Formation of the disperse phase

we will discuss two important examples of zeroth-order point processes as seen from the perspective of the particle-phase NDF. However, some zeroth-order point processes such as the formation of the disperse phase from the fluid phase are accompanied by a change of state in the fluid phase (i.e. the total mass and momentum of the two phases are conserved). Thus, seen in the perspective of the particle and fluid phase, the overall process requires a decrease in the mass of the fluid phase equal to the mass of the formed particle, which is represented by the term 5m in Eq. (4.68) on page 119. In other words, the term 5m in Eq. (4.77) representing the rate of addition of mass to the particle phase from the fluid phase must follow from the source term for the zeroth-order point process for formation of the disperse phase. Using the properties of delta functions, we can formally write the source term in Eq. (5.1) for a zeroth-order point process as 

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Theoretical aspects of emulsion formation in porous media were addressed by Raghavan and Marsden (51-53). They considered the stability of immiscible liquids in porous media under the action of viscous and surface forces and concluded that interfacial tension and viscosity ratio of the immiscible liquids played a dominant role in the emulsification of these liquids in porous media. A mechanism was proposed whereby the disruption of the bulk interface between the two liquids led to the initial formation of the dispersed phase. The analysis is based on the classical Raleigh-Taylor and Kelvin-Helmholz instabilities. 

It is important to stress here that in Eq. (7.145) there are explicit dependences on spatial coordinates in the normalized NDF F and fluid velocity V, but also implicit dependences on the rates of change of internal coordinates the rate of formation of the disperse phase J, and the kernels jS and b. In fact, as described in Chapter 5, these rates and the kernels depend on the flow properties, which change from point to point in the system. 

If the rate of change of internal coordinates, the rate of formation of the disperse phase, and the kernels for second- and first-order processes do not exhibit a strong variation according to the spatial coordinates, then their volume-average values appearing in Eq. (7.146) can be easily estimated. 

In the above, AGmax is essentially the barrier to the formation of the dispersed phase. If once a nucleus with the critical size is formed, the addition of the next molecule makes it free-growing and consequently, a liquid drop will appear. The presence of emulsifying agents preserves the stability of the droplets. However, surface-active materials can also influence a and thus, may have a direct influence on the nucleation. 

The sol-gel process performed in low concentrated polymer-solvent solutions is another attractive route to develop hybrid membranes because it allows an in situ dispersion of metal-based nanoparticles within the polymeric matrix, achieving a suitable interfacial morphology between the continuous and the dispersed phase. Silica particles and polyimide have been frequently used to produce these hybrid membranes [107,108]. In general, hydrolysis and condensation reactions are involved in the sol-gel process, when alkoxides are involved in the formation of the dispersed phase. The advantage of using this method is the formation of an inorganic network largely interconnected with the polymeric materials mainly with noncovalent interactions [109]. In Fig. 7.10 a... 

Surface tension-driven breakup into droplets is rarely important in melt spinning, where the large viscous and elastic forces overwhelm the surface tension forces, ft is an important mechanism in the formation of the dispersed phase in polymer blends, and it is important in solution processing. The surface tension-driven breakup of a viscoelastic filament has been analyzed using both thin filament equations and a transient finite element analysis, but we will not pursue the topic here because it is not relevant to our present discussion. 

Eckert indicated that the rate of mass transfer decreased rapidly as the residence time of the dispersed-phase droplets in the continuous phase increased [19]. Thus, the act of formation of the dispersed-phase droplets contributes significantly to the overall mass transfer. Therefore, the use of packed beds of 8 to 12 ft depth followed by redispersion tends to minimize column height. Seibert et al. ran tests using two beds of packing, each 1L5 ft deep, in a 16.7- in. ID extractor [14]. With 25 IMTP packing, they found a 40% improvement in the overall mass transfer coefficient when redispersion of the organic phase occurred between the two packed beds. 

The viscosity of the mixture is thus almost equal to the viscosity of the LC components, which could not only indicate specific fiber formation of the disperse phase but also its emergence in the surface layers of flow. Practical grounds for a significant decrease in the viscosity of a macromolecular isotropic thamoplastic and the system as a whole arise as a result. We find that ultrathin fib of the LC polymer are also fibrillated, but in the matrix of a flexible-chain polymer. This protects the system from macrodecomposition to some degree and causes an increase in the strength of the matrix. Substances of the isotropic matrix-LC fibrils type can be considered composite materials with their characteristic mechanisms of intensification of the physical-mechanical properties. 

Atomization. A gas or Hquid may be dispersed into another Hquid by the action of shearing or turbulent impact forces that are present in the flow field. The steady-state drop si2e represents a balance between the fluid forces tending to dismpt the drop and the forces of interfacial tension tending to oppose distortion and breakup. When the flow field is laminar the abiHty to disperse is strongly affected by the ratio of viscosities of the two phases. Dispersion, in the sense of droplet formation, does not occur when the viscosity of the dispersed phase significantly exceeds that of the dispersing medium (13). 

Figure 4a represents interfacial polymerisation encapsulation processes in which shell formation occurs at the core material—continuous phase interface due to reactants in each phase diffusing and rapidly reacting there to produce a capsule shell (10,11). The continuous phase normally contains a dispersing agent in order to faciUtate formation of the dispersion. The dispersed core phase encapsulated can be water, or a water-immiscible solvent. The reactant(s) and coreactant(s) in such processes generally are various multihmctional acid chlorides, isocyanates, amines, and alcohols. For water-immiscible core materials, a multihmctional acid chloride, isocyanate or a combination of these reactants, is dissolved in the core and a multihmctional amine(s) or alcohol(s) is dissolved in the aqueous phase used to disperse the core material. For water or water-miscible core materials, the multihmctional amine(s) or alcohol(s) is dissolved in the core and a multihmctional acid chloride(s) or isocyanate(s) is dissolved in the continuous phase. Both cases have been used to produce capsules. 

The second step is to disperse the core material being encapsulated in the solution of shell material. The core material usually is a hydrophobic or water-knmiscible oil, although soHd powders have been encapsulated. A suitable emulsifier is used to aid formation of the dispersion or emulsion. In the case of oil core materials, the oil phase is typically reduced to a drop size of 1—3 p.m. Once a suitable dispersion or emulsion has been prepared, it is sprayed into a heated chamber. The small droplets produced have a high surface area and are rapidly converted by desolvation in the chamber to a fine powder. Residence time in the spray-drying chamber is 30 s or less. Inlet and outlet air temperatures are important process parameters as is relative humidity of the inlet air stream. 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

The controlled flocculation method may be used in conjunction with the addition of a polymeric material to form a structured vehicle. After the formation of the floes, an aqueous solution of polymeric material, usually negatively charged, such as carboxy-methylcellulose or carbopol, is added. The concentration employed depends on the consistency desired for the suspension, which also relates to the size and density of the dispersed phase. Care must be taken to ensure the absence of any incompatibility between the flocculating agent and the polymer used for the formation of the structured vehicle. 

The formation of the microporous phase dispersed in porous, amorphous matrices was followed by XRD and TEM. The XRD patterns of the BEA-composite prepared using the Al-poor aluminosilicate (6A187Si) are shown in Figure 1. BEA was the sole... 

Kalyanasundaram, Kumar, and Kuloor (K2) found the influence of dispersed phase viscosity on drop formation to be quite appreciable at high rates of flow. The increase in pd results in an increase in drop volume. To account for this, the earlier model was modified by adding an extra resisting force due to the tensile viscosity of the dispersed phase. The tensile viscosity is taken as thrice the shear viscosity of the dispersed phase, in analogy with the extension of an elastic strip where the tensile elastic modulus is represented by thrice the shear elastic modulus for an incompressible material. The actual force resulting from the above is given by 3nRpd v. 

In contrast to the highly interconnected pores mentioned previously, closed pores can also be obtained by microemulsion polymerization if the initial volume fraction of the dispersed phase is kept lower than 30%. Recently two systems have been reported where the polymerization of the continuous phase and the subsequent removal of the Hquid dispersed phase resulted in the formation... 

At low flow velocity of the dispersed phase, the interfacial tension does not influence the droplet diameter but it affects the time-scale parameters for droplet formation [35-37] the detachment time becomes shorter at high interfacial tension (low surfactant concentration) [38]. 

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