A simple extension of cubic equations of state(EOS)to polymer systems has been proposed.The So-ave-Redlich-Kwong(SRK)EOS was taken as a prototype to be used to describe the PVT behavior of polymer melts in a wide temp...A simple extension of cubic equations of state(EOS)to polymer systems has been proposed.The So-ave-Redlich-Kwong(SRK)EOS was taken as a prototype to be used to describe the PVT behavior of polymer melts in a wide temperature and pressure range.Combined with a modified Huron-Vidal gE-mixing rule it was applied for modeling vapor-liquid equilibria of polymer-solvent solutions and the solubility of supercritical gases in polymer melts.Satisfactory results are obtained.展开更多
A method of slope reliability analysis was developed by imposing a state equation on the limit equilibrium theory, given the basis of a fixed safety factor technique. Among the many problems of reliability analysis, t...A method of slope reliability analysis was developed by imposing a state equation on the limit equilibrium theory, given the basis of a fixed safety factor technique. Among the many problems of reliability analysis, the most important problem is to find a performance function. We have created a new method of building a limit state equation for planar slip surfaces by applying the mathematical cusp catastrophe theory. This new technique overcomes the defects in the traditional rigid limit equilibrium theory and offers a new way for studying the reliability problem of planar slip surfaces. Consequently, we applied the technique to a case of an open-pit mine and compared our results with that of the traditional approach. From the results we conclude that both methods are essentially consistent, but the reliability index calculated by the traditional model is lower than that from the catastrophic model. The catastrophe model takes into consideration two possible situations of a slope being in the limit equilibrium condition, i.e., it may or may not slip. In the traditional method, however, a slope is definitely considered as slipping when it meets the condition of a limit equilibrium. We conclude that the catastrophe model has more actual and instructive importance compared to the traditional model.展开更多
A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous ...A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous general equations is that it is in simple form, and is easy to manipulate mathematically.展开更多
Alpha functions of Soave-Redlich-Kwong （SRK） equation of state proposed by Soave, Twu, and Luo were different in mathematic tendency. They were compared in modeling methane-alkanes equilibria with van der Waals mixi...Alpha functions of Soave-Redlich-Kwong （SRK） equation of state proposed by Soave, Twu, and Luo were different in mathematic tendency. They were compared in modeling methane-alkanes equilibria with van der Waals mixing rule and Modified Huron-Vidal （MHV1） mixing rule, respectively. Results showed that Luo＇s alpha function was a little more accurate than Soave＇s, and Twu＇s alpha function lacked accuracy in modeling methane-alkanes equilibrium. SRK equation of state was expanded as virial form, and then the equivalent terms were contrasted with terms of virial equation of state. Results showed that Soave＇s and Luo＇s alpha functions matched the tendency of virial coefficient better than Twu＇s, and Luo＇s alpha function matched better than Soave＇s in wide temperature range, which sustained the conclusions of phase equilibria calculation. Luo＇s alpha function keeps decreasing when Tr〉 1 and becomes negative at sufficient high temperature, thus the conventional cubic equation of state expressed pressure as the sum of repulsion pressure PR （〉0）, and attraction pressure PA （〈0） could be improved to be the sum of hard-sphere repulsion pressure PH （〉0） and intermolecular force pressure P1 （P1〈0 at low temperature and p1〉0 at sufficient high temperature）.展开更多
Combining Peng-Robinson （PR） equation of state （EoS） with an association model derived from shield-sticky method （SSM） by Liu et al., a new cubic-plus-association （CPA） EoS is proposed to describe the ther-mod...Combining Peng-Robinson （PR） equation of state （EoS） with an association model derived from shield-sticky method （SSM） by Liu et al., a new cubic-plus-association （CPA） EoS is proposed to describe the ther-modynamic properties of pure ionic liquids （ILs） and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall aver-age deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their mo-lecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter kij, satisfactory correlations of vapor-liquid equilibria （VLE） for binary mixtures of ILs ＋ non-associating solvents and ＋ associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs ＋ non-associating mixtures from CPA, lattice-fluid （LF） and square-well chain fluids with variable range （SWCF-VR） EoSs are compared.展开更多
We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier mod...We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.展开更多
基金Supported by the Zhejiang Provincial Foundation for Returned Scholarsthe Scientific Research Foundation of the State Human Resource Ministry.
文摘A simple extension of cubic equations of state(EOS)to polymer systems has been proposed.The So-ave-Redlich-Kwong(SRK)EOS was taken as a prototype to be used to describe the PVT behavior of polymer melts in a wide temperature and pressure range.Combined with a modified Huron-Vidal gE-mixing rule it was applied for modeling vapor-liquid equilibria of polymer-solvent solutions and the solubility of supercritical gases in polymer melts.Satisfactory results are obtained.
基金financial support from Changjiang Scholars and Innovative Research Team in University, and research project of ‘SUST Spring Bud’
文摘A method of slope reliability analysis was developed by imposing a state equation on the limit equilibrium theory, given the basis of a fixed safety factor technique. Among the many problems of reliability analysis, the most important problem is to find a performance function. We have created a new method of building a limit state equation for planar slip surfaces by applying the mathematical cusp catastrophe theory. This new technique overcomes the defects in the traditional rigid limit equilibrium theory and offers a new way for studying the reliability problem of planar slip surfaces. Consequently, we applied the technique to a case of an open-pit mine and compared our results with that of the traditional approach. From the results we conclude that both methods are essentially consistent, but the reliability index calculated by the traditional model is lower than that from the catastrophic model. The catastrophe model takes into consideration two possible situations of a slope being in the limit equilibrium condition, i.e., it may or may not slip. In the traditional method, however, a slope is definitely considered as slipping when it meets the condition of a limit equilibrium. We conclude that the catastrophe model has more actual and instructive importance compared to the traditional model.
文摘A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous general equations is that it is in simple form, and is easy to manipulate mathematically.
文摘Alpha functions of Soave-Redlich-Kwong （SRK） equation of state proposed by Soave, Twu, and Luo were different in mathematic tendency. They were compared in modeling methane-alkanes equilibria with van der Waals mixing rule and Modified Huron-Vidal （MHV1） mixing rule, respectively. Results showed that Luo＇s alpha function was a little more accurate than Soave＇s, and Twu＇s alpha function lacked accuracy in modeling methane-alkanes equilibrium. SRK equation of state was expanded as virial form, and then the equivalent terms were contrasted with terms of virial equation of state. Results showed that Soave＇s and Luo＇s alpha functions matched the tendency of virial coefficient better than Twu＇s, and Luo＇s alpha function matched better than Soave＇s in wide temperature range, which sustained the conclusions of phase equilibria calculation. Luo＇s alpha function keeps decreasing when Tr〉 1 and becomes negative at sufficient high temperature, thus the conventional cubic equation of state expressed pressure as the sum of repulsion pressure PR （〉0）, and attraction pressure PA （〈0） could be improved to be the sum of hard-sphere repulsion pressure PH （〉0） and intermolecular force pressure P1 （P1〈0 at low temperature and p1〉0 at sufficient high temperature）.
基金Supported by the National Natural Science Foundation of China （20876041, 20736002）, the National Basic Research Program of China （2009CB219902）, the Program for Changjiang Scholars and Innovative Research Team in University of China （Grant IRT0721） and the Programme of Introducing Talents of Discipline to Universities （Grant B08021） of China.
文摘Combining Peng-Robinson （PR） equation of state （EoS） with an association model derived from shield-sticky method （SSM） by Liu et al., a new cubic-plus-association （CPA） EoS is proposed to describe the ther-modynamic properties of pure ionic liquids （ILs） and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall aver-age deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their mo-lecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter kij, satisfactory correlations of vapor-liquid equilibria （VLE） for binary mixtures of ILs ＋ non-associating solvents and ＋ associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs ＋ non-associating mixtures from CPA, lattice-fluid （LF） and square-well chain fluids with variable range （SWCF-VR） EoSs are compared.
基金partially supported by National Natural Science Foundation of China(Grant Nos.10871134,11011130029)the Huo Ying Dong Foundation (Grant No.111033)+3 种基金the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No.PHR201006107)partially supported by National Natural Science Foundation of China (Grant Nos.10871175,10931007,10901137)Zhejiang Provincial Natural Science Foundation of China (Grant No.Z6100217)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20090101120005)
文摘We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.
