Evaluation of WSS Distributions in Pulsatile Non-Newtonian Fluid Flows Using the MRT-LB Model

Understanding how fluids impact wall shear stress (WSS) is vital for various applications, especially in biomedical contexts where WSS may be a contributing factor to vascular diseases. This study evaluates the non-Newtonian lattice Boltzmann model (nN-LBM) implemented with single (BGK) and multiple relaxation time (MRT) collision operators using the Carreau-Yasuda equation. These operators assess WSS distribution in non-Newtonian fluids in a microscale stenosed channel. Comparing the WSS profiles with experimental data and a Navier-Stokes solver confirms the nN-LBM's accuracy. We examined shear-thinning fluids with different xanthan gum concentrations and a Newtonian fluid. Results indicate that non-Newtonian fluids show oscillating wall shear stress more than Newtonian ones under similar conditions. Additionally, we explored the effects of higher Reynolds numbers on WSS. Non-Newtonian fluids display pronounced fluctuations at elevated Reynolds numbers. The stability of the BGK is found to be influenced by the characteristic time scale (λ) inherent in the Carreau-Yasuda model. This sensitivity prompts the need for implementation of the MRT approach. Adopting a more advanced collision operator and precisely managing physical relaxation moments can enhance stability and computational efficiency. Considering a 0.042% Xanthan-gum fluid, the BGK remains stable for low values of λ where the viscosity gradient is smaller. However, by increasing this value to reflect more pronounced viscosity gradients, the MRT demonstrates its capability by maintaining robust numerical stability even at considerably higher values.