Dispersed Phase Size and Polydispersity

Thus far most of the relationships discussed apply to monodisperse systems in which the dispersed species have the same size and shape. Although for a monodisperse system, relative viscosity is often independent of droplet/bubble/particle size, at the high end of the dispersed phase volume fraction range the viscosity will often become influenced by size. The actual range of volume fraction for which this occurs depends strongly on the nature of a particular system, including factors such as surface rigidity [215]. 

For a polydisperse system, the size distribution tends to have an important influence on viscosity regardless of the volume fraction concerned. For a given volume fraction of dispersed species, having a size distribution tends to reduce the hydrody- 

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The polydispersity index of the dispersed phase in different screw configurations were plotted in Figure 5. It is seen that the distribution of the dispersed phase size is very narrow, and is insensitive to screw configurations. 

It is probable that numerous interfacial parameters are involved (surface tension, spontaneous curvature, Gibbs elasticity, surface forces) and differ from one system to the other, according the nature of the surfactants and of the dispersed phase. Only systematic measurements of > will allow going beyond empirics. Besides the numerous fundamental questions, it is also necessary to measure practical reason, which is predicting the emulsion lifetime. This remains a serious challenge for anyone working in the field of emulsions because of the polydisperse and complex evolution of the droplet size distribution. Finally, it is clear that the mean-field approaches adopted to measure > are acceptable as long as the droplet polydispersity remains quite low (P < 50%) and that more elaborate models are required for very polydisperse systems to account for the spatial fiuctuations in the droplet distribution. 

As mentioned previously, Bibette [95] has developed a very elegant method for the purification of coarse, polydisperse emulsions to produce monodisperse systems. This technique is based on the attractive depletion interaction between dispersed phase droplets, caused by an excess of surfactant micelles in the continuous phase. A phase separation occurs under gravity, between a cream layer and a dilute phase since the extent of the separation increases with increasing droplet diameter, a separation based on size occurs. By repeating this process, emulsions of very narrow size distribution can be produced. 

The most important factor controlling the morphologies generated is the location of the composition of the initial blend, < )mo with respect to the critical composition, < )M cnt (Figs 8.5 and 8.6). The latter may be calculated from the Flory-Huggins model as applied to a binary blend (step reactions) or a ternary blend (chain reactions), taking into account polydispersity (Kamide, 1990). The size of particles increases with the concentration of the component that forms the dispersed phase. Typically, for < )mo < < >M,crit, an increase in < )M0 will lead to an increase in both the volume fraction and the average size of dispersed phase modifier-rich particles. 

The rate of Ostwald ripening depends on the size, the polydispersity, and the solubility of the dispersed phase in the continuous phase. This means that a hydrophobic oil dispersed as small droplets with a low polydispersity already shows slow net mass exchange, but by adding an ultrahydrophobe , the stability can still be increased by additionally building up a counteracting osmotic pressure. This was shown for fluorocarbon emulsions, which were based on perfluo-rodecaline droplets stabilized by lecithin. By adding a still less soluble species, e.g., perfluorodimorphinopropane, the droplets stability was increased and could be introduced as stable blood substitutes [6,7]. 

Concurrently, special measures are necessary to reduce the rate of gas diffusion transfer and the related to it bubble expansion and increase in polydispersity. To produce a foam with bubbles of maximum uniform size additives are also introduced that decrease the rate of solving, desorption and molecular gas diffusion (often such substance increase also the surface viscosity). Besides, if it is possible, a gas with low solubility and diffusion rate can be used as a disperse phase. 

Coalescence is not the only mechanism by which dispersed phase droplets increase in size. If the emulsion is polydispersed and there is significant miscibility between the oil and water phases, then Ostwald... 

Valentas and Amundson (V3) studied the performance of continuous flow dispersed phase reactors as affected by droplet breakage processes and size distribution of the droplets. Various reaction cases with and without mass transfer were studied for both completely mixed or completely segregated dispersed phase. Droplet size distribution is shown to have a considerable effect on the efliciency of a segregated reaction system. They indicated that polydispersed drop populations require a larger reactor volume to obtain the same conversion as a monodispersed system for zero-order (or mass-transfer-controlled) reactions in higher conversion regions. As the dispersed phase becomes completely mixed, the distribution of droplet sizes becomes less important. These interactions are un-... 

We have compared these theoretical predictions of the low-frequency modulus to experimental measurements on compressed emulsions and concentrated dispersions of microgels [121]. The emulsions were dispersions of silicone oil (viscosity 0.5 Pas) in water stabilized by the nonionic surfactant Triton X-100 [102, 121]. The excess surfactant was carefully eliminated by successive washing operations to avoid attractive depletion interactions. The size distribution of the droplets was moderately polydisperse with a mean droplet diameter of 2pin. The interfacial energy F between oil and water was 4mJ/m. The contact modulus for these emulsions was thus F 35 kPa. The volume fraction of the dispersed phase was easily obtained from weight measurements before and after water evaporation. Concentrated emulsions have a plateau modulus that extends to the lowest accessible frequencies, from which the low-frequency modulus Gq was obtained. Figure 11 shows the variations of Gq/E"" with 0 measured for the emulsions against the values calculated in the... 

As mentioned above, macroscale models are written in terms of transport equations for the lower-order moments of the NDF. The different types of moments will be discussed in Chapters 2 and 4. However, the lower-order moments that usually appear in macroscale models for monodisperse particles are the disperse-phase volume fraction, the disperse-phase mean velocity, and the disperse-phase granular temperature. When the particles are polydisperse, a description of the PSD requires (at a minimum) the mean and standard deviation of the particle size, or in other words the first three moments of the PSD. However, a more complete description of the PSD will require a larger set of particle-size moments. 

The equilibrium or algebraic Eulerian model with a single conditional velocity that is based on the mean particle size small particle Stokes number and limited polydispersity (momentum-balance equation only for the continuous phase if the system is dilute or for the mixture of continuous and disperse phases if the system is dense). 

As explained throughout the book, disperse multiphase systems are characterized by multiple phases, with one phase continuous and the others dispersed (i.e. in the form of distinct particles, droplets, or bubbles). The term polydisperse is used in this context to specify that the relevant properties characterizing the elements of the disperse phases, such as mass, momentum, or energy, change from element to element, generating what are commonly called distributions. Typical distributions, which are often used as characteristic signatures of multiphase systems, are, for example, a crystal-size distribution (CSD), a particle-size distribution (PSD), and a particle-velocity distribution. 

A parameter that cannot be over looked is the dispersity in size of the particles. Indeed, polydispersity usually prevents long range positional ordering. For example, it is crucial in order to obtain (i) smectic phases to have nanoparticles of fairly homogeneous length and (ii) hexagonal phases to have nanoparticles with diameters as monodisperse as possible. 

Both sc-ethane and SC-CO2 provide density tunable dispersibility for nanocrystals. Partially fluorinated ligands enabled the first example of a sterically stabilized nanocrystal dispersion in pure CO2. The nanocrystals show LCST phase behavior with increased dispersibility at higher solvent densities. Additionally, arrested precipitation to synthesize nanocrystals in SC-CO2 has been developed. The technique yields chemically robust nanocrystals that are fully passivated with fluorinated ligands allowing for collection and redispersion of the particles without any change in size or polydispersity. The nanocrystal size produced depends on both the solvent density and length of the ligand, with smaller less polydisperse particles formed at conditions of adequate steric stabilization. 

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