Abstract
This paper proposes a truncated fractional-derivative constitutive model to consider the non-locality of non-Newtonian fluids. The single relaxation time lattice Boltzmann method (SRT-LBM) is used to simulate seepage of non-Newtonian fluid. The results are verified by analytical solutions while the flow characteristics of non-Newtonian fluids are explored. In the case of laminar flow, the steady-state velocity aistribution of shear-thinning and shear-thickening fluids after 10~5 - time steps are compared with the analytical distribution, and the results show an agreement within 2%. For non-Newtonian index simulation, the thicker the fluid, the larger the velocity and the more volatility, implying the more complex flow characteristics for shear-thickening fluid. Additionally, small fractional indexes correspond to large computational errors in regions away from the boundary. Flow characteristics research shows that the seepage of power-law fluid in fractured media exhibits non-Darcy phenomenon. As the fractional index decreases (i.e., fluid becomes thicker), the obstruction of the medium increases, resulting in a reduction in the medium's permeability. The shear stress of non-Newtonian fluids can be memorized by the mean section velocity distribution, and the memory capacity of different fluids can be captured by the fractional index. Furthermore, the fractional-derivative critical Reynolds number is introduced to clarify the applicable conditions of non-Newtonian flow equations, which increase with diameter and initial kinematic viscosity. The fractional-derivative critical Reynolds number of dilatant fluids is larger than pseudoplastic fluids, due to the memory properties of the fluid as well as the physical characteristics.
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