Three-dimensional model phases phase

Ben-Yoseph, E., Hartel, R.W., and Howling, D. (2000). Three-Dimensional Model of Phase Transition of Thin Sucrose Films During Drying, J. Food Eng. 44(1), 13-22. 

The correlation between log P and log k of standard compounds obtained for the molecular form of the analyte can be used to predict the maximum capacity ratios, and for the ionized form can be used to predict the minimum capacity ratios. Furthermore, these capacity ratios have been used to predict capacity ratios in eluents of different pH values. Drug analysis requires a three-dimensional model phase to take into account the contribution of the van der Waals energy, which is related to the contact surface area between the anal5de and the model phase. 

Because of the expanded scale and need to describe additional physical and chemical processes, the development of acid deposition and regional oxidant models has lagged behind that of urban-scale photochemical models. An additional step up in scale and complexity, the development of analytical models of pollutant dynamics in the stratosphere is also behind that of ground-level oxidant models, in part because of the central role of heterogeneous chemistry in the stratospheric ozone depletion problem. In general, atmospheric Hquid-phase chemistry and especially heterogeneous chemistry are less well understood than gas-phase reactions such as those that dorninate the formation of ozone in urban areas. Development of three-dimensional models that treat both the dynamics and chemistry of the stratosphere in detail is an ongoing research problem. 

Figure 4-13 shows an example from a three-dimensional model simulation of the global atmospheric sulfur balance (Feichter et al, 1996). The model had a grid resolution of about 500 km in the horizontal and on average 1 km in the vertical. The chemical scheme of the model included emissions of dimethyl sulfide (DMS) from the oceans and SO2 from industrial processes and volcanoes. Atmospheric DMS is oxidized by the hydroxyl radical to form SO2, which, in turn, is further oxidized to sulfuric acid and sulfates by reaction with either hydroxyl radical in the gas phase or with hydrogen peroxide or ozone in cloud droplets. Both SO2 and aerosol sulfate are removed from the atmosphere by dry and wet deposition processes. The reasonable agreement between the simulated and observed wet deposition of sulfate indicates that the most important processes affecting the atmospheric sulfur balance have been adequately treated in the model. 

The basic scheme for the numerical solution is the same as that used for the 1 -D model, except that in this case the solid temperature field used to solve the DAE system for each monolith channel must be calculated from the three-dimensional solid-phase energy balance equation. The three-dimensional energy balance equation can be solved by a nonlinear finite element solver (such as ABAQUS) for the solid-phase temperature field while a nonlinear finite difference solver for the DAE system calculates the gas-phase temperature and... 

A Three-Dimensional, Three-Phase Automatic History-IVlatching Model Reliability of Parameter Estimates... 

Tan, T.B. and N. Kalogerakis, "A Three-dimensional Three-phase Automatic History Matching Model Reliability of Parameter Estimates", J. Can Petr. Technology, 31(3), 34-41 (1992). 

In Fig. 30, a three-dimensional model is presented in which only the organic phases are shown. Hexagonal plates of MM alternate with pleated sheets of CP. The hydrophobic sides of MM are facing each other and encase the mineral phase. The relationship between hydrophobic bonding and accessible surface area in proteins, and the effect of polar and non-polar side groups on free energy values has recently been discussed246. For informations on hydrophobicity in protein systems see Refs.247-252. ... 

A three-dimensional model of a ternary phase diagram with a ternary eutectic. T-i corresponds to the AB binary eutectic temperature, T2 to the AC binary eutectic temperature, T3 to the BC binary eutectic temperature, and T4 to the ABC ternary eutectic temperature. 

Three-Dimensional Model. On the other hand, if the interfacial layer is thick enough compared to the molecular size of SRIOI and if SRIOI molecules adsorbed on the interface are weakly oriented, the rotational motions of SRIOI take place in three dimensions, similar to those in a bulk phase. If this is the case, the contribution of the fluorescence with the excited dipole moment of SR 101 directed along the z-axis cannot be neglected, so that the time profile of the total fluorescence intensity must be proportional to / (0 + 2/i(t). Thus, fluorescence dynamic anisotropy is given by Equation (15), as is well known for that in a macroscopically isotropic system [10,13] ... 

Figure 3.39. Water concentration in an interdigitated PEM fuel cell structure, for three planes at x-values corresponding to the flow channel exit (a top left), the middle (b top right) and the entrance (c bottom left). In each pair of pictures, the y-z plots depict the hydrogen side at the top (GDL is lower bar) and the oxygen side at the bottom (GDL is upper bar). The cell current is at its maximum (about 0.8 A cm" ). (From M. Hu et al, (2004). Three dimensional, two phase flow mathematical model for PEM fuel ceU Part II. Analysis and discussion of the internal transport mechanism. Energy Conversion Management. 45,1883-1916. Used with permission from Elsevier.)...

Hu, M., Zhu, X., Wang, M., Gu, A., Yu, L. (2004). Three dimensional, two phase flow mathematical model for PEM fuel cell Parts I and II. Analysis and discussion of the internal transport mechanism. Energy Conversion Management 45, 1861-... 

The PRISMA model developed by Nyiredy and co-workers (Nyiredy et al., 1985 Dallenbach-Tolke et al., 1986 Nyiredy and Fater, 1995 Nyiredy, 2002) for use in Over Pressured Layer Chromatography is a three-dimensional model that correlates solvent strength and the selectivity of different mobile phases. Silica gel is used as the stationary phase and solvent selection is performed according to Snyder s solvent classification (Tab. 4.7). 

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