Publication Date


Document Type


First Advisor

Tan, Jifu

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


The wall shear stress (WSS) in blood vessels influences many biological processes, such as atherosclerosis, clot growth, angiogenesis, aneurysm rupture, and blood cell transport and adhesion. The deformable red blood cells (RBCs) in blood flow make the WSS even more complex. To analyze the WSS in complex fluids with cell suspensions, numerical simulations of blood flows in simple straight channels were conducted, where the fluid-solid interactions were simulated by immersed boundary-lattice Boltzmann method. The spatiotemporal dynamics of WSS were analyzed using dynamic mode decomposition (DMD), which is a technique that can extract the low-rank spatiotemporal features from complex fluids. The velocity fields and traction forces on the wall were analyzed. The dynamic modes showed the fluctuations and distribution of the traction forces exerted by the cells on the vessel wall, where magnitudes of traction forces were sharply increased when RBCs were close to the wall. The dynamic distribution reflected the shapes and locations of the RBC contacting surfaces. The reconstruction of dynamic modes captured features of distribution of traction forces accurately, with an average root-mean-square error (RMSE) of 0.0095 and an average relative RMSE of 3.012%, and average mean absolute error (MAE) is 0.0040 and average relative MAE is 8.806%. The WSS was influenced by tube diameter, RBC deformation, and hematocrit. E.g., radially squeezed RBCs can block the flow and cause a local discrepancy of flow velocity for vessels with small diameters (5 and 8 um with hematocrits 22.93% and 28.95%, respectively), which are less than the diameter of an RBC (8 um). Dense distributions of footprints were found on the walls of vessels with large diameters (8, 10, and 15 um with a hematocrit around 30%), where more RBCs were moving and colliding with each other, and their maximum traction forces were around 0.3 Pa. Local peaks of fluctuated traction forces caused by wall contacting of RBCs were around 0.15 Pa for cases of large diameters (8, 10, and 15 um), and the traction forces increased as RBCs approached to the wall and then decreased as RBCs moved away. The dynamics of the footprint of traction forces were captured by DMD models, and the majority of trends of fluctuations of traction forces are matched. The current research can be potentially used to construct reduced order models for complex flows.


90 pages




Northern Illinois University

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