Impact of Wall-Slip on Real Shear Thickening Fluid Flow Behavior in Rectangular Channels: Insights from LBM and Theoretical Modeling

The liquid slip phenomenon are pivotal for understanding fluid behavior at small scales and has been investigated using the lattice Boltzmann method (LBM). Boundary conditions for the lattice Boltzmann liquid flow simulation, however, are much beyond from ideal and how to precisely determine the boundary conditions for liquid flow with slip remains a challenge. In this study, we integrate the slip boundary condition for fluid flow for Newtonian as well as non-Newtonian fluid. Our primary emphasis is to comprehend the influence of slip effects on the flow characteristics of real shear-thickening fluid (STF), encompassing Newtonian, shear-thinning, and shear-thickening behaviors under varying applied stresses or strain rates. In order to achieve this, we have introduced the combination of modified bounce back and specular reflection (MBSR) scheme and half way bounce back and specular reflection (HBSR) scheme. In theory, the interactions between the parameters of the combination and the slip length are explicitly deduced. The specified combination parameter is decided by the slip length given and the relaxation time. These slip boundary conditions are analyzed for their distinct results. Our process has been tested for accuracy and reliability for Newtonian flow as well as non-Newtonian flow and the results are compared with the analytical solution. We also develop a theoretical model to elucidate the flow characteristics of real shear-thickening fluid (STF) in a channel with slip effects. Investigating pressure and channel height variations, we observe nuanced responses. Initially, under increasing pressure, the regime with Newtonian flow rate $Q1$ dominates, reaching a peak. As pressure rises yielding dominance to another regime with shear-thinning flow rate $Q2$, while regime with shear-thickening flow rate $Q3$ remains zero. Further pressure escalation prompts a monotonically increasing trend in $Q3$, achieving dominance. Simultaneously, $Q1$ and $Q2$ approach zero. These trends hold true with and without slip effects, with higher flow rates in the presence of slips for a given pressure drop and viscosity. Additionally, as channel height increases, $Q1$ predominates at lower heights, transitioning to dominance by $Q2$ and then $Q3$ at larger heights.