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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 4736-4742 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate–adsorbate interactions in the Brag–Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with εaa as the adsorbate–adsorbate interaction parameter, the comparisons for different values of εaa*=εaaz/2kT, and number of sites per cage, n, illustrate that for −1〈εaa*〈0 and n≥10, the adsorption isotherms and heats of adsorption predicted with the two approaches are similar. In general, the deviation between the LMFA and GMFA is greater for smaller n and less sensitive to n for εaa*〉0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent εaa) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 4576-4586 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Grand canonical Monte Carlo simulations have been carried out for dumbbell (D) and spherical (S) models of N2 and Br2 in single-walled carbon nanotubes, with nanotube radii ranging from 4.029 to 25.142 Å. The radial density distributions between models S and D in the nanotube were compared under similar bulk conditions. For gas and liquid bulk densities of N2, differences between the pore density distributions for the S and D models in the nanotube were small and the inclusion of quadrupole moments to model D had little effect. In contrast, the density distributions between the S and D models for Br2 showed greater differences for the bulk liquid case. Angular density distributions show that molecules adjacent to the nanotube wall orient parallel to the wall. At high densities the wall layer contains a mixture of wall-parallel and wall-perpendicular orientations, giving rise to a shoulder in the density distributions for Br2. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 8714-8721 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Using a lattice model for adsorption in microporous materials, pure component adsorption isotherms are obtained within a mean field approximation for methane at 300 K and xenon at 300 and 360 K in zeolite NaA. It is argued that the increased repulsive adsorbate–adsorbate interactions at high coverages must play an important role in determining the adsorption behavior. Therefore, this feature is incorporated through a "coverage-dependent interaction" model, which introduces a free, adjustable parameter. Another important feature, the site volume reduction, has been treated in two ways: a van der Waal model and a 1D hard-rod theory [van Tassel et al., AIChE J. 40, 925 (1994)]; we have also generalized the latter to include all possible adsorbate overlap scenarios. In particular, the 1D hard-rod model, with our coverage-dependent interaction model, is shown to be in best quantitative agreement with the previous grand canonical Monte Carlo isotherms. The expressions for the isosteric heats of adsorption indicate that attractive and repulsive adsorbate–adsorbate interactions increase and decrease the heats of adsorption, respectively. It is concluded that within the mean field approximation, our simple model for repulsive interactions and the 1D hard-rod model for site volume reduction are able to capture most of the important features of adsorption in confined regions. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 365-372 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The approximate equations of Hassler and Brunner and of van Domselaar are often used to deduce the capillary pressure curve of a porous medium from centrifuge data. The use of these equations restricts the centrifuge method to short samples. Also, these equations require differentiation of data. We report here methods to determine the capillary pressure curve by the midpoint and least-squares solution of the fundamental equation, relating the average saturation S1 of liquid in the porous medium to the capillary pressure Pc1 at the end of the sample nearest the axis of rotation. The methods do not require differentiation of data and are not restricted to short samples. We introduce and evaluate an approximation based on an exact result derived by Rajan. This new approximation requires the same inputs as do the Hassler-Brunner and the van Domselaar approximations, but it is accurate over a wider range of sample sizes. In addition, an approximate solution which can be used to estimate capillary pressure curves for long cores is developed.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 313-322 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Transient temperature profiles in multilayer slabs are predicted, by simultaneously solving Maxwell's equations with the heat conduction equation, using Galerkin finite elements. It is assumed that the medium is homogeneous and has temperature-dependent dielectric and thermal properties. The method is illustrated with applications involving the heating of food and polymers with microwaves. The temperature dependence of dielectric properties affects the heating appreciably, as is shown by comparison with a constant property model.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 1789-1800 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The finite element method was used to model microwave thawing of pure-water and 0.1-M NaCl cylinders. The electromagnetic field was described by Maxwell's equations with temperature-dependent dielectric properties, while the heat equation, coupled with the Stefan and Robin conditions, was used to describe the thawing process. An additional equation for the frozen volume fraction was used, when necessary, to account for the presence of a mushy region. Two microwave frequencies, 915 MHz and 2,450 MHz, were examined and the microwave radiation was assumed to be radially isotropic and normal to the surface of the cylinder. Results show that a two-phase mushy region may exist, and an additional thawing front may appear at the center of the cylinder. Salt cylinders have a higher dielectric loss than pure-water cylinders and therefore thaw more quickly. Internal resonance occurs when the wavelength of the radiation is a harmonic of the cylinder radius. Resonance increases power deposition and expedites the thawing process. The onset of resonance alters thawing times and complicates the development of heuristic rules for microwave thawing.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 40 (1994), S. 1268-1272 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 38 (1992), S. 1577-1592 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Transient temperature profiles for long rods of lossy dielectric materials with thermally-dependent dielectric properties exposed to uniform plane waves are obtained. Maxwell's equation and the heat equation are simultaneously solved using the finite element method to predict the power absorbed and the resulting temperature rise in samples of square and circular cross-section. Following the method introduced recently, we derive an exact radiation boundary condition which is independent of the rod cross-section. For a cylindrical sample, the boundary condition is imposed on the cylinder itself. For a square rod, the boundary condition is imposed on a cylinder containing the rod. The temperature dependence of dielectric properties and sample dimensions appreciably influence heating patterns. For square samples, the edges focus radiation, causing preferential heating at the edges. This effect is pronounced for larger samples. In addition, the incident wave polarization influences the heating of the rod. For waves where the electric field is polarized along the long axis of the sample (TMz polarization) the power absorbed is higher than when the electric field is perpendicular to the axis (TEz polarization). A case involving runaway heating is also investigated.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 40 (1994), S. 1433-1439 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is generally believed that oil samples heat faster in a microwave oven than do water samples of the same mass. For sufficiently large and thich samples this conventional wisdom is indeed correct, but this trend can be far from true in smaller samples. In a commercially-made home microwave oven, we observed that with decreasing sample size the heating rate of a water sample increases much faster than that of an oil sample. At 50 g the heating rate of a water sample is several times greater than that of an oil sample. Additionally, in studies of cylindrical samples in a customized oven having a unidirectional microwave source, the heating rate of water samples smaller than 2.4 cm in radius is greater than that of oil samples and is a strongly oscillatory increasing function of decreasing sample radius. Combining Maxwell's theory of microwave penetration and the heat conduction equation, we show that this previously unreported oscillatory heating behavior results from the added power absorbed by samples due to resonant absorption of microwaves. The added power arises from standing waves produced by internally reflected microwaves. This effect is small for oil because only 3% of the microwave power is reflected at an oil-air interface. On the other hand, 64% is reflected at a water-air interface, which causes strong resonant heating. Our findings might prove to be useful for future consumer food product development or oven design.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 43 (1997), S. 615-624 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Resonant power absorption is an important phenomenon during microwave heating. The resonances that occur when plane electromagnetic waves are incident on infinitely long cylinders and slabs are investigated as a function of sample dimensions. For cylinders two kinds of incident waves are studied: TMz when the electric field is oriented along the axis of the cylinder and TEz when the magnetic field is oriented along the axis. At a resonant condition the overage power absorbed by the sample is a local maximum. Due to attenuation within the sample the resonances decrease in intensity as the sample size increases. Using the dielectric properties of water, resonances are found to be a function of the ratio of the sample dimension to the wavelength of radiation, λs, in the sample. For slabs of thickness L and integer values of n, resonances occurred at L/λs = 0.5n; for cylinders of diameter D, resonances occurred at D/λs = 0.5n - 0.257. The generality of these relations to predict resonances in other food samples are shown using existing dielectric data. Resonances in cylinders for both polarizations occurred at similar radii. However, the radius at which the first resonance occurred for the TMz case was absent in the TEz case.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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