Behavior of Two-Phased Systems

The two techniques, dynamic mechanical spectroscopy and electron microscopy, yield complementary data. Dynamic mechanical spectroscopy shows more clearly the extent of molecular mixing, while electron microscopy shows the phase domain sizes and shapes. Both techniques contribute to an understanding of phase continuity. 

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Fig. 1 Schematic behavior of two-phase systems as functions of temperature T. (a) A small system, with relatively large jumps in the distribution D at the freezing and melting limits, and a gradual change in D between these two limits, (b) a somewhat larger system, with smaller jumps and a steeper variation in D with temperature, and (c) a still larger system, for which the jumps in D are not discemable and its variation from —1 to +1 is very steep...

Dynamic mechanical characteristics, mostly in the form of the temperature response of shear or Young s modulus and mechanical loss, have been used with considerable success for the analysis of multiphase polymer systems. In many cases, however, the results were evaluated rather qualitatively. One purpose of this report is to demonstrate that it is possible to get quantitative information on phase volumes and phase structure by using existing theories of elastic moduli of composite materials. Furthermore, some special anomalies of the dynamic mechanical behavior of two-phase systems having a rubbery phase dispersed within a rigid matrix are discussed these anomalies arise from the energy distribution and from mechanical interactions between the phases. 

The fourth chapter presents some constitutive theories and equations for suspensions. Suspension rheology normally deals with the flow behavior of two-phase systems in which one phase is solid particles like fillers but the other phase is water, organic liquids or pol)oner solutions. Literature on suspension rheology does not include flow characteristics of filled polymer systems. Neverttieless, ttiis chapter needs to be included as the foimdations for understanding ttie basics of filled polymer rheology stem from the flow behavior of suspensions. In fact, most of the constitutive theories and equations that are used for filled polymer systems are borrowed firom those that were initially developed for suspension rheology. 

Finally, an area which is in need of much further research is that of the dielectric properties of two-phase systems such as frozen foods, emulsions, whips and foams. It is well known that the dielectric behavior of particles of one dielectric property imbedded in a substrate of another, behave very differently from a distributive mixture of both. Fricke (1955) developed a model for randomly oriented oblate spheroids suspended in a continuous medium. It is expected that this model may be used successfully to model two-phase food systems, but to date there is very little literature reporting such studies. 

The existence of the extracting reagent in the stationary phase is one of the essential factors in the enrichment of inorganic elements as well as in the separation itself. However, the values of the distribution ratios, determined by batch extraction measurements in the two-phase system, is sometimes considerably different from that of the dynamic distribution ratios calculated from the elution curve. Further theoretical and basic investigations are necessarily concerned with extraction kinetics, as well as hydrodynamics behavior of two phases in the high-speed CCC (HSCCC) column [1]. 

Three theoretical parameters were introduced by Menet et al. in order to better understand the hydro-dynamic behaviors of two-phase solvent systems [2]. We will not discuss, here, the capillary wavelength, as it only enables the description of the formation of droplets of one liquid in another liquid. The two other parameters were introduced because it appeared interesting to introduce other theoretical parameters to better describe the dynamic phenomena occurring inside a CCC column (i.e., after the formation of the droplet described by the capillary wavelength). Two of these are presented here, namely for the fall of a droplet of the heavier liquid phase (lower) in the continuous lighter one (upper) and y p for the rise of a droplet of the lighter liquid phase in the continuous heavier one, and are defined as follows ... 

Cg), which are important components in gasoline. The vapor-liquid phase behavior of two-component systems is a little more complicated, because I have an additional variable — composition — as well as T and P. Instead of a single temperature at which both liquid and vapor can co-exist, there is a range of temperatures. 

Figure 1. Famous early simulation results showing the existence of extended metastable behavior of two phases in a finite system of hard spheres. The heavy curves and plus signs (+) represent 108 and 32 particle molecular dynamics data of Alder and Wainwright the circles are MC data due to Wood and Jacobson (F0 is the close-packed volume). [Reprinted with permission from W. W. Wood and J. D. Jacobson, J. Chem. Phys. 27,1207 (1957).]...

The measurements of the local properties of two-phase systems during cultivation indicate that radial profiles of ds are fairly uniform. Also, their longitudinal variations are fairly moderate, except in the neighborhood of the aerator (1, 4). The same holds true for the spacial variations of the local relative gas holdups. At low superficial gas velocities the specific interfacial area, a, is fairly uniform also At high superficial gas velocities (turbulent or heterogeneous flow range) the radial profile of a has a shape of an error function, with its maximum in the column center (5). The behavior of these parameters near the aerator depends on the aerator itself and on the medium character. 

Recalling the observation (Table 1) concerning the occurrence of low and almost the same interfacial tension values between the middle phase/oil and the middle phase/aqueous phase systems, we were interested in the study of the phase separation behavior of these two phase systems. Therefore, three different combinations of two phase systems out of one three phase system were made by selectively deleting the third phase (Figure 6). Macroemulsions were produced as described in the experimental section. 

Equation (A.160), known as Torod s law , is generally valid for arbitrary two-phase systems. Indeed, an asymptotic law S q) 1/q is the characteristic signature of two-phase systems with sharp boundaries. According to Eq. (A.160), the asymptotic behavior depends only on the interface area per unit volume, multiplied by the square of the density difference. 

Theoretical approaches to the linear response of two-phase systems, even in the simplest uncoupled case, are based on various model rules. Recently, it was pointed out that the state d the interface between the filler and the matrix [17-20] as well as the microgeometry [21] affect the macroscopic behavior of composites. 

The mathematical treatment described so far applies to ideal two-phase systems with infinitesimal sharp density steps and perfectly constant densities within the two types of domains. While this situation can be approximated in very good approximation for certain types of samples, for example, porous silica prepared by calcination of a polymer template, in the majority of two-phase systems formed by polymers, the interface between the two domain is not sharp but fuzzy on a certain length scale, see Figure 2 for semicrystalline polymers or Figure 4 for block copolymers, and there are also density fluctuations within one or both of the two domains, deviating from the assumed constant density. Both types of effeas lead to deviations from the ideal asymptotic Porod behavior that may need to be taken into account in an SAXS analysis. 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

To understand how the dispersed phase is deformed and how morphology is developed in a two-phase system, it is necessary to refer to studies performed specifically on the behavior of a dispersed phase in a liquid medium (the size of the dispersed phase, deformation rate, the viscosities of the matrix and dispersed phase, and their ratio). Many studies have been performed on both Newtonian and non-Newtonian droplet/medium systems [17-20]. These studies have shown that deformation and breakup of the droplet are functions of the viscosity ratio between the dispersity phase and the liquid medium, and the capillary number, which is defined as the ratio of the viscous stress in the fluid, tending to deform the droplet, to the interfacial stress between the phases, tending to prevent deformation ... 

In contrast to two-phase physical blends, the two-phase block and graft copolymer systems have covalent bonds between the phases, which considerably improve their mechanical strengths. If the domains of the dispersed phase are small enough, such products can be transparent. The thermal behavior of both block and graft two-phase systems is similar to that of physical blends. They can act as emulsifiers for mixtures of the two polymers from which they have been formed. 

The mechanisms by which this interaction occurs may be divided into two distinct groups (S4) first, the hydrodynamic behavior of a multiphase system can be changed by the addition of surface-active agents, and, as a result, the rate of mass transfer is altered secondly, surface contaminants can interfere directly with the transport of matter across a phase boundary by some mechanism of molecular blocking. 

Norden, B Elvingson, C Jonsson, M Akerman, B, Microscopic Behavior of DNA Duing Electrophoresis Electrophoretic Orientation, Quarterly Reviews of Biophysics 24, 103,1991. Nozad, I Carbonell, RG Whitaker, S, Heat Conduction in Multiphase Systems—I Theory and Experiment for Two-Phase Systems, Chemical Engineering Science 40, 843, 1985. 

The graph in Figure 11-37 shows that adding heat to boiling water does not cause the temperature of the water to increase. Instead, the added energy is used to overcome intermolecular attractions as molecules leave the liquid phase and enter the gas phase. Other two-phase systems, such as an ice-water mixture, show similar behavior. 

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