Emulsion model

An emulsion model that assumes the locus of reaction to be inside the particles and considers the partition of AN between the aqueous and oil phases has been developed (50). The model predicts copolymerization results very well when bulk reactivity ratios of 0.32 and 0.12 for styrene and acrylonitrile, respectively, ate used. 

A hydrodynamic model of fluidization attempts to account for several essential features of fluidization mixing and distribution of solids and fluid in a so-called emulsion region, the formation and motion of bubbles through the bed (the bubble region ), the nature of the bubbles (including their size) and how they affect particle motion/distribution, and the exchange of material between the bubbles (with little solid content) and the predominantly solid emulsion. Models fall into one of three classes (Yates, 1983, pp. 74-78) ... 

Stokes, J. R., Wolf, B., and Frith, W. J. 2001. Phase-separated biopolymer mixture rheology prediction using a viscoelastic emulsion model. J. Rheol 45 1173-1191. 

Table 7.11. Blend Viscoelasticity from Emulsion Models [Graebling and Miller, 1991]...

The rheological consequences of these changes can be predicted from a model system. The emulsion model indicates that making the interface more rigid causes the intrinsic viscosity of the emulsion to increase (see Eq 7.50). Similarly, an increase of the apparent volume of the dispersed phase causes the relative viscosity to increase (see Eqs 7.24-7.25). Furthermore, enhanced interactions between the phases will reduce the possibility of the interlayer slip, and increase formation of associative network formation, which may result in the yield stress. In short, compatibilization is expected to increase melt viscosity, elasticity and the yield stress. 

Effects of addition of a compatibilizing block copolymer, poly(styrene-b-methyl methacrylate), P(S-b-MMA) on the rheological behavior of an immiscible blend of PS with SAN were studied by dynamic mechanical spectroscopy [Gleisner et al., 1994]. Upon addition of the compatibilizer, the average diameter of PS particles decreased from d = 400 to 120 nm. The data were analyzed using weighted relaxation-time spectra. A modified emulsion model, originally proposed by Choi and Schowalter [1975], made it possible to correlate the particle size and the interfacial tension coefficient with the compatibilizer concentration. It was reported that the particle size reduction and the reduction of occur at different block-copolymer concentrations. 

One concludes that modeling of concentrated emulsions becomes possible by combining experimental investigation of the simplest emulsion model system with computer simulation accounting for the characteristics of a concentrated emulsion (high droplet-volume fraction, etc.). 

Emulsion Crude Ratio of w/o used Inversion point Crude based emulsion Model oil based emulsion... 

Paheme emulsion model failed to describe the dynamic modulus of the PP/EPDM blends after radiation, because the viscosity ratio increased significantly and the rubber phase changed from deformed droplets to hard domains after radiation (Cao et al. 2007). Intercoimections among inclusions of the dispersed phase (Shi et al. 2006) and the existence of multiple emulsion (emulsion-in-emulsion) structure exhibiting different relaxation domains in compatibilized systems are other factors contributing to the failure of Palieme s model (Friedrich and Antonov 2007 Pal 2007). 

From the discussion of phase inversion in Sect. 7.1.2, the emulsion model predicts that immiscible blends should show positive deviation, PDB, from the log-additivity rule In r] = X In T]i. However, while PDB has been found in about 60 % of such blends, the remaining four types (see Fig. 7.32) must also be accounted for. This means that at least one other mechanism must be considered when modeling the viscosity-concentration dependence of polymer blends. This second mechanism should lead to the opposite effect, which is to the negative deviation fi om the log-additivity rule, NDB. 

Table 7.13 Blend viscoelasticity from emulsion models (Graebling and Muller 1991) ...

Fang et al. (2005) studied the thermal and rheological properties of two types of m-LLDPEs, two LDPEs, and their blends. The C2+6 m-LLDPE-1 was immiscible, whereas the C2+8 m-LLDPE-2 was miscible with the LDPEs, indicating that increasing the length of SCB in m-LLDPEs promoted miscibility with LDPE. The Palieme (1990, 1991) emulsion model provided good predictions of the linear viscoelastic behavior for both miscible and immiscible blends. The low-frequency data showed an influence of the interfacial tension on the elastic modulus of the blends for the immiscible blends. 

Scholz, P., Froelich, D., and Muller, R. (1989) Viscoelastic properties and morphology of two-phase polypropylene/ polyamide 6 blends in the melt. Interpretation of results with an emulsion model. J. Rheol, 33 (3), 481-499. 

Ait-Kadi, A., Ajji, A., and Brahimi, B. (1992) Linear rheology of copolymer modified blends Fxperiments and predictions of emulsion models in Theoretical and Applied Rhedogy,... 

To study the inter-relationship between rheological characteristics of interfacial layers and stability of water-in-oil concentrated emulsions, model emulsions containing 50% water and 50% soap in n-decane were prepared and their properties studied. In our previous work (3,4) high stabilities of emulsions stabilized by aluminum and iron soaps were observed, rheological properties of stabilizing interfacial layers being compared with the stability of drops. 

T. G. Redgrave and R. C. Maranhao, Metabolism of protein-free lipid emulsion models of chylomicrons in rats. Biochim. Biophys. Acta., 835,104-112 (1985). 

Structure and properties for binary blends of PLA and PBS are studied both in the solid and molten states. It is foimd that PLA and PBS are immiscible in the molten state and the blends exhibit phase-separated structure. The interfacial tension between PLA and PBS is estimated using a rheological emulsion model proposed by Palieme and foimd to be 3.5 mN/m as shown in Figs. 4.29,4.30 and 4.31. Basic theological parameters are also evaluated for PLA and PBS. It is suggested that the entanglement molecular weight of PLA is lower than that of PBS. 

The viscoelastic properties of partially miscible mixtures can be analyzed by applying incompressible emulsion models (Palierne 1990). Various studies (Graebling et al. 1993 Lacroix et al. 1998 Vinckier and Launn 1999) have confirmed the success of this model, providing information on the complex, typically bimodal, terminal relaxation of two immiscible or partially miscible polymers subjected to phase separation and capable of attaining dynamic equilibrium. Assuming that the droplet size is uniform, the complex modulus G (co) can be written as... 

Emulsion Models To simulate the core-annulus strueture, the cross section in emulsion models is divided into an inner dilute core region where particles are transported upwards, and a denser annular region where partieles descend along the wall, as in Fig. 26, but without the clusters. The thickness of the solid layer along the vertical heat transfer surfaces is often approximated as uniform. However, for membrane wall heat transfer surfaces, the annulus layer tends to be thicker at the fin than at the tube crest (Grace, 1990 Golriz 1992). 

The emulsion model is similar to the cluster renewal model, but instead of clusters, the heat transfer surface is assumed to be fully covered by a uniform emulsion layer of voidage significantly higher than The pre-dietions from this model are in reasonable agreement with experimental findings (Luan et al., 1999). 

---