*Shear thinning effects on blood flow in straight and curved tubes*. E. Cherry and J.K. Eaton. *Physics of Fluids*, 25:073104, 2013. (URL)

Simulations were performed to determine the magnitude and types of errors one can expect when approximating blood in large arteries as a Newtonian fluid, particularly in the presence of secondary flows. This was accomplished by running steady simulations of blood flow in straight and curved tubes using both Newtonian and shear-thinning viscosity models. In the shear-thinning simulations, the viscosity was modeled as a shear rate-dependent function fit to experimental data. Simulations in straight tubes were modeled after physiologically relevant arterial flows, and flow parameters for the curved tube simulations were chosen to examine a variety of secondary flow strengths. The diameters ranged from 1 mm to 10 mm and the Reynolds numbers from 24 to 1500. Pressure and velocity data are reported for all simulations. In the straight tube simulations, the shear-thinning flows had flattened velocity profiles and higher pressure gradients compared to the Newtonian simulations. In the curved tube flows, the shear-thinning simulations tended to have blunted axial velocity profiles, decreased secondary flow strengths, and decreased axial vorticity compared to the Newtonian simulations. The cross-sectionally averaged pressure drops in the curved tubes were higher in the shear-thinning flows at low Reynolds number but lower at high Reynolds number. The maximum deviation in secondary flow magnitude averaged over the cross sectional area was 19\% of the maximum secondary flow and the maximum deviation in axial vorticity was 25\% of the maximum vorticity.

`@ARTICLE { cherry_eaton13,`

AUTHOR = { E. Cherry and J.K. Eaton },

TITLE = { Shear thinning effects on blood flow in straight and curved tubes },

YEAR = { 2013 },

JOURNAL = { Physics of Fluids },

VOLUME = { 25 },

PAGES = { 073104 },

ABSTRACT = { Simulations were performed to determine the magnitude and types of errors one can expect when approximating blood in large arteries as a Newtonian fluid, particularly in the presence of secondary flows. This was accomplished by running steady simulations of blood flow in straight and curved tubes using both Newtonian and shear-thinning viscosity models. In the shear-thinning simulations, the viscosity was modeled as a shear rate-dependent function fit to experimental data. Simulations in straight tubes were modeled after physiologically relevant arterial flows, and flow parameters for the curved tube simulations were chosen to examine a variety of secondary flow strengths. The diameters ranged from 1 mm to 10 mm and the Reynolds numbers from 24 to 1500. Pressure and velocity data are reported for all simulations. In the straight tube simulations, the shear-thinning flows had flattened velocity profiles and higher pressure gradients compared to the Newtonian simulations. In the curved tube flows, the shear-thinning simulations tended to have blunted axial velocity profiles, decreased secondary flow strengths, and decreased axial vorticity compared to the Newtonian simulations. The cross-sectionally averaged pressure drops in the curved tubes were higher in the shear-thinning flows at low Reynolds number but lower at high Reynolds number. The maximum deviation in secondary flow magnitude averaged over the cross sectional area was 19\% of the maximum secondary flow and the maximum deviation in axial vorticity was 25\% of the maximum vorticity. },

URL = { http://dx.doi.org/10.1063/1.4816369 },

}