Lattice Boltzmann Modeling of Non-Newtonian Fluid Flows Under Non-Linear Slip Velocity Boundary Conditions in Microchannels (Communications in Computational Physics, 2025)
Fluid flows in microfluidic devices are often characterized by non-Newtonian rheology with non-linear wall slip behavior also observed. This worksolves this problem class with the lattice Boltzmann method (LBM), proposing newadvanced boundary scheme formulations to model the joint contribution of non-linearrheology and non-linear wall slip laws in application to microchannels of planar andcircular cross-section. The non-linear stress-strain-rate relationship of the microflowis described by a generalized Newtonian model where the viscosity function followsthe Sisko model. To guarantee that LBM steady-state solutions are not contaminatedby numerical errors that depend on the viscosity local value, the two-relaxation-time(TRT) collision is adopted. The fluid-wall accommodation model considers different slip laws, such as the Navier linear, Navier non-linear, empirical asymptotic andHatzikiriakos slip laws. They are transcribed into the LBM framework by adapting thelocal second-order boundary (LSOB) scheme strategy to this problem class. Theoreticaland numerical analyses developed for a steady and slow viscous fluid within 2D slitand 3D circular pipe channels demonstrate the parabolic level of accuracy of the developed LSOB scheme throughout the considered non-linear slip and non-Newtonianmodels.