A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper ...A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper is a continuation of the recent publication [1] to study extrusion-extensional flow of the fluid. A new concept of simple anisotropic fluid is introduced. On the basis of anisotropic simple fluid, stress behavior is described by velocity gradient tensor F and spin tensor W instead of the velocity gradient tensor D in the classic Leslie?Ericksen continuum theory. A special form of the constitutive equation of the co-rotational type is established for the fluid. Using the special form of the constitutive equation in components a computational analytical theory of the extrusion-extensional flow is developed for the LC polymer liquids - anisotropic viscoelastic fluid. Application of the constitutive theory to the flow is successful in predicting bifurcation of elongational viscosity and contraction of extrudate for LC polymer liquids–anisotropic viscoelastic fluid. The contraction of extrudate of LC polymer liquids may be associated with the stored elastic energy conversion into that necessary for bifurcation of elongational viscosity in extrusion extensional flow of the fluid.展开更多
Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional vis-cosity, normal stress and shear-thin...Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional vis-cosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Max- well (UCM) models to represent the behavior of so-called Boger fluids in axisymmetric contrac-tion flows, in (unsuccessful) attempts to predict the very large enhancements that were ob-served experimentally. In more recent studies, other constitutive models have been employed to interpret observed behavior and some pro-gress has been made, although finding a (re-spectable) model to describe observed contrac-tion-flow behavior, even qualitatively, has been frustratingly difficult. With this in mind, the present study discusses the ability of a well- known FENE type model (the so-called FENE- CR model) to describe observed behavior. For various reasons, an axisymmetric (4:1:4) con-traction/expansion geometry, with rounded corners, is singled out for special attention, and a new hybrid finite element/volume algo-rithm is utilized to conduct the modeling, which reflects an incremental pressure-correction time-stepping structure. New to this algo-rithmic formulation are techniques in time discretization, discrete treatment of pressure terms, and compatible stress/velocity-gradient representation. We shall argue that the current simulations for the FENE-CR model have re-sulted in a major improvement in the sort-for agreement between theory and experiment in this important bench-mark problem.展开更多
Perovskite K(Ta,Nb)O_(3)(KTN)single crystal has drawn great interests for its outstanding electro-optic performance and excellent piezoelectric response.However,growth of compositionally uniform KTN single crystals ha...Perovskite K(Ta,Nb)O_(3)(KTN)single crystal has drawn great interests for its outstanding electro-optic performance and excellent piezoelectric response.However,growth of compositionally uniform KTN single crystals has always been a great challenge for the great segregation difference between Nb and Ta.In this work,we propose a thermal field optimization strategy to resolve this challenge.Homogenous Sn doped KTN(Sn:KTN)single crystal with significantly reduced composition gradient(0.003 mol/mm,1/4 e1/8 of other KTN system),minimal TC variation(13℃)and excellent piezoelectric and dielectric response(d_(33)=373 pC/N andε^(T)_(33)=5206)has been successfully achieved.We found that the functional properties of Sn:KTN were greatly affected by the near-room temperature tetragonal-cubic phase transition.From the intrinsic aspect,longitudinal lattice deformation becomes much easier,resulting in maximum piezoelectric(d^(*)_(33)),dielectric(ε^(T*)_(33)),elastic(s^(E*)_(33))and electromechanical coupling(k^(*)_(33))coefficients along polar direction[001]_(C).From the extrinsic aspect,both domain wall density and domain wall mobility are greatly improved for the reduced lattice distortion,which also contribute a lot to the functional properties.This work provides a simple and practical route for designing and growing high quality crystals,and more importantly,reveals the fundamental mechanism of the phase transitions/boundaries on the functional properties.展开更多
文摘A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper is a continuation of the recent publication [1] to study extrusion-extensional flow of the fluid. A new concept of simple anisotropic fluid is introduced. On the basis of anisotropic simple fluid, stress behavior is described by velocity gradient tensor F and spin tensor W instead of the velocity gradient tensor D in the classic Leslie?Ericksen continuum theory. A special form of the constitutive equation of the co-rotational type is established for the fluid. Using the special form of the constitutive equation in components a computational analytical theory of the extrusion-extensional flow is developed for the LC polymer liquids - anisotropic viscoelastic fluid. Application of the constitutive theory to the flow is successful in predicting bifurcation of elongational viscosity and contraction of extrudate for LC polymer liquids–anisotropic viscoelastic fluid. The contraction of extrudate of LC polymer liquids may be associated with the stored elastic energy conversion into that necessary for bifurcation of elongational viscosity in extrusion extensional flow of the fluid.
文摘Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional vis-cosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Max- well (UCM) models to represent the behavior of so-called Boger fluids in axisymmetric contrac-tion flows, in (unsuccessful) attempts to predict the very large enhancements that were ob-served experimentally. In more recent studies, other constitutive models have been employed to interpret observed behavior and some pro-gress has been made, although finding a (re-spectable) model to describe observed contrac-tion-flow behavior, even qualitatively, has been frustratingly difficult. With this in mind, the present study discusses the ability of a well- known FENE type model (the so-called FENE- CR model) to describe observed behavior. For various reasons, an axisymmetric (4:1:4) con-traction/expansion geometry, with rounded corners, is singled out for special attention, and a new hybrid finite element/volume algo-rithm is utilized to conduct the modeling, which reflects an incremental pressure-correction time-stepping structure. New to this algo-rithmic formulation are techniques in time discretization, discrete treatment of pressure terms, and compatible stress/velocity-gradient representation. We shall argue that the current simulations for the FENE-CR model have re-sulted in a major improvement in the sort-for agreement between theory and experiment in this important bench-mark problem.
基金This work was supported by the National Natural Science Foundation of China(Grants Nos.52072218,and 52072189)Natural Science Foundation of Shandong Province,China(ZR2020KE019)+1 种基金the Project for Introduced Innovation Team in Jinan,China(2020GXRC037)the Primary Research&Development Plan of Shandong Province,China(No.2019JZZY010313).REFERENCES.
文摘Perovskite K(Ta,Nb)O_(3)(KTN)single crystal has drawn great interests for its outstanding electro-optic performance and excellent piezoelectric response.However,growth of compositionally uniform KTN single crystals has always been a great challenge for the great segregation difference between Nb and Ta.In this work,we propose a thermal field optimization strategy to resolve this challenge.Homogenous Sn doped KTN(Sn:KTN)single crystal with significantly reduced composition gradient(0.003 mol/mm,1/4 e1/8 of other KTN system),minimal TC variation(13℃)and excellent piezoelectric and dielectric response(d_(33)=373 pC/N andε^(T)_(33)=5206)has been successfully achieved.We found that the functional properties of Sn:KTN were greatly affected by the near-room temperature tetragonal-cubic phase transition.From the intrinsic aspect,longitudinal lattice deformation becomes much easier,resulting in maximum piezoelectric(d^(*)_(33)),dielectric(ε^(T*)_(33)),elastic(s^(E*)_(33))and electromechanical coupling(k^(*)_(33))coefficients along polar direction[001]_(C).From the extrinsic aspect,both domain wall density and domain wall mobility are greatly improved for the reduced lattice distortion,which also contribute a lot to the functional properties.This work provides a simple and practical route for designing and growing high quality crystals,and more importantly,reveals the fundamental mechanism of the phase transitions/boundaries on the functional properties.
