Two-dimensional phases

Divisek et al. presented a similar two-phase, two-dimensional model of DMFC. Two-phase flow and capillary effects in backing layers were considered using a quantitatively different but qualitatively similar function of capillary pressure vs liquid saturation. In practice, this capillary pressure function must be experimentally obtained for realistic DMFC backing materials in a methanol solution. Note that methanol in the anode solution significantly alters the interfacial tension characteristics. In addition, Divisek et al. developed detailed, multistep reaction models for both ORR and methanol oxidation as well as used the Stefan—Maxwell formulation for gas diffusion. Murgia et al. described a one-dimensional, two-phase, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymer membrane for a liquid-feed DMFC. 

For a case that one stable steady state exists transient temperature profiles calculated agree satisfactorily with the measurements. For a case of three steady states the situation is quite complicated. The model used describes propagation of the fronts however, apparently cannot describe front multiplicity. A detailed calculation of the two-dimensional steady state equations including also the radial dispersion terms indicates that the onedimensional model is a very rough approximation for the diffusion" regime. We expect that dynamic calculations with the one-phase two-dimensional model could explain multiplicity of the fronts. 

An orthogonal collocation method for elliptic partial differential equations is presented and used to solve the equations resulting from a two-phase two-dimensional description of a packed bed. Comparisons are made between the computational results and experimental results obtained from earlier work. Some qualitative discrimination between rival correlations for the two-phase model parameters is possible on the basis of these comparisons. The validity of the numerical method is shown by applying it to a one-phase packed-bed model for which an analytical solution is available problems arising from a discontinuity in the wall boundary condition and from the semi-infinite domain of the differential operator are discussed. 

This simple phase-incrementation idea, not particularly emphasized by the authors at the time, has more recently had a considerable impact on NMR methodology. First, it was made the basis of one of the standard methods for obtaining pure-phase two-dimensional spectra, replacing the undesirable phase-twist line shape with a pure absorption-mode signal. Secondly, it has provided a neat way to generate an extensive array of simultaneous soft radiofrequency pulses covering an... 

Surface science results have thrown new light on modified (chiral) metal surfaces, highlighting new phenomena such as complex adsorption phases, two-dimensional organization and the creation of extended chiral surfaces [307]. New strategies to immobilize an asymmetric catalyst onto a support (adsorption, encapsulation, tethering using a covalent bond and electrostatic interaction) also result in an... 

Analysis times can be almost an hour per injection by capillary GC. Fast-GC methods for the analysis of PAHs include the use of more selective stationary phases, two-dimensional GC (GC X GC), short narrow-bore capillary columns, selective detection, advanced MS detection techniques, and faster temperature programming. Faster column heating at 100°C min from 50 to 320°C has been achieved with resistive heating of a 5 m X 0.25 mm i.d. 5% phenyl methylpolysiloxane capillary column inside a metal tube. ° This apparatus was used to separate a mixture of the EPAis in under 4 min. Although geometric isomers were not resolved, the method could be an effective screening tool. With FID detection, LODs of 5 pg /rl were demonstrated for PAHs. 

Figure 29. Phase diagram of SDS/water (reproduced from [62]). (H, hexagonal phase two-dimensional monoclinic phase rhombo-hedral phase cubic phase tetragonal phase C, C and C" refer to different polymorphic varieties for the same SDS hydrate otherwise as for Fig. 14.)...

The solution NMR experiments were performed at 500 MHz using a Tecmag Apollo NMR spectrometer. Hypercomplex pure-phase two-dimensional spin exchange spectra were measured using the (90°-ti-90°-Xm-90°-t2) pulse sequence (7,8). 

Source From Determination of aR-trans- and 13-cis-retinoic acids by two-phase, two-dimensional thin layer chromatography in creams and by high-performance thin-layer chromatography in gel formulations, in J. Chromatogr. ... 

Seigel et al. [51] developed a multi-phase, two-dimensional model. The model was a two-dimensional steady state model, which studied transport limitations due to water build up in the cathode catalyst region. They considered water in three phases liquid, gas and dissolved (membrane phase). They found that treating the catalyst layer as a very thin interface imderestimates the transport limitations due to water build-up. Hence, they modeled the catalyst layer as a finite region. Their model showed that 20-40% of the water building up at the cathode catalyst layer comes fi om water which is transported across the membrane. This problem may be coimteracted by applying a pressure differential to force back diffusion of water, i.e., from cathode to anode. 

FIGURE 1.38 Lipid monolayer phases (two-dimensional) (monolayer phases are dependent on both molecular structure and temperature). 

We already described the determination of all-rrons- and 13-c/s-retinoic acid in gel formulations on silica gel plates as described by DePaolis (15). Cream samples contain more interfering excepients and need a two-phase, two-dimensional thin-layer chromatography. The plates were divided into two parts, one C g strip and one silica gel part. The sample is applied on the C g strip and eluted with 80% ethanol in water. This reversed-phase step is a necessary cleanup to separate cream excipients from the isomers of retinoic acid. In the adsorption mode the silica part of the plate is eluted with diethyl ether cyclohexane acetone glacial acetic acid (40 60 2 1, by vol), allowing a separation between... 

Figure 1.2 Examples of ordering in soft materials. A nematic liquid crystal has no long-range translational order, but the molecules (here shown as ellipses) are orientationally ordered. The lamellar phase has one-dimensional translational order, the hexagonal phase two-dimensional translational order and cubic phases three-dimensional orientational order. The layers in the lamellar phase can be formed from molecules (smectic phase) or amphiphilic bilayers. A hexagonal structure can be formed by disc-like molecules (then being termed columnar phase) or rod-like micelles. The cubic phase shown here is formed by spherical micelles. Bicontinuous cubic structures are also found (see Fig. 4.25d)...

LCPs exhibit multiple thermal transitions. The transitions of greatest interest are those of the crystalline to nematic phase (three dimensional order to two dimensional order) and nematic to isotropic phase (two dimensional order to disorder). 

Yu KT, Yuan XG, You XY, Liu CJ (1999) Computational fluid-dynamics and experimental verification of two-phase two-dimensional flow on a sieve column tray. Chem Eng Res Des... 

To examine this hypothesis, the two-phase, two-dimensional particle bed model has been used to simulate the two matched systems (Chen et al., 2001). The geometric arrangement for the simulations is shown in Figure 16.6. The gas flux was 217m/in both cases. Instantaneous pressure and void fraction measurements were recorded for data analysis at the points A, B, C and D. The initial conditions corresponded to beds at the point of minimum fluidization gas rates were then set to 2C/m/, resulting in the development of freely bubbling beds. The results reported below are representative of all the measured data, and confirm the equivalence of fluidization quality in the two matched beds. 

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