Research advances of un-symmetric constitutive equation of anisotropic fluid,influence of un-symmetric stress tensor on material functions,vibrational shear flow of the fluid with small amplitudes and rheology of anis...Research advances of un-symmetric constitutive equation of anisotropic fluid,influence of un-symmetric stress tensor on material functions,vibrational shear flow of the fluid with small amplitudes and rheology of anisotropic suspension were reported.A new concept of simple anisotropic fluid was introduced.On the basis of anisotropic principle,the simple fluid stress behaviour was described by velocity gradient tensor F and spin tensor W instead of velocity gradient tensor D in the classic Leslie-Ericksen continuum theory.Two relaxation times analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equation of co-rotational type was introduced.More general model LCP-H for the fluid was developed.The unsymmetry of the shear stress was predicted by the present continuum theory for anisotropic viscoelastic fluid-LC polymer liquids.The influence of the relaxation times on material functions was specially studied.It is important to study the unsteady vibrational rotating flow with small amplitudes,as it is a best way to obtain knowledge of elasticity of the LC polymer,i.e.dynamic viscoelasticity.For the shear-unsymmetric stresses,two shear stresses were obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) were introduced by the constitutive equation which was defined by rotating shear rate introduced by author.For the two stability problems of fluid,such as stability of hydrodynamic flow and orientational motion,were discussed.The results show that the polymer suspension systems exhibit anisotropic character.The PNC systems can exhibit significant shear-thinning effects.For more concentrated polymer nano-suspensions,the first normal stress difference change from positive to negative,which is similar to LC polymer behavior.展开更多
Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represen...Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represents relaxation of the normal-symmetric stress components;λs represents relaxation of the shear-unsymmetric stress components.A vibrational rotating flow in gap between cylinders with small amplitudes is studied for the anisotropic viscoelastic fluid-liquid crystalline polymer.The time-dependent constitutive equation are linearized with respect to parameter of small amplitude.For the normal-symmetric part of stress tensor analytical expression of the shear stress is obtained by the constitutive equation.The complex viscosity,complex shear modulus,dynamic and imaginary viscosities,storage modulus and loss modulus are obtained for the normal-symmetric stress case which are defined by the common shear rate.For the shear-unsymmetric stress part,two shear stresses are obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) are given by the constitutive equation which are defined by rotating shear rate introduced by author.The dynamic and imaginary viscosities,storage modulus and loss modulus are given for each complex viscosities and complex shear modulus.Using the constituive equation the rotating flow with small amplitudes in gap between two coaxial cylinders is studied.展开更多
基金Project(10772177) supported by the National Natural Science Foundation of China
文摘Research advances of un-symmetric constitutive equation of anisotropic fluid,influence of un-symmetric stress tensor on material functions,vibrational shear flow of the fluid with small amplitudes and rheology of anisotropic suspension were reported.A new concept of simple anisotropic fluid was introduced.On the basis of anisotropic principle,the simple fluid stress behaviour was described by velocity gradient tensor F and spin tensor W instead of velocity gradient tensor D in the classic Leslie-Ericksen continuum theory.Two relaxation times analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equation of co-rotational type was introduced.More general model LCP-H for the fluid was developed.The unsymmetry of the shear stress was predicted by the present continuum theory for anisotropic viscoelastic fluid-LC polymer liquids.The influence of the relaxation times on material functions was specially studied.It is important to study the unsteady vibrational rotating flow with small amplitudes,as it is a best way to obtain knowledge of elasticity of the LC polymer,i.e.dynamic viscoelasticity.For the shear-unsymmetric stresses,two shear stresses were obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) were introduced by the constitutive equation which was defined by rotating shear rate introduced by author.For the two stability problems of fluid,such as stability of hydrodynamic flow and orientational motion,were discussed.The results show that the polymer suspension systems exhibit anisotropic character.The PNC systems can exhibit significant shear-thinning effects.For more concentrated polymer nano-suspensions,the first normal stress difference change from positive to negative,which is similar to LC polymer behavior.
基金Project(10772177) supported by the National Natural Science Foundation of China
文摘Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represents relaxation of the normal-symmetric stress components;λs represents relaxation of the shear-unsymmetric stress components.A vibrational rotating flow in gap between cylinders with small amplitudes is studied for the anisotropic viscoelastic fluid-liquid crystalline polymer.The time-dependent constitutive equation are linearized with respect to parameter of small amplitude.For the normal-symmetric part of stress tensor analytical expression of the shear stress is obtained by the constitutive equation.The complex viscosity,complex shear modulus,dynamic and imaginary viscosities,storage modulus and loss modulus are obtained for the normal-symmetric stress case which are defined by the common shear rate.For the shear-unsymmetric stress part,two shear stresses are obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) are given by the constitutive equation which are defined by rotating shear rate introduced by author.The dynamic and imaginary viscosities,storage modulus and loss modulus are given for each complex viscosities and complex shear modulus.Using the constituive equation the rotating flow with small amplitudes in gap between two coaxial cylinders is studied.
