Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method

TLDR

The lattice Boltzmann method was adapted to simulate non‑Newtonian shear‑dependent viscosity, implementing Casson and Carreau‑Yasuda models to compare two‑dimensional Newtonian and non‑Newtonian flows in steady and oscillatory conditions in straight and curved pipes. Compared to Newtonian flows, both Casson and Carreau‑Yasuda models exhibit significant differences in steady flow, with larger disparities at low Reynolds and Womersley numbers in straight‑pipe oscillatory flows—especially for the Casson model—and moderate velocity differences near walls in curved‑pipe Carreau‑Yasuda flows, highlighting potential implications for atherosclerotic progression.

Abstract

The lattice Boltzmann method is modified to allow the simulation of non-Newtonian shear-dependent viscosity models. Casson and Carreau-Yasuda non-Newtonian blood viscosity models are implemented and are used to compare two-dimensional Newtonian and non-Newtonian flows in the context of simple steady flow and oscillatory flow in straight and curved pipe geometries. It is found that compared to analogous Newtonian flows, both the Casson and Carreau-Yasuda flows exhibit significant differences in the steady flow situation. In the straight pipe oscillatory flows, both models exhibit differences in velocity and shear, with the largest differences occurring at low Reynolds and Womersley numbers. Larger differences occur for the Casson model. In the curved pipe Carreau-Yasuda model, moderate differences are observed in the velocities in the central regions of the geometries, and the largest shear rate differences are observed near the geometry walls. These differences may be important for the study of atherosclerotic progression.