Monodispersed potymeric microparticles were prepared by seed-poly- merization.High performance packings were obtained for anion chromatography by coating the surface-sutfonated partictes with quarternized latexes.
Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximatin...Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.展开更多
This paper presents the results of an experimental study carried out using large scale equipment to observe the effect of geometry on gas distribution properties of a high capacity corrugated sheet structured packing ...This paper presents the results of an experimental study carried out using large scale equipment to observe the effect of geometry on gas distribution properties of a high capacity corrugated sheet structured packing （Montz-pak B 1-250M） and to compare it with that of its conventional counterpart （Montz-pak B1-250）. Although the high capacity packing exhibits a significantly lower overall pressure drop, the gas distribution performance is similar to that of the conventional packing, and in both cases consistently good one.展开更多
Liquid-liquid equilibrium (LLE) data of water-caprolactam-benzene-(NH4)2SO4 system at 303 K were measured for extraction of caprolactam from aqueous ammonium sulfate solution. The influence of fluid flow rate, pulsati...Liquid-liquid equilibrium (LLE) data of water-caprolactam-benzene-(NH4)2SO4 system at 303 K were measured for extraction of caprolactam from aqueous ammonium sulfate solution. The influence of fluid flow rate, pulsation intensity on flooding velocity and mass transfer was studied for extraction of caprolactam from ammonium sulfate solution in a laboratory pulsed packed column. The flooding velocities and overall apparent height of a transfer unit were given under various operation conditions. An industrial column developed based on above study is operated well. The scale-up effect is discussed.展开更多
A mathematical model of nitrogen oxide （NOx） absorption is adopted and solved for adiabatic operation of a column with structured packings on the basis of the film theory. Removal rate, outlet concentration, oxidati...A mathematical model of nitrogen oxide （NOx） absorption is adopted and solved for adiabatic operation of a column with structured packings on the basis of the film theory. Removal rate, outlet concentration, oxidation degree of NOx and outlet acid concentration, liquid acid temperature are simulated and tested. The gas phase reactions and equilibria, gas phase mass transfer, interracial equilibria, and liquid phase reactions are considered in the model. Absorption of nitrogen oxides is studied in packed with Mellapak 250Y columns in series in an industrial process of 20000 t oxalic acid per year. Favorable agreement is shown between the model predictions and the on-site observations.展开更多
This paper studies the mass transfer performance of structured packings in the absorption of CO2 from air with aqueous Na OH solution. The Eight structured packings tested are sheet metal ones with corrugations of dif...This paper studies the mass transfer performance of structured packings in the absorption of CO2 from air with aqueous Na OH solution. The Eight structured packings tested are sheet metal ones with corrugations of different geometry parameters. Effective mass transfer area and overall gas phase mass transfer coefficient have been measured in an absorption column of 200 mm diameter under the conditions of gas F-factor in 0.38–1.52 Pa0.5and aqueous Na OH solution concentration of 0.10–0.15 kmol·m-3. The effects of gas/liquid phase flow rates and packing geometry parameters are also investigated. The results show that the effective mass transfer area changes not only with packing geometry parameters and liquid load, but also with gas F-factor. A new effective mass transfer area correlation on the gas F-factor and the liquid load was proposed, which is found to fit experiment data very well.展开更多
Modem packing technology is presented in terms of correlations and criteria for an extensive evaluation of up-to-date packing design used in current mass transfer operations. The corresponding basic information covers...Modem packing technology is presented in terms of correlations and criteria for an extensive evaluation of up-to-date packing design used in current mass transfer operations. The corresponding basic information covers the process engineering aspects, e.g. volumetric effectiveness and optimum geometry of the packing, and the techno-economic aspects, e.g. when selecting a packing adopted in practice for a certain application task. The correlations required for this investigation are derived and evaluated on the basis of a comprehensive experimental re- search by testing and comparison of modem packings, such as Raschig Super-Rings and reference packings. The results thus obtained are correlated and presented in graphic presentation of diagrams, figures and tables.展开更多
Modern chromatography is increasingly focused on miniaturization and integration. Compared to conventional liquid chromatography, microfluidic chip liquid chromatography(microchip-LC) has the potential due to its zero...Modern chromatography is increasingly focused on miniaturization and integration. Compared to conventional liquid chromatography, microfluidic chip liquid chromatography(microchip-LC) has the potential due to its zero-dead volume connection and ease of integration. Nano-sized packings have the potential to significantly enhance separation performance in microchip-LC. However, their application has been hindered by packing difficulties. This study presents a method for packing nano-sized silica particles into a microchannel as the stationary phase. The microchip-LC packed column was prepared by combining the weir and the porous silica single-particle as frit to retain the packing particles. A surface tensionbased single-particle picking technique was established to insert porous single-particle frit into glass microchannels. Additionally, we developed a slurry packing method that utilizes air pressure to inject nano-sized packing into the microchannel. Pressure-driven chromatographic separation was performed using this nano-packed column integrated into a glass microchip. The mixture of four PAHs was successfully separated within just 8 min using a 5 mm separation channel length, achieving high theoretical plates(10~6plates/m). Overall, these findings demonstrate the potential of utilizing nano-sized packings for enhancing chromatographic performance in microchip systems.展开更多
Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. ...Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.展开更多
Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ...Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ＋4 is a family of edge-disjoint subgraphs isomorphic to G in Kv. In this paper, the maximum number of subgraphs in a （v, G, 1）-packing is determined when G is K2 x K3, the Cartesian product of K2 and K3, leaving two orders undetermined. This design originated from the use of DNA library screening.展开更多
The objective of this work is to study a comprehensive performance of three types of structured parking in CO2 absorption application. One of them was developed in Mexican National Institute of Nuclear Research （ININ...The objective of this work is to study a comprehensive performance of three types of structured parking in CO2 absorption application. One of them was developed in Mexican National Institute of Nuclear Research （ININ abbreviation in Spanish of Instituto Nacional de lnvestigaciones Nucleates）, and the other two, Sulzer BX and Mellapak 250Y, by Sulzer Brothers Ltd. Aqueous solution of 30 weight % Monoethanolamine was employed as absorption solvent. The performance of the structured packing was evaluated in terms of the pressure drop, holds up, volumetric overall mass transfer coefficient and height of a global transfer unit of gas and liquid side as a function of the process operating parameters including gas and liquid load, by using hydrodynamic and mass transfer models. The pressure drop of ININ packing was higher than Sulzer BX and Mellapak 250Y, and volumetric overall mass transfer coefficient values are similar of Sulzer BX values and higher than Mellapak 250Y, although Sulzer BX and ININI 8 packing had less height of a global transfer unit of gas side values than Mellapak 250Y packing. The above-mentioned are consequences of the geometric characteristics and operational behavior for each packing.展开更多
A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs...A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.展开更多
Packed bed reactors of non-spherical particles are widely used in chemical industry with the aim to obtain a high active surface area and achieve a homogeneous flow.Despite this,little is known about the arrangement o...Packed bed reactors of non-spherical particles are widely used in chemical industry with the aim to obtain a high active surface area and achieve a homogeneous flow.Despite this,little is known about the arrangement of particles within the bed and the influence of this arrangement on the fluid flow distribution.Magnetic Resonance Imaging (MRI) is a non-invasive tomographic imaging technique that allows 3D visualisation of the packing and flow structure.However,the individual particle information is not obtained using MRI.In this work we investigate different particle detection methods to retrieve the particle position and orientation from MRI images.Results show the successful reconstruction of random packing structures of various non-spherical particle shapes: ellipsoid,spherocylinder,cylinder and cube.The applicability of each method in relation to the particle shape,as well as strengths and drawbacks of each particle detection method are discussed.This paper shows the ability to reconstruct real packed beds of non-spherical particle shapes from MRI images,which opens several research opportunities in the field of chemical engineering.展开更多
Metastability,disorder and jamming are the typical characteristics of amorphous systems,while the related structure changes remain unclear.Sphere packing is often used as a structure model for amorphous and crystallin...Metastability,disorder and jamming are the typical characteristics of amorphous systems,while the related structure changes remain unclear.Sphere packing is often used as a structure model for amorphous and crystalline states.In this article,sphere packing systems with packing densities ranging from 0.50 to 0.74 were simulated by using Discrete Element Method(DEM),and the obtained packing structures were assessed to investigate the densification process and jamming properties.An order parameter that can effectively distinguish the order and disorder of packing structures was proposed based on the distribution characteristics of jamming angles.Then the evolution of jamming characteristics during the transition from Random Loose Packing(RLP)to Random Close Packing(RCP)and the jamming-jamming relations of different packing structures were demonstrated.On this basis,a correlation between order-jamming-metastable states from the microscopic structural perspective was established,which is of valuable theoretical and practical implications for the characterization and synthesis of crystalline and amorphous materials.展开更多
The role of number of grain size fractions on structural and mechanical properties of uniaxially com- pressed granular packings with a uniform particle size distribution in terms of number of particles and with variou...The role of number of grain size fractions on structural and mechanical properties of uniaxially com- pressed granular packings with a uniform particle size distribution in terms of number of particles and with various particle size dispersities was studied using the discrete element method. The study addressed packing density, coordination number, contact forces, global stress, and energy dissipation in assemblies composed of frictional spheres. Packing density was found to change with increasing num- ber of granulometric fractions in mixtures with a small ratio of the diameters of the largest to smallest particles. Results indicated a certain value of particle size ratio below which the number of particle size fractions strongly affected packing density. The average coordination number decreased with increasing number of fractions. Detailed analysis of the effect of particle size dispersity on mechanical coordination number, including particles with no less than four contacts, revealed that, contrary to the average coordi- nation number, the mechanical coordination number increased with increasing ratio of the diameters of the largest to smallest particles in the sample. The composition of polydisperse samples strongly affected stress distribution and energy dissipation in granular packings.展开更多
The investigation of the problem of particle packing has provided basic insights into the structure,symmetry,and physical properties of condensed matter.Dense packings of non-spherical particles have many applications...The investigation of the problem of particle packing has provided basic insights into the structure,symmetry,and physical properties of condensed matter.Dense packings of non-spherical particles have many applications,both in research and industry.We report the two-dimensional dense packing patterns of bending and assembled rods,which are non-convexly deformed from simple objects and modeled as entangled particles.Monte Carlo simulations and further analytical constructions are carried out to explore possible densely packed structures.Two typical densely packed structures of C-bending rods are found,and their packing densities are identified as being functions of the aspect ratio and central angle.Six shapes of assembled rods,representing the combined deformations of rods,are employed in simulations with the packing structures classified into three types.The dense packing density of each packing pattern is derived as a function of different shape parameters.In contrast with the case of disordered packings,both the shape and order are verified to affect the packing density.展开更多
We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if ...We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if a closed surface X admits a circle packing with all the vertex degrees d_(i)≥7, then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X. This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d_(i)≤6. As a corollary, we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover, any hyperbolic closed surface has a geometric decomposition. To obtain our results, we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.展开更多
We employ the lattice Boltzmann method and random walk particle tracking to simulate the time evolution of hydrodynamic dispersion in bulk,random,monodisperse,hard-sphere packings with bed porosities(interparticle voi...We employ the lattice Boltzmann method and random walk particle tracking to simulate the time evolution of hydrodynamic dispersion in bulk,random,monodisperse,hard-sphere packings with bed porosities(interparticle void volume fractions)between the random-close and the random-loose packing limit.Using JodreyTory and Monte Carlo-based algorithms and a systematic variation of the packing protocols we generate a portfolio of packings,whose microstructures differ in their degree of heterogeneity(DoH).Because the DoH quantifies the heterogeneity of the void space distribution in a packing,the asymptotic longitudinal dispersion coefficient calculated for the packings increases with the packings’DoH.We investigate the influence of packing length(up to 150 d_(p),where d_(p) is the sphere diameter)and grid resolution(up to 90 nodes per d_(p))on the simulated hydrodynamic dispersion coefficient,and demonstrate that the chosen packing dimensions of 10 d_(p)×10 d_(p)×70 d_(p) and the employed grid resolution of 60 nodes per d_(p) are sufficient to observe asymptotic behavior of the dispersion coefficient and to minimize finite size effects.Asymptotic values of the dispersion coefficients calculated for the generated packings are compared with simulated as well as experimental data from the literature and yield good to excellent agreement.展开更多
Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independen...Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independently of the component volume fraction, the mixture packing density increases and then decreases with the growth of the aspect ratio of spherocylinders, and the packing density reaches its maximum at the aspect ratio of 0.35. With the same volume particles, results show that the dependence of the mixture packing density on the volume fraction of spherocylinders is approximately linear. With the same diameter particles, the relationship between the mixture packing density and component volume fraction is also roughly linear for short spherocylinders, but when the aspect ratio of spherocylinders is greater than 1.6, the curves turn convex which means the packing of the mixture can be denser than either the sphere or spherocylinder packing alone. To validate the sphere assembly model and relaxation algorithm, binary mixtures of spheres and random packings of spherocylinders were also simulated. Simulation results show the packing densities of sphere mixtures agree with previous prediction models and the results of spherocylinders correspond with the simulation results in literature.展开更多
Rodin (1987) proved the Schwarz’s lemma analog for the circle packings based on the hexagonal combinatorics. In this paper, we prove the Schwarz’s lemma for the circle packings with the general combinatorics and our...Rodin (1987) proved the Schwarz’s lemma analog for the circle packings based on the hexagonal combinatorics. In this paper, we prove the Schwarz’s lemma for the circle packings with the general combinatorics and our proof is more simpler than Rodin’s proof. At the same time, we obtain a rigidity property for those packings with the general combinatorics.展开更多
文摘Monodispersed potymeric microparticles were prepared by seed-poly- merization.High performance packings were obtained for anion chromatography by coating the surface-sutfonated partictes with quarternized latexes.
基金This project is supported in part by NSF of China(60575004, 10231040)NSF of GuangDong, Grants from the Ministry of Education of China(NCET-04-0791)Grants from Sun Yat-Sen University
文摘Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.
文摘This paper presents the results of an experimental study carried out using large scale equipment to observe the effect of geometry on gas distribution properties of a high capacity corrugated sheet structured packing （Montz-pak B 1-250M） and to compare it with that of its conventional counterpart （Montz-pak B1-250）. Although the high capacity packing exhibits a significantly lower overall pressure drop, the gas distribution performance is similar to that of the conventional packing, and in both cases consistently good one.
文摘Liquid-liquid equilibrium (LLE) data of water-caprolactam-benzene-(NH4)2SO4 system at 303 K were measured for extraction of caprolactam from aqueous ammonium sulfate solution. The influence of fluid flow rate, pulsation intensity on flooding velocity and mass transfer was studied for extraction of caprolactam from ammonium sulfate solution in a laboratory pulsed packed column. The flooding velocities and overall apparent height of a transfer unit were given under various operation conditions. An industrial column developed based on above study is operated well. The scale-up effect is discussed.
文摘A mathematical model of nitrogen oxide （NOx） absorption is adopted and solved for adiabatic operation of a column with structured packings on the basis of the film theory. Removal rate, outlet concentration, oxidation degree of NOx and outlet acid concentration, liquid acid temperature are simulated and tested. The gas phase reactions and equilibria, gas phase mass transfer, interracial equilibria, and liquid phase reactions are considered in the model. Absorption of nitrogen oxides is studied in packed with Mellapak 250Y columns in series in an industrial process of 20000 t oxalic acid per year. Favorable agreement is shown between the model predictions and the on-site observations.
基金Supported by the National Natural Science Foundation of China(51134017)and Petro China(2011E-24-09)
文摘This paper studies the mass transfer performance of structured packings in the absorption of CO2 from air with aqueous Na OH solution. The Eight structured packings tested are sheet metal ones with corrugations of different geometry parameters. Effective mass transfer area and overall gas phase mass transfer coefficient have been measured in an absorption column of 200 mm diameter under the conditions of gas F-factor in 0.38–1.52 Pa0.5and aqueous Na OH solution concentration of 0.10–0.15 kmol·m-3. The effects of gas/liquid phase flow rates and packing geometry parameters are also investigated. The results show that the effective mass transfer area changes not only with packing geometry parameters and liquid load, but also with gas F-factor. A new effective mass transfer area correlation on the gas F-factor and the liquid load was proposed, which is found to fit experiment data very well.
文摘Modem packing technology is presented in terms of correlations and criteria for an extensive evaluation of up-to-date packing design used in current mass transfer operations. The corresponding basic information covers the process engineering aspects, e.g. volumetric effectiveness and optimum geometry of the packing, and the techno-economic aspects, e.g. when selecting a packing adopted in practice for a certain application task. The correlations required for this investigation are derived and evaluated on the basis of a comprehensive experimental re- search by testing and comparison of modem packings, such as Raschig Super-Rings and reference packings. The results thus obtained are correlated and presented in graphic presentation of diagrams, figures and tables.
基金supported by the National Natural Science Foundation of China (No.21936001)the Beijing Outstanding Young Scientist Program (No.BJJWZYJH01201910005017)。
文摘Modern chromatography is increasingly focused on miniaturization and integration. Compared to conventional liquid chromatography, microfluidic chip liquid chromatography(microchip-LC) has the potential due to its zero-dead volume connection and ease of integration. Nano-sized packings have the potential to significantly enhance separation performance in microchip-LC. However, their application has been hindered by packing difficulties. This study presents a method for packing nano-sized silica particles into a microchannel as the stationary phase. The microchip-LC packed column was prepared by combining the weir and the porous silica single-particle as frit to retain the packing particles. A surface tensionbased single-particle picking technique was established to insert porous single-particle frit into glass microchannels. Additionally, we developed a slurry packing method that utilizes air pressure to inject nano-sized packing into the microchannel. Pressure-driven chromatographic separation was performed using this nano-packed column integrated into a glass microchip. The mixture of four PAHs was successfully separated within just 8 min using a 5 mm separation channel length, achieving high theoretical plates(10~6plates/m). Overall, these findings demonstrate the potential of utilizing nano-sized packings for enhancing chromatographic performance in microchip systems.
基金supported by the National Natural Science Foundation of China(10701084)Chongqing Natural Science Foundation (2008BB0151)
文摘Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.
文摘Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ＋4 is a family of edge-disjoint subgraphs isomorphic to G in Kv. In this paper, the maximum number of subgraphs in a （v, G, 1）-packing is determined when G is K2 x K3, the Cartesian product of K2 and K3, leaving two orders undetermined. This design originated from the use of DNA library screening.
文摘The objective of this work is to study a comprehensive performance of three types of structured parking in CO2 absorption application. One of them was developed in Mexican National Institute of Nuclear Research （ININ abbreviation in Spanish of Instituto Nacional de lnvestigaciones Nucleates）, and the other two, Sulzer BX and Mellapak 250Y, by Sulzer Brothers Ltd. Aqueous solution of 30 weight % Monoethanolamine was employed as absorption solvent. The performance of the structured packing was evaluated in terms of the pressure drop, holds up, volumetric overall mass transfer coefficient and height of a global transfer unit of gas and liquid side as a function of the process operating parameters including gas and liquid load, by using hydrodynamic and mass transfer models. The pressure drop of ININ packing was higher than Sulzer BX and Mellapak 250Y, and volumetric overall mass transfer coefficient values are similar of Sulzer BX values and higher than Mellapak 250Y, although Sulzer BX and ININI 8 packing had less height of a global transfer unit of gas side values than Mellapak 250Y packing. The above-mentioned are consequences of the geometric characteristics and operational behavior for each packing.
文摘A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.
文摘Packed bed reactors of non-spherical particles are widely used in chemical industry with the aim to obtain a high active surface area and achieve a homogeneous flow.Despite this,little is known about the arrangement of particles within the bed and the influence of this arrangement on the fluid flow distribution.Magnetic Resonance Imaging (MRI) is a non-invasive tomographic imaging technique that allows 3D visualisation of the packing and flow structure.However,the individual particle information is not obtained using MRI.In this work we investigate different particle detection methods to retrieve the particle position and orientation from MRI images.Results show the successful reconstruction of random packing structures of various non-spherical particle shapes: ellipsoid,spherocylinder,cylinder and cube.The applicability of each method in relation to the particle shape,as well as strengths and drawbacks of each particle detection method are discussed.This paper shows the ability to reconstruct real packed beds of non-spherical particle shapes from MRI images,which opens several research opportunities in the field of chemical engineering.
基金the National Natural Science Foundation of China(grant No.51374070)Liaoning Revitalization Talents Program(grant No.XLYC1805007)of ChinaNatural Science Foundation of Jiangsu Province(grant No.BK20200269)for the financial support to this work.
文摘Metastability,disorder and jamming are the typical characteristics of amorphous systems,while the related structure changes remain unclear.Sphere packing is often used as a structure model for amorphous and crystalline states.In this article,sphere packing systems with packing densities ranging from 0.50 to 0.74 were simulated by using Discrete Element Method(DEM),and the obtained packing structures were assessed to investigate the densification process and jamming properties.An order parameter that can effectively distinguish the order and disorder of packing structures was proposed based on the distribution characteristics of jamming angles.Then the evolution of jamming characteristics during the transition from Random Loose Packing(RLP)to Random Close Packing(RCP)and the jamming-jamming relations of different packing structures were demonstrated.On this basis,a correlation between order-jamming-metastable states from the microscopic structural perspective was established,which is of valuable theoretical and practical implications for the characterization and synthesis of crystalline and amorphous materials.
文摘The role of number of grain size fractions on structural and mechanical properties of uniaxially com- pressed granular packings with a uniform particle size distribution in terms of number of particles and with various particle size dispersities was studied using the discrete element method. The study addressed packing density, coordination number, contact forces, global stress, and energy dissipation in assemblies composed of frictional spheres. Packing density was found to change with increasing num- ber of granulometric fractions in mixtures with a small ratio of the diameters of the largest to smallest particles. Results indicated a certain value of particle size ratio below which the number of particle size fractions strongly affected packing density. The average coordination number decreased with increasing number of fractions. Detailed analysis of the effect of particle size dispersity on mechanical coordination number, including particles with no less than four contacts, revealed that, contrary to the average coordi- nation number, the mechanical coordination number increased with increasing ratio of the diameters of the largest to smallest particles in the sample. The composition of polydisperse samples strongly affected stress distribution and energy dissipation in granular packings.
基金the National Natural Science Foundation of China(Nos.11602088,11672110 and 11472110)Natural Science Foundation of Guangdong Province(No.2017A030313014)+1 种基金the opening project of the State Key Lab-oratory for Strength and Vibration of Mechanical Structures(Xi'an Jiaotong University)(Nos.SV2018-KF-33 and SV2017-KF-04)Fundamental Research Funds for the Central Universities(Nos.2017BQ094 and 2018PY21).
文摘The investigation of the problem of particle packing has provided basic insights into the structure,symmetry,and physical properties of condensed matter.Dense packings of non-spherical particles have many applications,both in research and industry.We report the two-dimensional dense packing patterns of bending and assembled rods,which are non-convexly deformed from simple objects and modeled as entangled particles.Monte Carlo simulations and further analytical constructions are carried out to explore possible densely packed structures.Two typical densely packed structures of C-bending rods are found,and their packing densities are identified as being functions of the aspect ratio and central angle.Six shapes of assembled rods,representing the combined deformations of rods,are employed in simulations with the packing structures classified into three types.The dense packing density of each packing pattern is derived as a function of different shape parameters.In contrast with the case of disordered packings,both the shape and order are verified to affect the packing density.
基金supported by National Natural Science Foundation of China (Grant Nos. 11871094 and 12122119)supported by National Natural Science Foundation of China (Grant No. 12171480)+1 种基金Hunan Provincial Natural Science Foundation of China (Grant Nos. 2020JJ4658 and 2022JJ10059)Scientific Research Program Funds of National University of Defense Technology (Grant No. 22-ZZCX-016)。
文摘We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if a closed surface X admits a circle packing with all the vertex degrees d_(i)≥7, then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X. This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d_(i)≤6. As a corollary, we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover, any hyperbolic closed surface has a geometric decomposition. To obtain our results, we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.
基金supported by the Deutsche Forschungsgemeinschaft DFG(Bonn,Germany)under grants TA 268/4-1 and TA 268/5-1the John von Neumann Institute for Computing(NIC)and the Julich Supercomputing Centre(JSC)for allocation of a special CPU-time grant(NIC project number:4717,JSC project ID:HMR10)。
文摘We employ the lattice Boltzmann method and random walk particle tracking to simulate the time evolution of hydrodynamic dispersion in bulk,random,monodisperse,hard-sphere packings with bed porosities(interparticle void volume fractions)between the random-close and the random-loose packing limit.Using JodreyTory and Monte Carlo-based algorithms and a systematic variation of the packing protocols we generate a portfolio of packings,whose microstructures differ in their degree of heterogeneity(DoH).Because the DoH quantifies the heterogeneity of the void space distribution in a packing,the asymptotic longitudinal dispersion coefficient calculated for the packings increases with the packings’DoH.We investigate the influence of packing length(up to 150 d_(p),where d_(p) is the sphere diameter)and grid resolution(up to 90 nodes per d_(p))on the simulated hydrodynamic dispersion coefficient,and demonstrate that the chosen packing dimensions of 10 d_(p)×10 d_(p)×70 d_(p) and the employed grid resolution of 60 nodes per d_(p) are sufficient to observe asymptotic behavior of the dispersion coefficient and to minimize finite size effects.Asymptotic values of the dispersion coefficients calculated for the generated packings are compared with simulated as well as experimental data from the literature and yield good to excellent agreement.
基金supported by the National Natural Science Foundation of China (Grant No. 10772005)the National Basic Research Program of China (Grant Nos. 2007CB714603 and 2010CB832701)
文摘Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independently of the component volume fraction, the mixture packing density increases and then decreases with the growth of the aspect ratio of spherocylinders, and the packing density reaches its maximum at the aspect ratio of 0.35. With the same volume particles, results show that the dependence of the mixture packing density on the volume fraction of spherocylinders is approximately linear. With the same diameter particles, the relationship between the mixture packing density and component volume fraction is also roughly linear for short spherocylinders, but when the aspect ratio of spherocylinders is greater than 1.6, the curves turn convex which means the packing of the mixture can be denser than either the sphere or spherocylinder packing alone. To validate the sphere assembly model and relaxation algorithm, binary mixtures of spheres and random packings of spherocylinders were also simulated. Simulation results show the packing densities of sphere mixtures agree with previous prediction models and the results of spherocylinders correspond with the simulation results in literature.
基金supported by National Natural Science Foundation of China (Grant Nos.10701084, 10501046)the Natural Science Foundation of Chongqing, China (Grant No. CSTC2008BB0151)
文摘Rodin (1987) proved the Schwarz’s lemma analog for the circle packings based on the hexagonal combinatorics. In this paper, we prove the Schwarz’s lemma for the circle packings with the general combinatorics and our proof is more simpler than Rodin’s proof. At the same time, we obtain a rigidity property for those packings with the general combinatorics.
