999 resultados para Van der Pol equation
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Mode of access: Internet.
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Mode of access: Internet.
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The title-pages of vol. 30-33 vary slightly.
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.
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The caffeine solubility in supercritical CO2 was studied by assessing the effects of pressure and temperature on the extraction of green coffee oil (GCO). The Peng-Robinson¹ equation of state was used to correlate the solubility of caffeine with a thermodynamic model and two mixing rules were evaluated: the classical mixing rule of van der Waals with two adjustable parameters (PR-VDW) and a density dependent one, proposed by Mohamed and Holder² with two (PR-MH, two parameters adjusted to the attractive term) and three (PR-MH3 two parameters adjusted to the attractive and one to the repulsive term) adjustable parameters. The best results were obtained with the mixing rule of Mohamed and Holder² with three parameters.
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This paper compares the critical impeller speed results for 6 L Denver and Wemco bench-scale flotation cells with findings from a study by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2007. Evaluation of solids suspension in a pilot-scale mechanical flotation cell: the critical impeller speed. Minerals Engineering 20,233-240; Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] conducted in a 125 L Batequip flotation cell. Understanding solids suspension has become increasingly important due to dramatic increases in flotation cell sizes. The critical impeller speed is commonly used to indicate the effectiveness of solids suspension. The minerals used in this study were apatite, quartz and hematite. The critical impeller speed was found to be strongly dependent on particle size, solids density and air flow rate, with solids concentration having a lesser influence. Liquid viscosity was found to have a negligible effect. The general Zwietering-type critical impeller speed correlation developed by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] was found to be applicable to all three flotation machines. The exponents for particle size, solids concentration and liquid viscosity were equivalent for all three cells. The exponent for solids density was found to be less significant than that obtained by the previous authors, and to be consistent with values reported in the general literature for stirred tanks. Finally, a new dimensionless critical impeller speed correlation is proposed where the particle size is divided by the impeller diameter. This modified equation generally predicts the experimental measurements well, with most predictions within 10% of the experimental. (C) 2009 Elsevier Ltd. All rights reserved.
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A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.
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Solubilities of red 153, (3-[[4-[[5,6(or 6,7)-dichloro-2-benzothiazolyl]azo]phenyl]ethylamino]propanenitrile), an azo compound, and disperse blue1 (1,4,5,8-tetraaminoantraquinone) in supercritical carbon dioxide (SC CO(2)) were measured at T = (333.2 to 393.2) K over the pressure range (12.0 to 40.0) MPa by a flow type apparatus. The solubility of red 153 (0.985. 10(-6) to 37.2. 10(-6)) in the overall region of measurements is found to be significantly higher than that of disperse blue 1 (1.12.10(-7) to 4.89.10(-7)). The solubility behavior of disperse red 153 follows the general solubility trend displayed by disperse dyes with a crossover pressure at about 20 MPa. On the other hand, blue 1, which is a disperse anthraquinone dye, exhibits unexpected behavior not recorded previously there is no crossover pressure at the temperature and pressure ranges studied, and the dye's solubility at T = 333.2 K practically does not increase with pressure. To the best of our knowledge, there are no previous measurements of blue 1 solubility in SC CO(2) reported in the literature. The experimental data were correlated by using the Soave Redlich Kwong equation of state (EoS) with the one-fluid van der Waals mixing rule, and an acceptable correlation of the solubility data for both dyes was obtained.
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v. 1 no.1
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v. 3
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v. 2
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v. 1 no.2