The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. A...The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.展开更多
The acoustic radiation force on a fluid sphere immersed in water between two boundaries given by a Gaussian beam is theoretically and numerically investigated in this work. Based on the finite series method, the Gauss...The acoustic radiation force on a fluid sphere immersed in water between two boundaries given by a Gaussian beam is theoretically and numerically investigated in this work. Based on the finite series method, the Gaussian beam is expressed in terms of Bessel function and a weighting parameter. The effects of the two boundaries concerned in our study is worked out by the image theory. This work also provides a reference when considering the effects of certain factors such as the radius of the sphere and the distance between the sphere and two boundaries. The contrast with the acoustic radiation force on a fluid sphere near only one boundary is also made in this paper. Our study can offer a theoretical basis for acoustics manipulation, acoustic sensors in the field of biomedical ultrasound and material science.展开更多
A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simp...A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.展开更多
A new approach to the computation of entropy-related properties of fluids has been pre-sented.Application of the new technique to hard sphere fluids shows that it is capable of providingreliable estimates of such prop...A new approach to the computation of entropy-related properties of fluids has been pre-sented.Application of the new technique to hard sphere fluids shows that it is capable of providingreliable estimates of such properties as the chemical potential and Helmholtz free energy,even athigh density where other existing methods are hardly applicable.The chemical potential of an infinitedilute component in hard sphere systems has been estimated,and compared with that calculated fromthe Carnahan-Starling equation.展开更多
The thixotropy properties and the motion law of a sphere in the Bingham fluid have been studied. Through observation of the settling motion of a single sphere in the Bingham fluid on the X-ray screen, it has been disc...The thixotropy properties and the motion law of a sphere in the Bingham fluid have been studied. Through observation of the settling motion of a single sphere in the Bingham fluid on the X-ray screen, it has been discovered that the mud in estuaries and along sea bay, and the hyperconcentrated flow all behave as the Bingham fl fluid with thixotropy properties as the large sediment concentration. Through derivation, the theoretical relationship between the yield stress and non-settling maximum sphere supported by the stress for the Bingham fluid has been developed, the equations for calculating the increasing yield stress and the non-settling maximum sphere diameter with the duration at rest of the slurry have been obtained. In consideration of the effect of thixotropy on fluid motion, the Navier-Stokes equation group for the Bingham thixotropy fluid has been developed. Through further study of the flow boundary condition of settling motion of ii single sphere in the Bingham thixotropy fluid, and the solving of the Navier-Stokes equation group, under the small Reynolds number, the theoretical equation of the drag force of the Bingham thixotropy fluid flowing around a sphere has been deduced. The theoretical relationship between drag coefficient and Reynolds number has been derived. By use of the experimental data of rheological test of various slurries measured with viscometer and those of single sphere motion observed on the X-ray screeen, the above equations have been verified. The equations are in good agreement with the experimental data for various slurries.展开更多
An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certa...An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certain interval. The present enhanced KR-FMF incorporates respectively, for aim of comparison, a recent 3rd-order expansion equation of state （EOS） and a Boublfk＇s extension of Kolafa＇s EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory （SPT） relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictions and corresponding density profiles produced in different periods indicates the excellent performance of the present enhanced KR-FMF-3rd-order EOS in comparison with other available density functional approximations （DFAs）. There are two anomalous situations from whose density profiles all DFAs studied deviate significantly; however, subsequent new computer simulation results for state conditions similar to the two anomalous situations are in very excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that （i） the validity of the ＂naive＂ substitution elaborated in the present paper and peculiar to the original KR-FMF is still in operation even if inhomogeneoas mixtures are being dealt with; （ii） the high accuracy and self-consistency of the third order EOS seem to allow for application of the KR-FMF-third order EOS to more severe state conditions; and （iii） the ＂naive＂ substitution enables very easy the combination of the original KR-FMF with future＇s more accurate but potentially more complicated EOS of hard sphere mixtures.展开更多
This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center...This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.展开更多
文摘The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.
基金supported by the National Key Research and Development Program of China(Grant No.2016YFF0203000)State Key Program of National Natural Science of China(Grant No.11834008)+2 种基金National Natural Science Foundation of China(Grant No.11774167)State Key Laboratory of Acoustics,Chinese Academy of Science(Grant No.SKLA201809)Administration of Quality Supervision,Inspection and Quarantine(AQSIQ)Technology Research and Development Program,China(Grant No.2017QK125)
文摘The acoustic radiation force on a fluid sphere immersed in water between two boundaries given by a Gaussian beam is theoretically and numerically investigated in this work. Based on the finite series method, the Gaussian beam is expressed in terms of Bessel function and a weighting parameter. The effects of the two boundaries concerned in our study is worked out by the image theory. This work also provides a reference when considering the effects of certain factors such as the radius of the sphere and the distance between the sphere and two boundaries. The contrast with the acoustic radiation force on a fluid sphere near only one boundary is also made in this paper. Our study can offer a theoretical basis for acoustics manipulation, acoustic sensors in the field of biomedical ultrasound and material science.
文摘A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.
文摘A new approach to the computation of entropy-related properties of fluids has been pre-sented.Application of the new technique to hard sphere fluids shows that it is capable of providingreliable estimates of such properties as the chemical potential and Helmholtz free energy,even athigh density where other existing methods are hardly applicable.The chemical potential of an infinitedilute component in hard sphere systems has been estimated,and compared with that calculated fromthe Carnahan-Starling equation.
文摘The thixotropy properties and the motion law of a sphere in the Bingham fluid have been studied. Through observation of the settling motion of a single sphere in the Bingham fluid on the X-ray screen, it has been discovered that the mud in estuaries and along sea bay, and the hyperconcentrated flow all behave as the Bingham fl fluid with thixotropy properties as the large sediment concentration. Through derivation, the theoretical relationship between the yield stress and non-settling maximum sphere supported by the stress for the Bingham fluid has been developed, the equations for calculating the increasing yield stress and the non-settling maximum sphere diameter with the duration at rest of the slurry have been obtained. In consideration of the effect of thixotropy on fluid motion, the Navier-Stokes equation group for the Bingham thixotropy fluid has been developed. Through further study of the flow boundary condition of settling motion of ii single sphere in the Bingham thixotropy fluid, and the solving of the Navier-Stokes equation group, under the small Reynolds number, the theoretical equation of the drag force of the Bingham thixotropy fluid flowing around a sphere has been deduced. The theoretical relationship between drag coefficient and Reynolds number has been derived. By use of the experimental data of rheological test of various slurries measured with viscometer and those of single sphere motion observed on the X-ray screeen, the above equations have been verified. The equations are in good agreement with the experimental data for various slurries.
基金Supported by the National Natural Science Foundation of China under Grant No.20973202
文摘An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certain interval. The present enhanced KR-FMF incorporates respectively, for aim of comparison, a recent 3rd-order expansion equation of state （EOS） and a Boublfk＇s extension of Kolafa＇s EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory （SPT） relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictions and corresponding density profiles produced in different periods indicates the excellent performance of the present enhanced KR-FMF-3rd-order EOS in comparison with other available density functional approximations （DFAs）. There are two anomalous situations from whose density profiles all DFAs studied deviate significantly; however, subsequent new computer simulation results for state conditions similar to the two anomalous situations are in very excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that （i） the validity of the ＂naive＂ substitution elaborated in the present paper and peculiar to the original KR-FMF is still in operation even if inhomogeneoas mixtures are being dealt with; （ii） the high accuracy and self-consistency of the third order EOS seem to allow for application of the KR-FMF-third order EOS to more severe state conditions; and （iii） the ＂naive＂ substitution enables very easy the combination of the original KR-FMF with future＇s more accurate but potentially more complicated EOS of hard sphere mixtures.
文摘This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.
