Disperse phase volume

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

Electrical conductivity is an easily measured transport property, and percolation in electrical conductivity appears a sensitive probe for characterizing microstructural transformations. A variety of field (intensive) variables have been found to drive percolation in reverse microemulsions. Disperse phase volume fraction has been often reported as a driver of percolation in electrical conductivity in such microemulsions [17-20]. 

Lagues et al. [17] found that the percolation theory for hard spheres could be used to describe dramatic increases in electrical conductivity in reverse microemulsions as the volume fraction of water was increased. They also showed how certain scaling theoretical tools were applicable to the analysis of such percolation phenomena. Cazabat et al. [18] also examined percolation in reverse microemulsions with increasing disperse phase volume fraction. They reasoned the percolation came about as a result of formation of clusters of reverse microemulsion droplets. They envisioned increased transport as arising from a transformation of linear droplet clusters to tubular microstructures, to form wormlike reverse microemulsion tubules. 

Several unifying conclusions may be based upon the order parameter results illustrated here for microstructural transitions driven by three different field variables, (1) disperse phase volume fraction, (2) temperature, and (3) chemical potential. It appears that the onset of percolating cluster formation may be experimentally and quantitatively distinguished from the onset of irregular bicontinuous structure formation. It also appears that... 

Coalescence is important for dispersed phase volumes fraction () greater than about 0.005 the rate of coalescence increases with . 

Among the various branches in colloid and interface science, polymer adsorption and its effect on the colloid stability is one of the most crucial problems. Polymer molecules are increasingly used as stabilizers in many industrial preparations, where stability is needed at a high dispersed phase volume fraction, at a high electrolyte concentration, as well as under extreme temperature and flow velocity conditions. 

Wieringa, J.A. Dieren, F. van Janssen, J.J.M. Agterof, W.G.M., 1996, Droplet breakup mechanisms during emulsification in colloid mills at high dispersed phase volume fraction, Chemical Engineering Research Design, 74, 554-562. 

The non-aqueous HIPEs showed similar properties to their water-containing counterparts. Examination by optical microscopy revealed a polyhedral, poly-disperse microstructure. Rheological experiments indicated typical shear rate vs. shear stress behaviour for a pseudo-plastic material, with a yield stress in evidence. The yield value was seen to increase sharply with increasing dispersed phase volume fraction, above about 96%. Finally, addition of water to the continuous phase was studied. This caused a decrease in the rate of decay of the emulsion yield stress over a period of time, and an increase in stability. The added water increased the strength of the interfacial film, providing a more efficient barrier to coalescence. 

The top-down approach involves size reduction by the application of three main types of force — compression, impact and shear. In the case of colloids, the small entities produced are subsequently kinetically stabilized against coalescence with the assistance of ingredients such as emulsifiers and stabilizers (Dickinson, 2003a). In this approach the ultimate particle size is dependent on factors such as the number of passes through the device (microfluidization), the time of emulsification (ultrasonics), the energy dissipation rate (homogenization pressure or shear-rate), the type and pore size of any membranes, the concentrations of emulsifiers and stabilizers, the dispersed phase volume fraction, the charge on the particles, and so on. To date, the top-down approach is the one that has been mainly involved in commercial scale production of nanomaterials. For example, the approach has been used to produce submicron liposomes for the delivery of ferrous sulfate, ascorbic acid, and other poorly absorbed hydrophilic compounds (Vuillemard, 1991 ... 

Calculate the dispersed-phase volume fraction (())) of the emulsion using the equation... 

Figure 13. Ultrasonic determination of creaming profiles. is the disperse phase volume fraction, t is the time and x is the height of the emulsion.

I> ) = (dispersed phase volume)/)volume of dispersed and continuous phases)... 

The Sauter mean diameter (d32) is related to the interfacial area per unit volume (a) and dispersed phase volume fraction by... 

The correlation was developed for five 50-mm SMV elements (dH = 8 mm) and covered Reynolds numbers (ReH) in the range 200-20,000 and dispersed-phase volume fraction up to 0.25. 

Small volume of dispersed phase - this reduces the frequency of collisions and aggregation. Higher volumes are possible, for dose-packed spheres the dispersed phase volume fraction would be 0.74, but in practice the fraction can be even higher. 

Note from Table 6.8 that the reduced viscosity gives the relative increase in the viscosity of the solution over the solvent, per unit of concentration. Since r/ is the limiting value of the reduced viscosity, it is a measure of the first increment of viscosity due to the dispersed particles and is therefore characteristic of the particles. Equation (6.33) predicts that the intrinsic viscosity should equal 2.5 for spherical particles. If the dispersed phase volume fraction is used to reflect the dry-weight concentration of particles that may become solvated when dispersed, then intrinsic viscosity measurements can be used to determine the extent of solvation as follows. Suppose the mass of colloidal solute in a solution is converted to the volume of unsolvated material using the dry density. If the particles are assumed to be uniformly solvated throughout the dispersion then the solvated particle volume exceeds that of the unsolvated particle volume by the factor 1 + (m], b/m2)(p2/Pi) where my, is the mass of bound solvent, m2 is the mass of the solute particle, p2 is the density of the particle and pi is the density of the solvent. Since 4>[Pg.185]

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]. 

Figure 6.21 The influence of emulsifier concentration on the relative viscosity of sorbitan mono-oleate stabilised W/O emulsions in paraffin. The emulsions had dispersed phase volume fractions in the range 0.37 to 0.68 and mean droplet diameters, am, as plotted along the x-axis. From data in Sherman [215].

With an increase in dispersed-phase volume fraction, the viscosity of an emulsion increases. This increase in viscosity is linear at a low droplet concentration (McClements, 1999) the viscosity of an emulsion of milk fat globules in milk plasma increases linearly with fat content up to 30% (Bakshi and Smith, 1984 Kyazze and Starov, 2004), whereas the viscosity of low-fat milk (<2.0% fat) increases in a near linear fashion with fat content (Phillips et al., 1995). However, above a certain volume fraction of the dispersed phase, the droplets in emulsions are packed so closely that flow is impaired, giving the emulsion a gel-like character (McClements, 1999). For instance, the viscosity of cream increases rapidly with increasing fat content when the fat content is >50% (Prentice, 1968 Mulder Walstra, 1974). 

We now consider a 40% silicone oil premixed emulsion dispersed in an aqueous phase. In Fig. 9 the evolution of mean diameter is plotted as a function of the applied shear rate. The dispersed phase volume fraction is kept constant at 75%, while the emulsifier concentration in the continuous medium is varied from 15 wt % to 45 wt %. The error bars show the distribution width deduced from the measured uniformity. At a given shear rate, smaller droplets with lower uniformity are produced (see Fig. 9) when surfactant concentration increases. For example at 45% of Ifralan 205 the uniformity never exceeds 15% whatever the applied shear rate, whereas it is of the order of 25% for 15% of Ifralan 205. Some microscope pictures of the emulsions obtained are given in Fig. 10. To understand the evolution, we may argue that the continuous phase viscosity increases... 

Here 0 is the dispersed phase volume fraction and the subscripts 1 and 2 refer to the continuous and dispersed phase, respectively. 

The concentration of droplets in an emulsion is one of the key parameters influencing its appearance, texture, stability, and flavor. For example, opacity, viscosity, and creaming stability of emulsions usually increase as the droplet concentration increases. The droplet concentration is normally expressed in terms of the disperse-phase volume fraction (< )), which is equal to the volume of emulsion droplets (Vd) divided by the total volume of the emulsion (Ve) < ) = Vd/Ve- Nevertheless, it can also be expressed in terms of the disperse-phase mass fraction (( )nj), which is equal to the mass of emulsion droplets (Md) divided by the total mass of the emulsion (Me) = M-q/Me- The mass fraction can be related to the volume... 

Experiments have shown that the smallest droplet size that can be achieved using a high-pressure valve homogenizer increases as the disperse phase volume fraction increases (52). There are a number of possible reasons for this, (1) increasing the viscosity of an emulsion may suppress the formation of eddies responsible for breaking up droplets, (2) if the emulsifier concentration is kept constant, there may be insufficient emulsifier molecules present to completely cover the droplets, and (3) the rate of droplet coalescence is increased. 

Disperse phase volume fraction. The viscosity of food emulsions tends to increase with increased disperse phase volume fraction (Figure 10). The viscosity increases relatively slowly, with 4> at low droplet concentrations, but increases steeply when the droplets become closely packed together. At higher droplet concentrations, the particle network formed has predominantly elastic characteristics. 

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