The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relation...The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relationship between extensional viscosity and strain rates. The results obtained qualitatively agree with the experimental results. The study makes it practicable to simulate the rheologic behaviors of spinning flow of liquid crystalline polymer using co-rotational Oldroyd fluid B model.展开更多
This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit,...This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.展开更多
In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using d...In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.展开更多
In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interf...In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence （de-stabilizing effects） depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.展开更多
This paper is concerned with the numerical simulation of the transient effect of an inertialess Boger flow past a confined circular cylinder and the comparison of predictions with particle image velocimetry (PIV) meas...This paper is concerned with the numerical simulation of the transient effect of an inertialess Boger flow past a confined circular cylinder and the comparison of predictions with particle image velocimetry (PIV) measurements given by Shiang et al.. Dynamic simulation based on the Oldroyd-B constitutive model was carried out using a Lagrangian-Eulerian algorithm. The evolution of velocity field was obtained for the flow at two Deborah (De) numbers, i.e. De = 1.2 and 3.0. At low De, the flow reached steady state rapidly, and showed a symmetric flow regime. However, at high De, the time required to reach steady flow behind the cylinder increased significantly, and the distribution of the velocity field appears to be asymmetric with respect to the stagnation line. Fairly good agreement between the numerical results and the experimental observations is reported. It can be concluded that both the experimental measurements and the present simulations indicate that the elasticity of the polymeric flow strongly affect the flow regime of viscoelastic flow around a confined cylinder.展开更多
A Fourier-Chebyshev Petrov-Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables and is wr...A Fourier-Chebyshev Petrov-Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables and is written in FORTRAN. Systematic studies are presented of the dependence of eigenval-ues and other quantities on the axial and azimuthal wave numbers;the Reyn-olds’ number of up to 107 and the Weissenberg’s number that is considered lower here. The flow will be considered stable if all the real parts of the ei-genvalues obtained are negative and unstable if only one of these values is positive.展开更多
文摘The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relationship between extensional viscosity and strain rates. The results obtained qualitatively agree with the experimental results. The study makes it practicable to simulate the rheologic behaviors of spinning flow of liquid crystalline polymer using co-rotational Oldroyd fluid B model.
文摘This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.
基金supported by The project supported by the Natural Science Foundation of Shandong Province of China (Y2007A06)
文摘In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.
文摘In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence （de-stabilizing effects） depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.
基金This work is supported by the National Natural Science Foundation of China (No. 29634030) and subsidized by the Special Funds for Major State Basic Research Projects (G1999064800).
文摘This paper is concerned with the numerical simulation of the transient effect of an inertialess Boger flow past a confined circular cylinder and the comparison of predictions with particle image velocimetry (PIV) measurements given by Shiang et al.. Dynamic simulation based on the Oldroyd-B constitutive model was carried out using a Lagrangian-Eulerian algorithm. The evolution of velocity field was obtained for the flow at two Deborah (De) numbers, i.e. De = 1.2 and 3.0. At low De, the flow reached steady state rapidly, and showed a symmetric flow regime. However, at high De, the time required to reach steady flow behind the cylinder increased significantly, and the distribution of the velocity field appears to be asymmetric with respect to the stagnation line. Fairly good agreement between the numerical results and the experimental observations is reported. It can be concluded that both the experimental measurements and the present simulations indicate that the elasticity of the polymeric flow strongly affect the flow regime of viscoelastic flow around a confined cylinder.
文摘A Fourier-Chebyshev Petrov-Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables and is written in FORTRAN. Systematic studies are presented of the dependence of eigenval-ues and other quantities on the axial and azimuthal wave numbers;the Reyn-olds’ number of up to 107 and the Weissenberg’s number that is considered lower here. The flow will be considered stable if all the real parts of the ei-genvalues obtained are negative and unstable if only one of these values is positive.
