Wall shear stress in backward‐facing step flow of a red blood cell suspension

Abstract

An experimental investigation of the wall shear stress distribution downstream of a backward‐facing step is carried out. Flow in this geometry is considered to be representative of flow in large and medium sized curved arteries and bifurcations. The wall shear stress distribution was determined by measuring the deformation of a gel layer, attached to the wall downstream of the step. Speckle pattern interferometry was applied to measure the deformation of the gel layer. The measured deformation, combined with the properties of the gel layer, served as an input for a finite element solid mechanics computation to determine the stress distribution in the gel layer. The wall shear stress, required to generate the measured deformation of the gel layer, was determined from these computations.

A Newtonian buffer solution and a non‐Newtonian red blood cell suspension were used as measuring fluids. The deformation of the gel layer was determined for a Newtonian buffer solution to evaluate the method and to obtain the properties of the gel layer. Subsequently, the wall shear stress distribution for the non‐Newtonian red blood cell suspension was determined for three different flow rates.

The inelastic non‐Newtonian Carreau–Yasuda model served as constitutive model for the red blood cell suspension. Using this model, the velocity and wall shear stress distribution were computed by means of a finite element fluid mechanics computation. From the comparison between the numerical and the experimental results, it can be concluded that wall shear stresses, induced by the red blood cell suspension, can be modeled accurately by employing a Carreau–Yasuda model.