Using the multiple reference frames （MRF） impeller method, the three-dimensional non-Newtonian flow field generated by a double helical ribbon （DHR） impeller has been simulated. The velocity field calculated by th...Using the multiple reference frames （MRF） impeller method, the three-dimensional non-Newtonian flow field generated by a double helical ribbon （DHR） impeller has been simulated. The velocity field calculated by the numerical simulation was similar to the previous studies and the power constant agreed well with the experimental data. Three computational fluid dynamic （CFD） methods, labeled Ⅰ, Ⅱ and Ⅲ, were used to compute the Metzuer constant k5. The results showed that the calculated value from the slop method （method Ⅰ） was consistent with the experimental data. Method Ⅱ, which took the maximal circumference-average shear rate around the impeller as the effective shear rate to compute ks, also showed good agreement with the experiment. However, both methods suffer from the complexity of calculation procedures. A new method （method Ⅲ） was devised in this paper to use the area-weighted average viscosity around the impeller as the effective viscosity for calculating k5. Method Ⅲ showed both good accuracy and ease of use.展开更多
In the framework of elastic rod model, the Euler-Lagrange equations characterizing the equilibrium configuration of the polymer chain are derived from a free energy functional associated with the curvature, torsion, t...In the framework of elastic rod model, the Euler-Lagrange equations characterizing the equilibrium configuration of the polymer chain are derived from a free energy functional associated with the curvature, torsion, twisting angle, and its derivative with respect to the arc-length. The configurations of the helical ribbons with different cross-sectional shapes are given. The effects of the elastic properties, the cross-sectional shapes, and the intrinsic twisting on the helical ribbons are discussed. The results show that the pitch angle of the helical ribbon decreases with the increase in the ratio of the twisting rigidity to the bending rigidity and approaches the intrinsic twisting. If the bending rigidity is much greater than the twisting rigidity, the bending and twisting of the helical ribbon always appear simultaneously.展开更多
The solid acid of the first protonated zincoborophosphate, (H 3O)Zn(H 2O) 2BP 2O 8·H 2O (1), was soventothermally synthesized by the reaction of Zn(NO 3) 2·6H 2O and H 3BO 3 with H 3PO 4 in a mi...The solid acid of the first protonated zincoborophosphate, (H 3O)Zn(H 2O) 2BP 2O 8·H 2O (1), was soventothermally synthesized by the reaction of Zn(NO 3) 2·6H 2O and H 3BO 3 with H 3PO 4 in a mixed solvent, and structurally characterized by single-crystal X-ray diffraction analysis. It crystallizes in the hexagonal P6 122, a=0.9604(4) nm, c=1.5297(6) nm, V=1.2218(8) nm 3, D c=2.921 g/cm 3, Z=6, F(000)=1080, μ=3.495 mm -1. The structure features that the tetrahedra-tetrahedra helices interconnected by octahedra and strong hydrogen bond interactions form a three-dimensional framework. The protonated water molecules are located at unique positions. Other characterizations by IR and thermal analysis are also described.展开更多
基金Supported by the Natural Science Foundation of Tianjin （07JCZDJC02600）.
文摘Using the multiple reference frames （MRF） impeller method, the three-dimensional non-Newtonian flow field generated by a double helical ribbon （DHR） impeller has been simulated. The velocity field calculated by the numerical simulation was similar to the previous studies and the power constant agreed well with the experimental data. Three computational fluid dynamic （CFD） methods, labeled Ⅰ, Ⅱ and Ⅲ, were used to compute the Metzuer constant k5. The results showed that the calculated value from the slop method （method Ⅰ） was consistent with the experimental data. Method Ⅱ, which took the maximal circumference-average shear rate around the impeller as the effective shear rate to compute ks, also showed good agreement with the experiment. However, both methods suffer from the complexity of calculation procedures. A new method （method Ⅲ） was devised in this paper to use the area-weighted average viscosity around the impeller as the effective viscosity for calculating k5. Method Ⅲ showed both good accuracy and ease of use.
基金Project supported by the National Natural Science Foundation of China(No.11172130)
文摘In the framework of elastic rod model, the Euler-Lagrange equations characterizing the equilibrium configuration of the polymer chain are derived from a free energy functional associated with the curvature, torsion, twisting angle, and its derivative with respect to the arc-length. The configurations of the helical ribbons with different cross-sectional shapes are given. The effects of the elastic properties, the cross-sectional shapes, and the intrinsic twisting on the helical ribbons are discussed. The results show that the pitch angle of the helical ribbon decreases with the increase in the ratio of the twisting rigidity to the bending rigidity and approaches the intrinsic twisting. If the bending rigidity is much greater than the twisting rigidity, the bending and twisting of the helical ribbon always appear simultaneously.
文摘The solid acid of the first protonated zincoborophosphate, (H 3O)Zn(H 2O) 2BP 2O 8·H 2O (1), was soventothermally synthesized by the reaction of Zn(NO 3) 2·6H 2O and H 3BO 3 with H 3PO 4 in a mixed solvent, and structurally characterized by single-crystal X-ray diffraction analysis. It crystallizes in the hexagonal P6 122, a=0.9604(4) nm, c=1.5297(6) nm, V=1.2218(8) nm 3, D c=2.921 g/cm 3, Z=6, F(000)=1080, μ=3.495 mm -1. The structure features that the tetrahedra-tetrahedra helices interconnected by octahedra and strong hydrogen bond interactions form a three-dimensional framework. The protonated water molecules are located at unique positions. Other characterizations by IR and thermal analysis are also described.
