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Cubic Equations (cubic + equation)
Selected AbstractsGeneration and forward displacement analysis of two new classes of analytic 6-SPS parallel manipulatorsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2001Xianwen Kong Analytic manipulators are manipulators with a characteristic polynomial of fourth degree or lower. Using the component approach to generate analytic 6-SPS parallel manipulators (PMs), the generation process is reduced to the generation of analytic components for 6-SPS PMs. Two new classes of analytic components for 6-SPS PMs are generated at first. Then, two new classes, IX and X, of analytic 6-SPS PMs are generated. The forward displacement analysis (FDA) of the new analytic 6-SPS PMs is also performed. The FDA of the 6-SPS PMs of class IX is reduced to the solution of one univariate cubic equation and two univariate quadratic equations, in sequence, while that of the 6-SPS PMs of class X is reduced to the solution of three univariate quadratic equations in sequence. Both of the new analytic 6-SPS PMs have at most eight assembly modes. © 2001 John Wiley & Sons, Inc. [source] Determination of cubic equation of state parameters for pure fluids from first principle solvation calculationsAICHE JOURNAL, Issue 8 2008Chieh-Ming Hsieh Abstract A new method for estimation of parameters in cubic equations of state from ab initio solvation calculations is presented. In this method, the temperature-dependent interaction parameter a(T) is determined from the attractive component of solvation free energy, whereas the volume parameter b is assumed to be that of solvation cavity. This method requires only element-specific parameters, i.e., atomic radius and dispersion coefficient, and nine universal parameters for electrostatic and hydrogen-bonding interactions. The equations of state (EOS) parameters so determined allow the description of the complete fluid phase diagram, including the critical point. We have examined this method using the Peng,Robinson EOS for 392 compounds and achieved an accuracy of 43% in vapor pressure, 17% in liquid density, 5.4% in critical temperature, 11% in critical pressure, and 4% in critical volume. This method is, in principle, applicable to any chemical species and is especially useful for those whose experimental data are not available. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Hydrate phase equilibria of a near critical fluid: Effect of inhibition and separationAICHE JOURNAL, Issue 7 2001Kasper K. Østergaard The hydrate phase boundary of a near critical fluid (NCF) was measured at 275,289 K in the presence of distilled water, synthetic formation water, and synthetic formation water with 10.41 wt. % methanol. The results agreed well with the predictions of an in-house model, based on a cubic equation of state and statistical thermodynamics. To simulate a typical oil/gas production scenario, the NCF was flashed at 298.1 K and 17.189 MPa, and the resulting liquid was subsequently flashed at 298.0 K and 4.089 MPa. Hydrate free zones of the resulting liquid fractions were measured to investigate the physical separation effect on the hydrate phase boundary. The in-house thermodynamic model was used to simulate the separators conditions and to predict the hydrate free zone of the resulting liquid and the vapor fractions. The predictions agreed closely with the experimental data, demonstrating reliability of the thermodynamic model. The results also showed that the hydrate phase boundaries of the vapor and liquid phases, which resulted from physical separation, are similar to that of the NCF. [source] Structure and drug release in a crosslinked poly(ethylene oxide) hydrogelJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 5 2007Boris Y. Shekunov Abstract Hydrogels are a continuously expanding class of pharmaceutical polymers designed for sustained or controlled drug release. The structure and intermolecular interactions in such systems define their macroscopic properties. The aim of this study was to investigate the mechanism of swelling, drug impregnation, and drug release from poly(ethylene oxide) (PEO) gel crosslinked by urethane bonds. A combination of SAXS/WAXS/SANS techniques enabled us to determine the phase transition between lamellar and extended gel network, and to apply different descriptions of crystallinity, based on lamellar and crystal lattice structures. It is shown that even low (1,7% w/w) loading of model drugs acetaminophen and caffeine, produced significant disorder in the polymer matrix. This effect was particularly pronounced for acetaminophen due to its specific ability to form complexes with PEO. The drug-release profiles were analyzed using a general cubic equation, proposed for this work, which allowed us to determine the gel hydration velocity. The results indicate that the release profiles correlate inversely with the polymer crystallinity. © 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 96: 1320,1330, 2007 [source] CO2 Density-Raman Shift Relation Derived from Synthetic Inclusions in Fused Silica Capillaries and Its ApplicationACTA GEOLOGICA SINICA (ENGLISH EDITION), Issue 5 2009Yucai SONG Abstract: The densities of CO2 inclusions in minerals are commonly used to determine the crystallizing conditions of the host minerals. However, conventional microthermometry is difficult to apply for inclusions of small size (< 5,10 ,m) or low density. Raman analysis is an alternative method for determining CO2 density, provided that the CO2 density,Raman shift relation is known. This study aims to establish this CO2 density,Raman shift relation by using CO2 inclusions synthesized in fused silica capillaries. By using this newly-developed synthetic technique, we formed pure CO2 inclusions, and their densities were determined by microthermometry. The Raman analysis showed that the relation between CO2 density (D in g/cm3) and the separations (? in cm,1) between the two main bands (i.e. Fermi diad bands) in CO2 Raman spectra can be represented by a cubic equation: D (g/cm3)=0.74203(,0.019?3+5.90332?2,610.79472?+21050.30165),3.54278 (r2=0.99920). Our calculated D value for a given ? is between those obtained from two previously-reported equations, which were derived from different experimental methods. An example was given in this study to demonstrate that the densities of natural CO2 inclusions that could not be derived from microthermometry could be determined by using our method. [source] Determination of cubic equation of state parameters for pure fluids from first principle solvation calculationsAICHE JOURNAL, Issue 8 2008Chieh-Ming Hsieh Abstract A new method for estimation of parameters in cubic equations of state from ab initio solvation calculations is presented. In this method, the temperature-dependent interaction parameter a(T) is determined from the attractive component of solvation free energy, whereas the volume parameter b is assumed to be that of solvation cavity. This method requires only element-specific parameters, i.e., atomic radius and dispersion coefficient, and nine universal parameters for electrostatic and hydrogen-bonding interactions. The equations of state (EOS) parameters so determined allow the description of the complete fluid phase diagram, including the critical point. We have examined this method using the Peng,Robinson EOS for 392 compounds and achieved an accuracy of 43% in vapor pressure, 17% in liquid density, 5.4% in critical temperature, 11% in critical pressure, and 4% in critical volume. This method is, in principle, applicable to any chemical species and is especially useful for those whose experimental data are not available. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Solution technique for pure-component phase equilibria near the critical pointAICHE JOURNAL, Issue 4 2006L. N. Stapley Abstract An iterative technique is presented for determining pure-component phase equilibrium that essentially does not depend on initiation. The technique uses both the real and the complex conjugate root information obtained from the analytical solution to cubic equations of state to extend substantially the domain of convergence. The technique is robust and effective close to the critical point. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source] Volume-translated equations of state: Empirical approach and physical relevanceAICHE JOURNAL, Issue 6 2003Leonid V. Yelash The volume translation technique is widely applied in chemical engineering modeling of phase behavior and thermodynamic properties. This empirical correction of the molar volume improves the correlation of liquid densities when cubic equations of state are employed. Based on a recently proposed method of analyzing equations of state, the influence of the volume translation on the properties obtained from an equation of state, such as virial coefficients, as well as on the phase behavior, critical properties, the isobaric thermal expansion coefficient, and the heat capacities of pure substances is investigated. The influence of different kinds of temperature-dependent volume translations is investigated and compared to approaches that originate from theoretical considerations. The investigation shows that empirical as well as theoretical approaches for the development of equations of state can exhibit nonphysical behavior. However, the understanding of the reasons for such problems can help to develop reliable equations of state based on both kinds of method. [source] Calculation of densities from cubic equations of stateAICHE JOURNAL, Issue 4 2002Ulrich K. Deiters Some cubic equations of state can eventually have unphysical solutions for the molar volume. The conditions for this phenomenon are discussed. The computational accuracy and computing time requirements of the analytical root finding method (Cardano's formula) are investigated. A new, faster iterative root finder for cubic polynomials is proposed. [source] A novel equation of state (EOS) for prediction of solute solubility in supercritical carbon dioxide: Experimental determination and correlationTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2009Sh. Jafari Nejad Abstract Solubility data of organophosphorous metal extractants in supercritical fluids (SCF) are crucial for designing metal extraction processes. We have developed a new equation of state (EOS) based on virial equation including an untypical parameter as BP/RT, reduced temperature and pressure for prediction of solute solubility in supercritical carbon dioxide (SC CO2). Solubility experimental data (solubility of tributylphosphate in SC CO2) were correlated with the two cubic equations of state (EOS) models, namely the Peng,Robinson EOS (PR-EOS) and the Soave,Redlich,Kwong EOS (SRK-EOS), together with two adjustable parameter van der Waals mixing and combining rules and our proposed EOS. The AARD of our EOS is significantly lower than that obtained from the other EOS models. The proposed EOS presented more accurate correlation for solubility data in SC CO2. It can be employed to speed up the process of SCF applications in industry. Les données de solubilité d'extractants de métaux organo-phosphorés dans des fluides supercritiques (FSC) sont cruciales pour concevoir des processus d'extraction des métaux. Nous avons développé une nouvelle équation d'état (ÉÉ) basée sur une équation d'état du viriel comprenant un paramètre atypique tel que la température et la pression réduite pour la prédiction de la solubilité du soluté dans du dioxyde de carbone supercritique. Les données expérimentales de solubilité (solubilité du phosphate de tributyle dans CO2 SC) ont été corrélées avec les deux modèles d'équations d'état cubiques, soit l'ÉÉ Peng,Robinson (ÉÉ-PR) et l'ÉÉ Soave,Redlich,Kwong (ÉÉ-SRK), avec deux paramètres ajustables, les règles de mélange et de combinaison van der Waals et notre ÉÉ proposée. L'AARD de notre ÉÉ est significativement plus faible que celui obtenu à partir des autres modèles d'ÉÉ. L'ÉÉ proposée présentait une corrélation plus exacte pour les données de solubilité dans le CO2 SC. Elle peut être employée pour accélérer les processus des applications de FSC dans l'industrie. [source] | ||||||||||