Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequen...Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.展开更多
Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using exten...Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.展开更多
The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state （EOS） for a mixture of hard sphere （HS）, Lennar-Jones （L J） fluids. A su...The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state （EOS） for a mixture of hard sphere （HS）, Lennar-Jones （L J） fluids. A suitable flexible functional form for the radial distribution function G（R） is assumed for the mixture, with R as a variable. The function G（R） has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics （MD） result for pure HS and LJ fluid respectively.展开更多
By means of Gibbs-Bogoliubov (GB) thermodynamic variational calculation,the thermodynamic properties of the supercooled liquid metals,such as the 3rd family elements Al,Ga and Tl and transition metal Ti were calculate...By means of Gibbs-Bogoliubov (GB) thermodynamic variational calculation,the thermodynamic properties of the supercooled liquid metals,such as the 3rd family elements Al,Ga and Tl and transition metal Ti were calculated using the hard-sphere (HS) system as reference.The values of mean atomic volume,Helmholtz free energy,internal energy and entropy as well as specific heat at constant volume,isothermal bulk modulus,thermal expan- sion coefficient and specfic heat under constant pressure were evaluated.The glass transition temperature,T_g,is easily obtained from the C_p-T plot.The glass forming ability for metal can be predicted from T_g/T_m,which is in agreement with the experimental results.展开更多
Ion mobility spectra for ten alcohols have been studied in an ion mobility spectrometry apparatus equipped with a corona discharge ionization source. Using protonated water cluster ions as the reactant ions and clean ...Ion mobility spectra for ten alcohols have been studied in an ion mobility spectrometry apparatus equipped with a corona discharge ionization source. Using protonated water cluster ions as the reactant ions and clean air as the drift gas, the alcohols exhibit different product ion characteristic peaks in their ion mobility spectra. The detection limit for these alcohols is at low concentration pmol/L level according to the concentration calibration by exponential dilution method. Based on the measured ion mobilities, several chemical physics parameters of the ion-molecular interaction at atmosphere were obtained, including the ionic collision cross sections, diffusion coefficients, collision rate constants, and the ionic radii under the hard-sphere model approximation.展开更多
A coupled numerical method for the direct numerical simulation of particle-fluid systems is formulated and implemented, resolving an order of magnitude smaller than particle size. The particle motion is described by t...A coupled numerical method for the direct numerical simulation of particle-fluid systems is formulated and implemented, resolving an order of magnitude smaller than particle size. The particle motion is described by the time-driven hard-sphere model, while the hydrodynamic equations governing fluid flow are solved by the lattice Boltzmann method （LBM）, Particle-fluid coupling is realized by an immersed boundary method （IBM）, which considers the effect of boundary on surrounding fluid as a restoring force added to the governing equations of the fluid. The proposed scheme is validated in the classical flow-around-cylinder simulations, and preliminary application of this scheme to fluidization is reported, demonstrating it to be a promising computational strategy for better understanding complex behavior in particle-fluid systems.展开更多
We consider the Navier-Stokes equations with a pressure function satisfying a hard-sphere law.That means the pressure,as a function of the density,becomes infinite when the density approaches a finite critical value.U...We consider the Navier-Stokes equations with a pressure function satisfying a hard-sphere law.That means the pressure,as a function of the density,becomes infinite when the density approaches a finite critical value.Under some structural constraints imposed on the pressure law,we show a weak-strong uniqueness principle in periodic spatial domains.The method is based on a modified relative entropy inequality for the system.The main difficulty is that the pressure potential associated with the internal energy of the system is largely dominated by the pressure itself in the area close to the critical density.As a result,several terms appearing in the relative energy inequality cannot be controlled by the total energy.展开更多
In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state （EOS） for a hard sphere （HS） ...In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state （EOS） for a hard sphere （HS） and Lennard Jones （L J） fluids. A suitable axiomatic form for surface tension S（r） is assumed for the pure fluid, with r as a variable. The function S（r） has an arbitrary parameter rn. S（r） = A ＋ B（d/r）/[1 ＋ m（d/r）]. We use the condition in terms of radial distribution function G（λd,η） containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of rn and the EOS has a lower root-mean-square deviation than that of Barker-Henderson BH2 for LJ fluids.展开更多
We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms （n = 1, 2, 3, 4, 5） fo...We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms （n = 1, 2, 3, 4, 5） for surface tension Sn （r）, r≥ d/2 with intermolecular separation r as a variable, where m is an arbitrary real number （pole）. Among the equations of state obtained in this way are Percus-Yevick, scaled particle theory and Carnahan-Starling equations of state. In addition, we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately. It is found that for both hard sphere fluids as well as Lennard-Jones fluids, with m = 3/4 the derived equation of state （EOS） gives results which are in good agreement with computer simulation results. Furthermore, this equation of state gives the Percus-Yevick （pressure） EOS for the m = 0, the Carnahan-Starling EOS for rn = 4/5, while for the value of m = 1 it corresponds to a scaled particle theory EOS.展开更多
We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster. Efforts are made to estimate new physical parameter f in liqu...We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster. Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy. The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied. Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity（radial distribution function）.From the thermodynamic profile of the fluid, the model results are discussed in terms of the cavity due to the closed surface along with suitable energy. The present calculation is based upon the sample thermodynamic data for n-hexanol, such as the ultrasonic wave, density, volume expansion coefficient, and ratio of specific heat in the liquid state, and it is consistent with the thermodynamic relations containing physical parameters such as size and energy. Since the data is restricted to n-hexanol, we avoid giving the physical meaning of f, which is the key parameter studied in the present work.展开更多
This paper develops a mixed Finite Element Method (mFEM) based on both classical rectangular elements (with equal nodal points for all degrees of freedom) and Taylor-hood elements to solve Poisson-Nernst-Planck (PNP) ...This paper develops a mixed Finite Element Method (mFEM) based on both classical rectangular elements (with equal nodal points for all degrees of freedom) and Taylor-hood elements to solve Poisson-Nernst-Planck (PNP) equations with steric effects. The Nernst-Planck (NP) equation for ion fluxes is modified to incorporate finite-size effects in terms of hard-sphere repulsion. The resultant modified NP and Poisson equation representing electrostatic potential is then coupled to form a system of the equation that describes a realistic transport phenomenon in an ion channel. Consequently, we apply mFEM based on both Taylor-hood and classical rectangular elements to discretize the 2D steady system of equations with iterative linearization for the nonlinear components. The numerical scheme is first validated using a 2D analytical solution for PNP equations, the steric components varied and the effects on concentration analyzed and compared against PNP and modified PNP for two monovalent ion species. Classical rectangular elements presented a better comparable approximate solution than Taylor-hood.展开更多
Fully resolved simulations of particulate and aggregative fluidization systems are performed suc-cessfully with the so-called combined lattice Boltzmann method and time-driven hard-sphere model （LBM-TDHS）. In this m...Fully resolved simulations of particulate and aggregative fluidization systems are performed suc-cessfully with the so-called combined lattice Boltzmann method and time-driven hard-sphere model （LBM-TDHS）. In this method, the discrete particle phase is described by time-driven hard-sphere model, and the governing equations of the continuous fluid phase are solved with lattice Boltz-mann method. Particle-fluid coupling is implemented by immersed moving boundary method. Time averaged flow structure of the simulated results show the formation of core-annulus structure and sigmoid distribution of voidage in the axial direction, which are typical phenomena in fluidization systems. Combining the results of the simulation, the energy consumption Nst for suspending and transporting solids is calculated from the direct numerical simulation （DNS） of fluidization, and the stability criterion Nst/NT = rain proposed in EMMS/bubbling model is verified numerically. Further-more the numerical results show that the value of Nst/NT in particulate fiuidization is much higher than that in aggregative fluidization, but Nst/NT = rain is effective for both particulate and aggregative fluidization.展开更多
文摘Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.
基金Supported by the National Science Foundation of China (No. 29736170, No. 20025618) and the Doctoral Research Foundation by Ministry of Education of China (No. 1999025103). Additional support provided by the Visiting Researcher Foundation of University La
文摘Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.
文摘The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state （EOS） for a mixture of hard sphere （HS）, Lennar-Jones （L J） fluids. A suitable flexible functional form for the radial distribution function G（R） is assumed for the mixture, with R as a variable. The function G（R） has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics （MD） result for pure HS and LJ fluid respectively.
文摘By means of Gibbs-Bogoliubov (GB) thermodynamic variational calculation,the thermodynamic properties of the supercooled liquid metals,such as the 3rd family elements Al,Ga and Tl and transition metal Ti were calculated using the hard-sphere (HS) system as reference.The values of mean atomic volume,Helmholtz free energy,internal energy and entropy as well as specific heat at constant volume,isothermal bulk modulus,thermal expan- sion coefficient and specfic heat under constant pressure were evaluated.The glass transition temperature,T_g,is easily obtained from the C_p-T plot.The glass forming ability for metal can be predicted from T_g/T_m,which is in agreement with the experimental results.
基金V. ACKNOWLEDGMENTS This work was support by the National Natural Science Foundation of China （No.20577049, No.20707025, and No.20907054）, the Chinese-Slovak Scientific and Technological Cooperation Project （No.4-03）, the Excellent Youth Foundation of Anhui Province Scientific Committee （No.06045098）, the Hefei Institutes of Physical Science, Chinese Academy of Science are gratefully acknowledged, and the Slovak Research and Development Agency, projects （No.LPP-0143-06 and No.SK- CN-029-07）.
文摘Ion mobility spectra for ten alcohols have been studied in an ion mobility spectrometry apparatus equipped with a corona discharge ionization source. Using protonated water cluster ions as the reactant ions and clean air as the drift gas, the alcohols exhibit different product ion characteristic peaks in their ion mobility spectra. The detection limit for these alcohols is at low concentration pmol/L level according to the concentration calibration by exponential dilution method. Based on the measured ion mobilities, several chemical physics parameters of the ion-molecular interaction at atmosphere were obtained, including the ionic collision cross sections, diffusion coefficients, collision rate constants, and the ionic radii under the hard-sphere model approximation.
基金sponsored by Ministry of Finance under the grant ZDYZ2008-2National Key Science and Technology Project under the grant 2008ZX05014-003-006HZthe Chinese Academy of Sciences under the grant KGCX2-YW-124
文摘A coupled numerical method for the direct numerical simulation of particle-fluid systems is formulated and implemented, resolving an order of magnitude smaller than particle size. The particle motion is described by the time-driven hard-sphere model, while the hydrodynamic equations governing fluid flow are solved by the lattice Boltzmann method （LBM）, Particle-fluid coupling is realized by an immersed boundary method （IBM）, which considers the effect of boundary on surrounding fluid as a restoring force added to the governing equations of the fluid. The proposed scheme is validated in the classical flow-around-cylinder simulations, and preliminary application of this scheme to fluidization is reported, demonstrating it to be a promising computational strategy for better understanding complex behavior in particle-fluid systems.
基金the European Research Council under the European Union’s Seventh Framework Programme (Grant No. FP7/2007-2013)European Research Council (ERC) Grant Agreement (Grant No. 320078)The Institute of Mathematics of the Academy of Sciences of the Czech Republic was supported by Rozvoj Vyzkumn Organizace (RVO) (Grant No. 67985840)
文摘We consider the Navier-Stokes equations with a pressure function satisfying a hard-sphere law.That means the pressure,as a function of the density,becomes infinite when the density approaches a finite critical value.Under some structural constraints imposed on the pressure law,we show a weak-strong uniqueness principle in periodic spatial domains.The method is based on a modified relative entropy inequality for the system.The main difficulty is that the pressure potential associated with the internal energy of the system is largely dominated by the pressure itself in the area close to the critical density.As a result,several terms appearing in the relative energy inequality cannot be controlled by the total energy.
文摘In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state （EOS） for a hard sphere （HS） and Lennard Jones （L J） fluids. A suitable axiomatic form for surface tension S（r） is assumed for the pure fluid, with r as a variable. The function S（r） has an arbitrary parameter rn. S（r） = A ＋ B（d/r）/[1 ＋ m（d/r）]. We use the condition in terms of radial distribution function G（λd,η） containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of rn and the EOS has a lower root-mean-square deviation than that of Barker-Henderson BH2 for LJ fluids.
文摘We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms （n = 1, 2, 3, 4, 5） for surface tension Sn （r）, r≥ d/2 with intermolecular separation r as a variable, where m is an arbitrary real number （pole）. Among the equations of state obtained in this way are Percus-Yevick, scaled particle theory and Carnahan-Starling equations of state. In addition, we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately. It is found that for both hard sphere fluids as well as Lennard-Jones fluids, with m = 3/4 the derived equation of state （EOS） gives results which are in good agreement with computer simulation results. Furthermore, this equation of state gives the Percus-Yevick （pressure） EOS for the m = 0, the Carnahan-Starling EOS for rn = 4/5, while for the value of m = 1 it corresponds to a scaled particle theory EOS.
文摘We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster. Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy. The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied. Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity（radial distribution function）.From the thermodynamic profile of the fluid, the model results are discussed in terms of the cavity due to the closed surface along with suitable energy. The present calculation is based upon the sample thermodynamic data for n-hexanol, such as the ultrasonic wave, density, volume expansion coefficient, and ratio of specific heat in the liquid state, and it is consistent with the thermodynamic relations containing physical parameters such as size and energy. Since the data is restricted to n-hexanol, we avoid giving the physical meaning of f, which is the key parameter studied in the present work.
文摘This paper develops a mixed Finite Element Method (mFEM) based on both classical rectangular elements (with equal nodal points for all degrees of freedom) and Taylor-hood elements to solve Poisson-Nernst-Planck (PNP) equations with steric effects. The Nernst-Planck (NP) equation for ion fluxes is modified to incorporate finite-size effects in terms of hard-sphere repulsion. The resultant modified NP and Poisson equation representing electrostatic potential is then coupled to form a system of the equation that describes a realistic transport phenomenon in an ion channel. Consequently, we apply mFEM based on both Taylor-hood and classical rectangular elements to discretize the 2D steady system of equations with iterative linearization for the nonlinear components. The numerical scheme is first validated using a 2D analytical solution for PNP equations, the steric components varied and the effects on concentration analyzed and compared against PNP and modified PNP for two monovalent ion species. Classical rectangular elements presented a better comparable approximate solution than Taylor-hood.
基金supported by the National Natural Science Foundation of China under Grant No.21106155the Chinese Academy of Sciences under Grant No.XDA07080303
文摘Fully resolved simulations of particulate and aggregative fluidization systems are performed suc-cessfully with the so-called combined lattice Boltzmann method and time-driven hard-sphere model （LBM-TDHS）. In this method, the discrete particle phase is described by time-driven hard-sphere model, and the governing equations of the continuous fluid phase are solved with lattice Boltz-mann method. Particle-fluid coupling is implemented by immersed moving boundary method. Time averaged flow structure of the simulated results show the formation of core-annulus structure and sigmoid distribution of voidage in the axial direction, which are typical phenomena in fluidization systems. Combining the results of the simulation, the energy consumption Nst for suspending and transporting solids is calculated from the direct numerical simulation （DNS） of fluidization, and the stability criterion Nst/NT = rain proposed in EMMS/bubbling model is verified numerically. Further-more the numerical results show that the value of Nst/NT in particulate fiuidization is much higher than that in aggregative fluidization, but Nst/NT = rain is effective for both particulate and aggregative fluidization.
