fraction of the disperse phase, . In other words, the cross-over point shifts to lower frequency with increase in . For a given dispersion, r increases with increase in flocculation, provided that the particle size distribution remains the same (i.e., no Ostwald ripening). 

The value of G also increases with increase in flocculation, since aggregation of the particles usually results in liquid entrapment and the effective volume fraction of the dispersion will show an apparent increase. With flocculation, the net attraction between the particles also increases, and this results in an increase in G. The latter is determined by the number of contacts between the particles and the strength of each contact (which is determined by the attractive energy). 

Clearly, depends on the volume fraction of the dispersion, as well as the particle size distribution (which determines the number of contact points in a floe). Therefore, for quantitative comparison between various systems, it must be ensured that the volume fraction of the disperse particles is the same, and that the dispersions have very similar particle size distributions. also depends on the strength of the flocculated structure - that is, the energy of attraction between the droplets - and this in turn depends on whether the flocculation is in the primary or secondary minimum. Flocculation in the primary minimum is associated with a large attractive energy, and this leads to higher values of when compared to values obtained for secondary minimum flocculation (weak flocculation). For a weakly flocculated dispersion, as is the case for the secondary minimum flocculation of an electrostatically stabilised system, the deeper the secondary minimum the higher the value of (at any given volume fraction and particle size distribution of the dispersion). 

Note A stable dispersion of small solid or liquid particles may also show a kind of phase separation when conditions in the liquid are changed in such a way that attractive forces between the particles become dominant. A separation into a condensed phase (high volume fraction of particles) and a very dilute dispersion would then result. The interfacial tension between these phases is very small, e.g., a few pN m 1. Conditions for this to occur are (a) that the particles are about monodiperse and of identical shape and (b) that the attractive forces do not become large (because that would lead to fractal aggregation see Section 13.2.3). Since these conditions are rarely met in food systems, we will not further discuss the phenomenon. Nevertheless, phenomena like depletion flocculation (Section 12.3.3) show some resemblance to a phase separation. 

The presence of dispersed particles may significantly affect the value of dielectric constant of disperse system. In some cases, e.g. in non-aggregated (non-flocculated) inverse emulsions (Chapter VIII,3), the dielectric constant is related to the volume fraction of droplets in the emulsion, VKi, by the Bruggerman relationship... 

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