Spectral theory of anisotropic fluids

The spectral theory of symmetric viscoelastic fluids with arbitrary anisotropy, which is based on the generalized Maxwell relaxation law, is developed. A feature of the proposed approach is the use of a spectral (canonical) representation of tensors that describe the anisotropic properties of fluids. Simple special cases of the spectra of viscosity and relaxation-time tensors are considered. The orientation dynamics of anisotropic fluids is discussed. A theory of generation of eigenmodes that are related to stress relaxation is developed. On the basis of the spectral theory, the possibility of the existence of soft (zero energy) modes in anisotropic fluids with deep anisotropy is considered. The proposed theory opens up new alternatives for classifying anisotropic fluids.