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Title: 1D Models for Blood Flow in Small Vessels Using the Cosserat Theory
Authors: Carapau, Fernando
Keywords: Cosserat theory, blood flow, volume flow rate, shear-thinning flow, power law viscosity, Carreau-Yasuda viscosity
Issue Date: 1-Jan-2006
Abstract: This paper 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 cases of power law and Carreau-Yasuda viscosity functions, and also the correspondent equations for the wall shear stress which enters directly in the formulation as a dependent variable.
ISSN: 1109-2769
Type: article
Appears in Collections:MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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