A gas-liquid mass transfer model based on an unsteady state film mechanism applied to a single bubble is presented. The mathematical model was solved using Laplace transform to obtain an analytical solution of concent...A gas-liquid mass transfer model based on an unsteady state film mechanism applied to a single bubble is presented. The mathematical model was solved using Laplace transform to obtain an analytical solution of concentration profile in terms of the radial position r and time t. The dynamic mass transfer flux was deduced and the influence of the bubble size was also determined. A mathematical method for deducing the average mass transfer flux directly from the Laplace transformed concentration is presented. Its accuracy is verified by comparing the numerical results with those from the indirect method. The influences of the model parameters, namely, the bubble size R, liquid film thickness δ, and the surface renewal constant s on the average mass transfer flux were investigated. The proposed model is useful for a better understanding of the mass transfer mechanism and an optimum design of gas-liquid contact equipment.展开更多
Quantitative prediction of distribution function and adhesionefficiency of particles around a rising bubble in slurry systems ispresented in this work. By solving the convection-diffusion equation(Fokker-Planck equati...Quantitative prediction of distribution function and adhesionefficiency of particles around a rising bubble in slurry systems ispresented in this work. By solving the convection-diffusion equation(Fokker-Planck equation), the influence of Brownian diffusivity offine particles on concentration distribution and adhesion efficiencyis demonstrated with the hydrodynamic force and van der Waalsattractive potential between particles and bubble considered. It isfound that two kinds of mechanism dominate the adhesion process ofparticles on bubble according to different Peclet number or size ofparticles and bubble, as well as other properties of the slurrysystems. In addition, the viscosity ratio of bubble to the suspendingfluid was found to have obvious influence on particle adhesion.展开更多
Density functional theory (DFT) simulation was performed to investigate the adsorption mechanisms between frothers and gas–liquid interface. In water phase, the polar head group of the frother molecule was connected ...Density functional theory (DFT) simulation was performed to investigate the adsorption mechanisms between frothers and gas–liquid interface. In water phase, the polar head group of the frother molecule was connected with water molecules by hydrogen bonding, while the non-polar group showed that hydrophobic property and water molecules around it were repelled away. The adsorption of water molecules on single frother molecule suggests that the complexes of α-terpineol-7H2O, MIBC-7H2O and DF200-13H2O reach their stable structure. The hydration shell affects both the polar head group and the non-polar group. The liquid film drainage rate of DF200 is the lowest, while α-terpineol and MIBC are almost the same. The adsorption layer of frother molecules adsorbed at the gas-liquid interface reveals that the α-terpineol molecules are more neatly arranged and better distributed. The DF200 molecules are arranged much more loosely than MIBC molecules. These results suggest that the α-terpineol molecule layer could better block the diffusion of gas through the liquid film than DF200 and MIBC. The simulation results indicate that the foam stability of α-terpineol is the best, followed by DF200 and MIBC.展开更多
基金Supported by the National Science Foundation of China (No. 20276035) and the SINOPEC Fundamental Research Foundation (No.X500021).
文摘A gas-liquid mass transfer model based on an unsteady state film mechanism applied to a single bubble is presented. The mathematical model was solved using Laplace transform to obtain an analytical solution of concentration profile in terms of the radial position r and time t. The dynamic mass transfer flux was deduced and the influence of the bubble size was also determined. A mathematical method for deducing the average mass transfer flux directly from the Laplace transformed concentration is presented. Its accuracy is verified by comparing the numerical results with those from the indirect method. The influences of the model parameters, namely, the bubble size R, liquid film thickness δ, and the surface renewal constant s on the average mass transfer flux were investigated. The proposed model is useful for a better understanding of the mass transfer mechanism and an optimum design of gas-liquid contact equipment.
基金Supported by the National Natural Science Foundation of China (No. 20126010).
文摘Quantitative prediction of distribution function and adhesionefficiency of particles around a rising bubble in slurry systems ispresented in this work. By solving the convection-diffusion equation(Fokker-Planck equation), the influence of Brownian diffusivity offine particles on concentration distribution and adhesion efficiencyis demonstrated with the hydrodynamic force and van der Waalsattractive potential between particles and bubble considered. It isfound that two kinds of mechanism dominate the adhesion process ofparticles on bubble according to different Peclet number or size ofparticles and bubble, as well as other properties of the slurrysystems. In addition, the viscosity ratio of bubble to the suspendingfluid was found to have obvious influence on particle adhesion.
基金Projects(51574092,51874106)supported by the National Natural Science Foundation,ChinaProject supported by Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund(the second phase),China
文摘Density functional theory (DFT) simulation was performed to investigate the adsorption mechanisms between frothers and gas–liquid interface. In water phase, the polar head group of the frother molecule was connected with water molecules by hydrogen bonding, while the non-polar group showed that hydrophobic property and water molecules around it were repelled away. The adsorption of water molecules on single frother molecule suggests that the complexes of α-terpineol-7H2O, MIBC-7H2O and DF200-13H2O reach their stable structure. The hydration shell affects both the polar head group and the non-polar group. The liquid film drainage rate of DF200 is the lowest, while α-terpineol and MIBC are almost the same. The adsorption layer of frother molecules adsorbed at the gas-liquid interface reveals that the α-terpineol molecules are more neatly arranged and better distributed. The DF200 molecules are arranged much more loosely than MIBC molecules. These results suggest that the α-terpineol molecule layer could better block the diffusion of gas through the liquid film than DF200 and MIBC. The simulation results indicate that the foam stability of α-terpineol is the best, followed by DF200 and MIBC.
