Weakly Flocculated Dispersions

One of the characteristics of weak flocculation is that the system is reversible. At low volume fractions the system will form some clusters and some single particles. The clusters can be easily disrupted by gentle shaking. As the concentration is increased the system will reach a percolation threshold . The number of nearest neighbours around any test particle reaches 3 at about (p — 0.25 and the attractive forces between 

Let us first consider our disc around a test particle moving with velocity v in direction z in the flow. We can define an element of that disc as having a thickness dz. The angle subtended by the ends of that segment we define as 9. The velocity is thus 

We need to integrate this to obtain the volume. For a segment thickness dz and width x, 

Integrating to find the flux through the disc with p as the number density of particles  

The attractive energy between the particles can be calculated by plotting (7b versus p2. The first feature to note is the change in slope at 

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With nonadsorbing polymer, rheological effects of similar magnitude accompany the phase transitions described earlier (Patel and Russel, 1989a,b). Since macroscopic phase separation takes weeks or months, rheological measurements performed within a few days on samples formulated within the two-phase region, with — Q>miJkT 2 - 20, detect a metastable structure that changes little over time. The systems respond as flocculated dispersions, but the microstructure recovers relatively quickly to a reproducible rest state after shear. Hence these weakly flocculated dispersions are quite tractable materials. 

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). 

On the other hand, if the dispersion is flocculated, particles on contact lend to stick in the configuration in which they collide and thus lend to form a much more open structure (Figure 9.8). Of particular practical interest are weakly flocculated dispersions because, although they may sediment or cream, they form relatively open structures that arc readily dispersed by shaking or stirring. 

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. 

This process refers to aggregation of the droplets (without any change in primary droplet size) into larger units. It is the result of the van der Waals attractions that are universal with all disperse systems. Flocculation occurs when there is insufficient repulsion to keep the droplets apart at distances where the van der Waals attractions are weak. Flocculation may be either strong or weak, depending on the magnitude of the attractive energy involved. 

This occurs because, as the layer thickness is increased the van der Waals attraction is weakened, so that the superposition of attraction and repulsion will have a smaller minimum. For very small steric layers, may become deep enough to cause weak flocculation that would result in a weak attractive gel. Hence, it becomes apparent exactly how the interaction energies can also determine the dispersion rheology. 

The small droplet size also prevents any flocculation of the droplets. If weak flocculation can be prevented this enables the system to remain dispersed, with no separation. 

Most disperse systems used in practice are weakly flocculated, and they also contain thickeners or structuring agents to reduce sedimentation and to acquire the correct rheological characteristics for applications, such as handcreams and lotions. The exact values of G and G" required will depend on the system... 

With a sterically stabilised dispersion, weak flocculation can also occur when the thickness of the adsorbed layer decreases. Again, the value of E can be used as a measure of the flocculation the higher the value of E, the stronger the flocculation. 

Let us consider the case of aerosol suspensions. The suspended particles must be well dispersed so as to penetrate the lung. In this sense, an ideal aerosol suspensiem docs not sediment and form aggregates. However, particles eventually do aggregate, so it is convenient to formulate them in such a way as to promote weak flocculates that can be easily redispersed by shear (e.g agitation of the aerosol ermtainer). The formulation can be adjusted mea.suring viscosity as a function of shear rate or tdiear stress, as depicted in Refs. 6 and 30. 

The last criterion for effective steric stabilization is to have a sufficiently thick adsorbed layer to avoid any weak flocculation. This is particularly important for concentrated dispersions. As discussed previously, a value of 8 of the order of 5-10 nm is usually sufficient. Hence, the side PEO chains need to have a molecular weight of the order of 1000-2000. With most graft copolymers, these side chains are extended, and they provide a sufficiently thick layer. 

Russel, W., Distinguishing between dynamic yielding and wall slip in a weakly flocculated colloidal dispersion , Colloid and Surfaces, A Physiochem. and Eng. Asp., Vol. 161, No. 2 (December 1999)... 

With increasing interparticle collisions the probability of formation of floes from dispersed (nonflocculated) particles increases. Thus the horizontal axis can also be interpreted to mean a change from weakly flocculated particles on the left to increasingly flocculated particles toward the right. An outcome is that, irrespective of the degree of interparticle interaction, at low values of cp the viscosity rises slowly, but tends to increase rapidly when particle packing becomes dense.For randomly packed spheres this change occurs at about 95 = 0.60. A simple viscoplastic model is the Herschel-Bulkley equation... 

The predictions of different quantitative criteria for stability-instability transitions were investigated [461], having in mind that the oscillatory forces exhibit both maxima, which play the role of barriers to coagulation, and minima that could produce flocculation or coalescence in colloidal dispersions (emulsions, foams, suspensions). The interplay of the oscillatory force with the van der Waals surface force was taken into account. Two different kinetic criteria were considered, which give similar and physically reasonable results about the stability-instability transitions. Diagrams were constructed, which show the values of the micelle volume fraction, for which the oscillatory barriers can prevent the particles from coming into close contact, or for which a strong flocculation in the depletion minimum or a weak flocculation in the first oscillatory minimum could be observed [461]. 

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