Abstract: The aim of this talk is the development and study of 1D models using the Cosserat director theory. In particular we study mathematical models for blood flow in the vascular system. We consider blood modeled both as an incompressible viscous and viscoelastic fluid. Starting with the exact three-dimensional equations for an incompressible viscous or viscoelastic fluid, a system of one-dimensional nonlinear equations is derived for axisymmetric motion inside a slender surface of revolution with circular cross section. This system is obtained by introducing an approximate velocity field into weighted integrals of the momentum equation over the circular cross section. This approximate velocity is obtained by using the Cosserat theory in fluid dynamics.
In this talk we apply the Cosserat theory to both Newtonian and non-Newtonian fluids in tubes. For a specific model and geometry we obtain the unsteady relationship between average pressure gradient and volume flow rate over a finite section of the tube and the corresponding equation for the wall shear stress. Attention is focused on the steady case with rigid and impermeable walls with and without swirling motion, and flow properties as existence, uniqueness and stability of steady solutions are also given.