Interphase volume fraction

The volume fraction of the interphase layer, (ptp, was estimated in two ways. First, from the DSC data, the fractional interdiffused mass of each component was determined from the fractional decreases in the magnitudes of the corresponding Tg transitions. It was then assumed that the interphase mass fraction and interphase volume fraction are identical (since the densities of each component are similar). Knowing the size of the dispersed phase particles, the interphase thickness can then be calculated. Second, using the PALS data, (pip was estimated independently as follows First, the o-Ps intensity of the fully demixed system can be calculated as... 

Jancar et al. (154) attempted to calculate the effect of a soft interphase on the stress field around and in the platelet shaped and fibrous inclusions of small aspect ratio. Because of the presence of a shear component of the stress in the interphase, a transfer of a portion of the load from the matrix to the core-shell inclusion is possible, even when the interphase layer has modulus of elasticity substantially lower than the matrix. At least five to six times thicker soft interphase compared with spherical inclusion is necessary to reduce the reinforcing efficiency of platelets with aspect ratio of 5 to a negligible value. Above the elastomer interphase volume fraction equal to about 12 vol% of the inclusions, the elastic modulus of the complex core-shell inclusion equals that of the PP matrix. 

A key factor in the NIA theory is the constant value of the interfadal layer thickness at the domain-matrix boundary. There has been mudt discusaon on the existence and magnitude of an interfadal region where partial mixing of the two components takes place. Its existence has been established by positron annihalation studies whilst its magnitude is still a source of interest. Williams has proposed that this interface is unsymmetric and of considerable extent, in terms of volume fraction, whilst Krause concludes that the interphase volume fraction is very small. Mechanical and dynamical mechanical properties have been discussed , in greater or lesser detail, in terms of the interphase volume fraction and Williams has successfully... 

Fig. 14. Interphase volume fraction as a function of copolymer numba average molecular weight.

In order to study the influence of pyrolytic carbon interphase on the mechanical properties of the composite, porous C/C composites with the same carbon fiber fraction but different contents of pyrolytic carbon interphase (volume fractions of 12.4% and 34.2% other than 22.3%) were prepared. Bulk densities of the prepared C/C-ZrBj-ZrC-SiC composite are 0.51g/cm (sample A) and 0.88g/cm (sample C), respectively. Mono-ceramic matrix composite of C/C-SiC with the same fiber and pyrolytic carbon volume fractions and pyrolytic carbon interphase thickness as in sample B was also prepared by PIP using PCS as pre-ceramic precursor for... 

The important yet unexpected result is that in NR-s-SBR (solution) blends, carbon black preferably locates in the interphase, especially when the rubber-filler interaction is similar for both polymers. In this case, the carbon black volume fraction is 0.6 for the interphase, 0.24 for s-SBR phase, and only 0.09 in the NR phase. The higher amount in SBR phase could be due to the presence of aromatic structure both in the black and the rubber. Further, carbon black is less compatible with NR-cE-1,4 BR blend than NR-s-SBR blend because of the crystallization tendency of the former blend. There is a preferential partition of carbon black in favor of cis-1,4 BR, a significant lower partition coefficient compared to NR-s-SBR. Further, it was observed that the partition coefficient decreases with increased filler loading. In the EPDM-BR blend, the partition coefficient is as large as 3 in favor of BR. 

It was concluded that the filler partition and the contribution of the interphase thickness in mbber blends can be quantitatively estimated by dynamic mechanical analysis and good fitting results can be obtained by using modified spline fit functions. The volume fraction and thickness of the interphase decrease in accordance with the intensity of intermolecular interaction. 

This monomer concentration Ma in the formalism of the quasi-homogeneous approximation, unlike M a, refers to the whole volume of the two-phase system. The aforementioned quantities are connected by the simple relationship Ma = flM a where y01 stands for the volume fraction of the a-th phase in miniemulsion. An analogous relation, Ra = sdaR a, exists between the concentrations Ra of the a-th type active centers in the entire system and those R a in the surface layer of the a-th phase. This layer thickness da has the scale of average spatial size of the a-th type block, which hereafter is presumed to be small as compared to the average radius of miniemulsion drops. Apparently, in this case, the curvature of the interphase surface can be neg-... 

The prime difficulty of modeling two-phase gas-solid flow is the interphase coupling, which deals with the effects of gas flow on the motion of solids and vice versa. Elgobashi (1991) proposed a classification for gas-solid suspensions based on the solid volume fraction es, which is shown in Fig. 2. When the solid volume fraction is very low, say es< 10-6, the presence of particles has a negligible effect on the gas flow, but their motion is influenced by the gas flow for sufficiently small inertia. This is called one-way coupling. In this case, the gas flow is treated as a pure fluid and the motion of particle phase is mainly controlled by the hydrodynamical forces (e.g., drag force, buoyancy force, and so... 

Numerical simulations of the coarsening of several particles are now possible, allowing the particles to change shape due to diffusional interparticle transport in a manner consistent with the local interphase boundary curvatures [17]. These studies display interparticle translational motions that are a significant phenomenon at high volume fractions of the coarsening phase. 

The structures formed by polystyrene-poly(propylene imine) dendrimers have also been analyzed. Block copolymers with 8, 16, and 32 end-standing amines are soluble in water. They have a critical micelle concentration of the order of 10"7 mol/1. At 3x10 4 mol/l they form different types of micelles. The den-drimer with eight amine groups (80% PS) form bilayers. The dendrimer with 16 amine groups (65% PS) forms cylinders and the dendrimer with 32 amine groups (50% PS) forms spherical micelles [38,130,131]. These are the classical lamellar, cylindrical, and spherical phases of block copolymers. However, the boundary between the phases occurs at very different volume fractions, due to the very different packing requirements of the linear polymer and spherical dendrimer at the interphase. 

Figure 2.1. Fraction of interphase polymer as a function of volume fraction of fiber inclusion, where t is the interphase thickness and r, is the radius of the nanotube/ fiber inclusion. Reproduced from reference 1 with permission from Elsevier.

In order to obtain the interphase momentum transfer term in regions with a gas volume fraction less than 0,8 the Ergun equation is adapted ... 

With this approach, even the dispersed phase is treated as a continuum. All phases share the domain and may interpenetrate as they move within it. This approach is more suitable for modeling dispersed multiphase systems with a significant volume fraction of dispersed phase (> 10%). Such situations may occur in many types of reactor, for example, in fluidized bed reactors, bubble column reactors and multiphase stirred reactors. It is possible to represent coupling between different phases by developing suitable interphase transport models. It is, however, difficult to handle complex phenomena at particle level (such as change in size due to reactions/evaporation etc.) with the Eulerian-Eulerian approach. 

If the flows are unsteady, the terms containing apo can be added on both sides of Eq. (7.10) (refer to Section 6.4). It must be noted that for multiphase flows, the inflow and outflow terms require considerations of interpolations of phase volume fractions in addition to the usual interpolations of velocity and the coefficient of diffusive transport. The source term linearization practices discussed in the previous chapter are also applicable to multiphase flows. It is useful to recognize that special sources for multiphase flows, for example, an interphase mass transfer, is often constituted of terms having similar significance to the a and b terms. Such discretized equations can be formulated for each variable at each computational cell. The issues related to the phase continuity equation, momentum equations and the pressure correction equation are discussed below. 

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