International Journal of Dynamics of Fluids

The stability of the Poiseuille flow of a viscous incompressible fluid in a multilay-ered non-isotropic viscoelastic tube is investigated. The compliant wall of the tube is allowed to be in a dynamic interaction with the flow. The material and geometrical parameters of the model correspond to mechanical properties and structure of the arterial vessels. A numerical method is developed in order to find the eigenvalues of the system in the limit of the linear stability analysis. Both temporal and spatial eigenvalues of the system are computed and compared to the eigenvalues for the isotropic wall. The multivarious effects of the anisotropy on the eigenvalues of the system are investigated. The influence of the viscosities, shear and Young's modulus of the layers on the most unstable mode is examined. In view of the importance of the result in medical diagnostics, a particular attention is paid to the speed of propagation of the most unstable mode.