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Lattice Boltzmann Modeling of Non-Newtonian Fluid Flows Under Non-Linear Slip Velocity Boundary Conditions in Microchannels

Lattice Boltzmann Modeling of Non-Newtonian Fluid Flows Under Non-Linear Slip Velocity Boundary Conditions in Microchannels

Year:    2025

Author:    Francisco Reis, Goncalo Silva, Viriato Semiao

Communications in Computational Physics, Vol. 37 (2025), Iss. 1 : pp. 61–103

Abstract

Fluid flows in microfluidic devices are often characterized by non-Newtonian rheology with non-linear wall slip behavior also observed. This work solves this problem class with the lattice Boltzmann method (LBM), proposing new advanced boundary scheme formulations to model the joint contribution of non-linear rheology and non-linear wall slip laws in application to microchannels of planar and circular cross-section. The non-linear stress-strain-rate relationship of the microflow is described by a generalized Newtonian model where the viscosity function follows the Sisko model. To guarantee that LBM steady-state solutions are not contaminated by 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 and Hatzikiriakos slip laws. They are transcribed into the LBM framework by adapting the local second-order boundary (LSOB) scheme strategy to this problem class. Theoretical and numerical analyses developed for a steady and slow viscous fluid within 2D slit and 3D circular pipe channels demonstrate the parabolic level of accuracy of the developed LSOB scheme throughout the considered non-linear slip and non-Newtonian models.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2024-0087

Communications in Computational Physics, Vol. 37 (2025), Iss. 1 : pp. 61–103

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    43

Keywords:    Lattice Boltzmann method two-relaxation-time scheme slip velocity boundary conditions non-Newtonian fluids.

Author Details

Francisco Reis

Goncalo Silva

Viriato Semiao