A constitutive model for flow-induced anisotropic behavior of viscoelastic complex fluids

Flow-induced structural anisotropy could result when a complex fluid system is removed from equilibrium by means of hydrodynamic forces. In this paper, a general theory is developed to model flow-induced anisotropic behavior of complex viscoelastic systems such as polymer solutions/melts and suspensions. The rheological properties are characterized by viscosity and relaxation time tensors. We consider a second-rank tensor as a measure of the microstructure. We consider the effect of the flow on the structural changes, i.e. the evolution of the microstructure tensor is governed by a relaxation-type differential equation. We also propose that the viscosity and the relaxation time tensors depend on the second-rank microstructure tensor, that is as the microstructure tensor changes with the applied rate of deformation, the viscosity and relaxation time tensors evolve accordingly. As an example we consider the elongational flows of two complex fluids.