Vibrational shear flow of anisotropic viscoelastic fluid with small amplitudes

Abstract

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: λ _n represents relaxation of the normal-symmetric stress components; λ _s 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.