Solid modeling

Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream.

Neville, I.M. and Seider, W.D., 1980. Coal pre-treatment - extensions of ELOWTRAN to model solids-handling equipment. Computers and Chemical Engineering, 4, 49. 

Figure 3 Compositional dependence of the stacking fault energy calculated from the rigid-band model (solid line) compared with the more accurate results from the LKKR-CPA calculation (dashed line) for the Al-Cu alloy system.

C.G. Vayenas, and S. Brosda, Electrochemical promotion Experiment, rules and mathematical modeling, Solid State Ionics, submitted (2001). 

Tersoff, J., Modeling Solid-State Chemistry Interatomic Potentials for Multicomponent Systems," Phys. Rev. B, Vol. 39, No. 8,1989, pp. 5566-5568. 

Figure 11.6 Model (solid) versus experiments (points) for the temperature profile of an integrated SMR reactor.

Chemists use a variation on the ball-and-stick model to depict more clearly the three-dimensional character of molecules, as shown for methane in Figure 9-1 Icf. The central carbon atom is placed in the plane of the paper, hi these models, solid lines represent bonds lying in the plane of the paper, solid wedges represent bonds that protmde outward from the plane of the paper, and dashed wedges represent bonds extending backward, behind the plane. 

Fig. 1. Example of a functional estimation problem evolution of the model (solid line) and comparison with the real function (dashed line) as more data (asterisks) become available.

Main axis experimental conversions ( ) intrinsic kinetic model (solid line) kinetic model + mass transfer kinetics (dashed line). Secondary axis variation of computed k,o with flow rate. 

Figure 5.21 Comparison of reaction product concentrations (symbols) and model (solid line) as a function of residence time given in [6J. Toluene-2,4-diisocyanate (TDI) ...

Figure 12.9 The excitation-power dependence of the emission count rate of single DMPBI nanocrystals (dots), and a saturation curve calculated from a two-level model (solid line). One count rate value to one laser power was calculated as an average of 30 nanocrystals. S. Masuo, A. Masuhara, T. Akashi, M. Muranushi,...

Fig. 6. Excess chemical potential of hard-sphere solutes in SPC water as a function of the exclusion radius d. The symbols are simulation results, compared with the IT prediction using the flat default model (solid line). (Hummer et al., 1998a)...

Beck, T. L., Quantum path integral extension of Widom s test particle method for chemical potentials with application to isotope effects on hydrogen solubilities in model solids, J. Chem. Phys. 1992, 96, 7175-7177... 

Differential pressure measurements were made between several vertical elevations within the bed. The probability density function of the cold model and combustor gave very close agreement (Fig. 35). The solid fraction profiles were obtained from the vertical pressure profile with a hydrostatic assumption. The cold model solid fraction profile showed very close agreement with data taken from pressure taps in two different locations within the combustor (Fig. 36). The solid fraction shows a... 

Ishii and Murakami (1991) evaluated the CFB scaling relationships of Horio et al. (1989) using two cold CFB models. Solids flux, pressure drop, and optical probe measurements were used to measure a large number of hydrodynamic parameters to serve as the basis for the comparison. Fair to good similarity was obtained between the beds. Dependent hydrodynamic parameters such as the pressure drop and pressure fluctuation characteristics, cluster length and voidage, and the core diameter were compared between the two beds. The gas-to-solid density ratio was not varied between the beds. As seen in Table 7, the dimensionless solids flux decreased as the superficial velocity was increased because the solids flux was held constant. 

Figure 2. Comparison of adsorption isotherms based on the present model (solid lines) with the statistical theory of Scheutjens and Fleer (symbols). The following values of the parameters were used...

Fig. 2.25 Temporal mean (left) and standard deviation (right) of the zonal mean volatilisation rate over 10 years [kg/(kg s)]. Dashed lines show volatilisation rates derived from zonal mean SST and wind speed (denoted as zonally averaging model). Solid lines show volatilisation rates derived from zonally resolved SST and wind speed, which were zonally averaged afterwards (denoted as zonally resolved model).

The performance of a reactor for a gas-solid reaction (A(g) + bB(s) -> products) is to be analyzed based on the following model solids in BMF, uniform gas composition, and no overhead loss of solid as a result of entrainment. Calculate the fractional conversion of B (fB) based on the following information and assumptions T = 800 K, pA = 2 bar the particles are cylindrical with a radius of 0.5 mm from a batch-reactor study, the time for 100% conversion of 2-mm particles is 40 min at 600 K and pA = 1 bar. Compare results for /b assuming (a) gas-film (mass-transfer) control (b) surface-reaction control and (c) ash-layer diffusion control. The solid flow rate is 1000 kg min-1, and the solid holdup (WB) in the reactor is 20,000 kg. Assume also that the SCM is valid, and the surface reaction is first-order with respect to A. 

Figure 2. Pressure of the NCQM as a function of the chemical potential for the separable model (solid line) compared to a three-flavor (dotted line) and a two-flavor (dashed line) bag model. All models have the same critical chemical potential /j,c = 330 MeV for (light) quark deconfinement.

The first MC (16) and MD (17) studies were used to simulate the properties of single particle fluids. Although the basic MC (11,12) and MD (12,13) methods have changed little since the earliest simulations, the systems simulated have continually increased in complexity. The ability to simulate complex interfacial systems has resulted partly from improvements in simulation algorithms (15,18) or in the interaction potentials used to model solid surfaces (19). The major reason, however, for this ability has resulted from the increasing sophistication of the interaction potentials used to model liquid-liquid interactions. These advances have involved the use of the following potentials Lennard-Jones 12-6 (20), Rowlinson (21), BNS... 

Fig. 5. Complex behavior of a batch chromatographic reactor system. After an inlet step, three steady states were detected at the reactor outlet. Experimental data for acetic acid (filled circle), ethanol (x), water (+) and ethyl acetate (open circle) were successfully fitted by a mathematical model (solid and dashed lines). (Reprinted with permission from [159])... 

Figure 2.4. The normalized rate constants for proton transfer as a function of the negative enthalpy change (—AFkcal/mol) for the solvent butanenitrile. Experimental data = squares. The BH model = solid curve with Es — 1.5kcal/mol, Ea — l.Okcal/mol, q = 200 cm-1, and T — 298 K. 

The papers of Mallon and Ray [98, 123] can be regarded as the state of the art in understanding and modelling solid-state polycondensation. They assumed that chain ends, catalysts and by-products exist solely in the amorphous phase of the polymer. Because of the very low mobility of functional groups in the crystalline phase, the chemical reactions are modelled as occurring only in the amorphous phase. Additionally, the diffusion of by-products is hindered by the presence of crystallites. The diffusivity of small molecules was assumed to be proportional to the amorphous fraction. Figure 2.32 shows the diffusion coefficients for the diffusion of EG and water in solid PET. 

The experimental data (dots) are reproduced very well within the framework of the hydraulic permeation model (solid lines). For the basic case with zero gas pressure gradient between cathode and anode sides, APe = 0, the model (solid line) predicts uniform water distribution and constant membrane resistance at )p < 1 A cm and a steep increase in R/R beyond this point. These trends are in excellent agreement with experimental data (open circles) for Nafion 112 in Figure 6.15. A finife positive gas pressure gradient, APs = P/ - P/ > 0, improves the internal humidification of fhe membrane, leading to more uniform water distribution and significantly reduced dependence of membrane resistance on X. The latter trends are consistent with the predictions of fhe hydraulic permeation model. 

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