1D Models for Blood Flow in Small Vessels Using the Cosserat Theory
Fernando Carapau (Department of Mathematics, University of 'Evora)
(October 31, 2006 3:30 PM - 4:30 PM)
This talk is motivated by the study of 1D fluid models for blood flow in the vascular system. In our work, we consider blood modeled as an incompressible shear-thinning generalized Newtonian fluid in a straight rigid and impermeable vessel with circular cross-section of constant radius. To study this problem, we use an approach based on the Cosserat theory (also called director theory) related to fluid dynamics which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this new system we obtain the unsteady relationship between mean pressure gradient and volume flow rate over a finite section of the tube for the specific case of power law model and also the correspondent equation for the wall shear stress which enters directly in the formulation as a dependent variable.