A resident time model is proposed to evaluate the performance of agitated extraction columns. In this model, the resident time of dispersed drops is simulated with the discrete phase modeling, where the continuous pha...A resident time model is proposed to evaluate the performance of agitated extraction columns. In this model, the resident time of dispersed drops is simulated with the discrete phase modeling, where the continuous phase and the dispersed phase （drops） are described by the single-phase Navier-Stokes （turbulence） model and Lagrangian model, respectively. The interaction of dispersed phase and continuous phase is neglected for the low concentration of drop in the cases studied. The statistical parameters of drops （the average resident time and standard deviation） under different operation conditions are computed for four columns. The relation of the above statistical parameters with the performance of columns is discussed and the criterions for an optimal compartment are outlined. Our results indicate that the resident time model is useful to evaluate the performance and optimize the design of extraction columns.展开更多
The accurate prediction of the droplet size distribution(DSD)in liquid–liquid turbulent dispersions is of fundamental importance in many industrial applications and it requires suitable kernels in the population bala...The accurate prediction of the droplet size distribution(DSD)in liquid–liquid turbulent dispersions is of fundamental importance in many industrial applications and it requires suitable kernels in the population balance model.When a surfactant is included in liquid–liquid dispersions,the droplet breakup behavior will change as an effect of the reduction of the interfacial tension.Moreover,also the dynamic interfacial tension may be different with respect to the static,due to the fact that the surfactant may be easily desorbed from the droplet surface,generating additional disruptive stresses.In this work,the performance of five breakup kernels from the literature is assessed,to investigate their ability to predict the time evolution of the DSD and of the mean Sauter diameter,when different surfactants are employed.Simulations are performed with the Quadrature Method of Moments for the solution of the population balance model coupled with the two-fluid model implemented in the compressible Two Phase Euler Foam solver of the open-source computational fluid dynamics(CFD)code Open FOAM v.2.2.x.The time evolution of the mean Sauter diameter predicted by these kernels is validated against experimental data for six test cases referring to a stirred tank with different types of surfactants(Tween 20 and PVA 88%)at different concentrations operating under different stirrer rates.Our results show that for the dispersion containing Tween 20 additional stress is generated,the multifractal breakup kernel properly predicts the DSD evolution,whereas two other kernels predict too fast breakup of droplets covered by adsorbed PVA.Kernels derived originally for bubbles completely fail.展开更多
The axial concentration distribution of both particles with betterwetting (forming non-attached system) and poorer wetting (formingattached system) was investigated in a vertical gas-liquid-solidfluidized bed of 4.2 c...The axial concentration distribution of both particles with betterwetting (forming non-attached system) and poorer wetting (formingattached system) was investigated in a vertical gas-liquid-solidfluidized bed of 4.2 cm in diameters and 130 cm in height with thesolids holdup less than 0.05. The one-dimensionalsedimentation-dispersion model could be used satisfactorily todescribe the axial distribution of solids holdup by modifying only amodel parameter, i.e. by means of the terminal settling velocityminus a certain value, which is a functions of gas velocity andconsiders the effect of an additional drag force resulted fromattached rising bubbles.展开更多
A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed...A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux modei, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by k-ε-kp two-fluid modei, which shows a reasonable agreement. It is confirmed that the modified diffusion flux modei is suitable for simulating the multi-dimensional gas-particle two-phase flow.展开更多
In this paper, an SIRS epidemic model with high-risk immunization was investigated, where a susceptible neighbor of an infected node is immunized with rate h. Through analyzing the discrete-time model, we found that t...In this paper, an SIRS epidemic model with high-risk immunization was investigated, where a susceptible neighbor of an infected node is immunized with rate h. Through analyzing the discrete-time model, we found that the epidemic threshold above which an epidemic can prevail and persist in a population is inversely proportional to 1 - h value. We also studied the continuous-time epidemic model and obtained a different result： the epidemic threshold does not depend on the immunization parameter h. Our results suggest that the difference between the discrete-time epidemic model and the continuous-time epidemic model exists in the high-risk immunization.展开更多
In this paper, an SIQS epidemic model with constant recruitment and standard inci- dence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium t...In this paper, an SIQS epidemic model with constant recruitment and standard inci- dence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium to a reaction^diffusion system with homo- geneous Neumann boundary conditions is considered. Sufficient conditions for the local and global asymptotic stability are given by linearization and the method of upper and lower solutions and its associated monotone iterations. The result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small.展开更多
基金Supported by the National Natural Science Foundation of China (No. 20376053).
文摘A resident time model is proposed to evaluate the performance of agitated extraction columns. In this model, the resident time of dispersed drops is simulated with the discrete phase modeling, where the continuous phase and the dispersed phase （drops） are described by the single-phase Navier-Stokes （turbulence） model and Lagrangian model, respectively. The interaction of dispersed phase and continuous phase is neglected for the low concentration of drop in the cases studied. The statistical parameters of drops （the average resident time and standard deviation） under different operation conditions are computed for four columns. The relation of the above statistical parameters with the performance of columns is discussed and the criterions for an optimal compartment are outlined. Our results indicate that the resident time model is useful to evaluate the performance and optimize the design of extraction columns.
文摘The accurate prediction of the droplet size distribution(DSD)in liquid–liquid turbulent dispersions is of fundamental importance in many industrial applications and it requires suitable kernels in the population balance model.When a surfactant is included in liquid–liquid dispersions,the droplet breakup behavior will change as an effect of the reduction of the interfacial tension.Moreover,also the dynamic interfacial tension may be different with respect to the static,due to the fact that the surfactant may be easily desorbed from the droplet surface,generating additional disruptive stresses.In this work,the performance of five breakup kernels from the literature is assessed,to investigate their ability to predict the time evolution of the DSD and of the mean Sauter diameter,when different surfactants are employed.Simulations are performed with the Quadrature Method of Moments for the solution of the population balance model coupled with the two-fluid model implemented in the compressible Two Phase Euler Foam solver of the open-source computational fluid dynamics(CFD)code Open FOAM v.2.2.x.The time evolution of the mean Sauter diameter predicted by these kernels is validated against experimental data for six test cases referring to a stirred tank with different types of surfactants(Tween 20 and PVA 88%)at different concentrations operating under different stirrer rates.Our results show that for the dispersion containing Tween 20 additional stress is generated,the multifractal breakup kernel properly predicts the DSD evolution,whereas two other kernels predict too fast breakup of droplets covered by adsorbed PVA.Kernels derived originally for bubbles completely fail.
基金Supported by the Fujian Provincial Education Council (No. JB9940).
文摘The axial concentration distribution of both particles with betterwetting (forming non-attached system) and poorer wetting (formingattached system) was investigated in a vertical gas-liquid-solidfluidized bed of 4.2 cm in diameters and 130 cm in height with thesolids holdup less than 0.05. The one-dimensionalsedimentation-dispersion model could be used satisfactorily todescribe the axial distribution of solids holdup by modifying only amodel parameter, i.e. by means of the terminal settling velocityminus a certain value, which is a functions of gas velocity andconsiders the effect of an additional drag force resulted fromattached rising bubbles.
基金Special Funds for Major State Basic Research Projects of China(G1999022200)
文摘A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux modei, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by k-ε-kp two-fluid modei, which shows a reasonable agreement. It is confirmed that the modified diffusion flux modei is suitable for simulating the multi-dimensional gas-particle two-phase flow.
基金This research is supported by the National Natural Science Foundation of China （No. 61203153）.
文摘In this paper, an SIRS epidemic model with high-risk immunization was investigated, where a susceptible neighbor of an infected node is immunized with rate h. Through analyzing the discrete-time model, we found that the epidemic threshold above which an epidemic can prevail and persist in a population is inversely proportional to 1 - h value. We also studied the continuous-time epidemic model and obtained a different result： the epidemic threshold does not depend on the immunization parameter h. Our results suggest that the difference between the discrete-time epidemic model and the continuous-time epidemic model exists in the high-risk immunization.
基金This work was financially supported by the Natural Science Foundation of China （11271236, 11401356） and the Natural Science Basic Research Plan in Shaanxi Province of China （No. 2015JM1008）.
文摘In this paper, an SIQS epidemic model with constant recruitment and standard inci- dence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium to a reaction^diffusion system with homo- geneous Neumann boundary conditions is considered. Sufficient conditions for the local and global asymptotic stability are given by linearization and the method of upper and lower solutions and its associated monotone iterations. The result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small.
