Inner phase volume fraction

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. 

The inner phase volume fraction determines many properties of an emulsion. One example is the viscosity r/em. For small volume fractions one can often regard the disperse phase as consisting of rigid, spherical particles instead of liquid, flexible drops. Then we can apply Einstein s3 equation [541], with rj being the viscosity of the pure dispersing agent ... 

Although it is hard to draw a sharp distinction, emulsions and foams are somewhat different from systems normally referred to as colloidal. Thus, whereas ordinary cream is an oil-in-water emulsion, the very fine aqueous suspension of oil droplets that results from the condensation of oily steam is essentially colloidal and is called an oil hydrosol. In this case the oil occupies only a small fraction of the volume of the system, and the particles of oil are small enough that their natural sedimentation rate is so slow that even small thermal convection currents suffice to keep them suspended for a cream, on the other hand, as also is the case for foams, the inner phase constitutes a sizable fraction of the total volume, and the system consists of a network of interfaces that are prevented from collapsing or coalescing by virtue of adsorbed films or electrical repulsions. 

Apart from chemical composition, an important variable in the description of emulsions is the volume fraction, outer phase. For spherical droplets, of radius a, the volume fraction is given by the number density, n, times the spherical volume, 0 = Ava nl2>. It is easy to show that the maximum packing fraction of spheres is 0 = 0.74 (see Problem XIV-2). Many physical properties of emulsions can be characterized by their volume fraction. The viscosity of a dilute suspension of rigid spheres is an example where the Einstein limiting law is [2]... 

Figure 5.13 Predicted phase diagrams for physical gels made from low-molecular-weight molecules with junctions of unrestricted functionality 4> is the total volume fraction of polymer, and Tr is here the reduced distance from the theta temperature, Tr = — Q/T. The parameter Aq controls the equilibrium constant among aggregates of various sizes. The outer solid lines are binodals, the inner solid lines are spinodals, and the dashed lines are gelation transitions. CP is a critical solution point, CEP is a critical end point, and TCP is a tricriti-cal point. (Reprinted with permission from Tanaka and Stockmayer, Macromolecules 27 3943. Copyright 1994 American Chemical Society.)...

Information about the adsorbed layer strueture of P-casein at the hydrophobic surface can be obtained by employing neutron refleetivity, small-angle X-ray scattering (SAXS), and dynamic light scattering. It was found that the layer of P-casein adsorbed to a hydrocarbon oil/water interface or an air/water interface (70, 71) consisted of a dense inner part, 2 nm thick, and a protein volume fraction of 0.96, immediately adjacent to the interface. Beyond that a second dilute region with a protein volume fraction of 0.15 extended into the aqueous phase. A similar structure of P-casein adsorbed on to polystyrene latex particles was observed with SAXS (65). The electron-density profile cal-... 

A small-angle X-ray scattering(SAXS) study of a model copolymer latex, based on styrene and pentabromobenzyl acrylate(PBBA, 40 wt %), was conducted. The contrast variation method used was shown to be a sensitive probe for inhomogeneity in the particles. The separation of the homogeneous function allowed direct calculation of the size distribution of the spherical particles. The SAXS analysis revealed a particle s inner structure which was a continuous copolymer phase, the composition of which was slightly richer in PBBA, within which domains of PS were randomly distributed. The volume fraction of the PS domains was estimated as 11 vol % and their characteristic length as 5.1 nm. 24 refs. 

Generally, the only bundles that will be hard to clean will be those between the bottom of the fractionator and the reactor. These units may be coked if the process was upset. The other bundles can be cleaned by first circulating the light cycle oil, which is a cut off the fractionator. Diesel fuel may also be used. The addition of a surfactant to the diesel will help disperse the deposits, but more than one system volume will probably be needed. An emulsion can be used with the last stage to remove iron oxides. If the acid is the inner phase, passivation may not be required. If the cleaning stages are separate, or if the organic is the inner phase, then ammonium citrate is recommended for passivation because sodium is also a catalyst poison. 

The inter-relationship between the volume fraction of the inner phase and the relative viscosity of the W/O/W emulsion can be represented by Equation 8.58 noting that o will remain constant after the loss of the internal water phase while should decrease with the increasing incidence of breakdown... 

Figure 8.36 Decrease of the volume fraction of inner aqueous phase wi as a function of the ageing period of W/O/W emulsions (where O = liquid paraffin) calculated from Equation 8.58. Hydrophobic surfactant Span 80 hydrophilic surfactant Tween 20. From Kita et al. [189] with permission.

Consider two closed air-sampling vessels made out of (a) teflon and (b) glass (assume like quartz) with an air volume Fa = 10 3m3 (1 L) and an inner surface area of ASUTf = 6 x 10" 2m2. In these vessels you capture air samples that you want to analyze for phenanthrene. Calculate the fraction of the total phenanthrene present in the air in the two vessels after adsorption equilibrium between the gas phase and the walls of the vessel has been established at 15°C (288 K) and 50% relative humidity. Assume that only adsorption at the surface of the walls is important. (Note that in the case of teflon, absorption could also be important.)... 

The measurements were done in a phase equilibria cell by the synthetic method. The cell has an inner diameter of 25mm, an outer diameter of 80 mm, a saphire window and a movable piston. The volume can be varied from 20 cm3 to 50 cm3.The maximum pressure is 500 bar. First the solid component is filled in and then the cell is evacuated. The liquid carbon dioxide is added from a high pressure cylinder, which can be weighed with an accuracy of 0.1 grams. Figure 2 shows the p-T-dependance of the solubility of paraffin in carbon dioxide for different weight fractions of paraffin. 

Inner loop. The search begins by computing the liquid phase and vapor phase fugacity coefficients. The equations of state used in these problems are explicit in pressure, so the (ps are determined from (4.4.23), which involves an integration over the volume. This requires us to compute the molar volumes and from the equation of state. If the equation is cubic in v, then it should be solved analytically using Cardan s method (Appendix C). However, if the equation is fifth order or higher, then it will have to be solved by trial for v. With the qis known, we compute the K-factors from (11.1.2) and hence get calculated values for the vapor mole fractions xf). Typi-... 

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