Lattice Boltzmann methods for simulating non-Newtonian fluids: A comprehensive review

TL;DR

This paper reviews the latest lattice Boltzmann methods for simulating complex non-Newtonian fluids, emphasizing recent advancements, applications, and ongoing challenges in accurately modeling their nonlinear behaviors.

Contribution

It provides a comprehensive overview of recent lattice Boltzmann techniques for non-Newtonian fluids, highlighting new methods, validation benchmarks, and future research directions.

Findings

Advancements in lattice Boltzmann models for shear-dependent viscosity.

Successful application to viscoplastic and viscoelastic flow problems.

Identification of current challenges and future research directions.

Abstract

Non-Newtonian fluids encompass a large family of fluids with additional nonlinear material properties, contributing to non-trivial flow behaviour that cannot be captured through a single constant viscosity term. Common non-Newtonian characteristics include shear-thinning, shear-thickening, viscoplasticity, and viscoelasticity, commonly encountered in everyday fluids, such as ketchup, blood, toothpaste, mud, etc., as well as practical applications involving porous media, cosmetics, food processing, and pharmaceuticals. Due to the complex nature of these fluids, accurate computational fluid dynamics simulations are essential for predicting their behaviour under various flow conditions. Recent advancements have highlighted the growing trend of using the lattice Boltzmann method to solve such complex flows, owing to its ability to handle intricate boundary conditions, ease of including additional multiphysics, and providing computationally efficient parallel simulations. Since the initial review over a decade ago [Phillips & Roberts, IMA J. Appl. Math. 76, 790-816 (2011)], significant advancements have been made to the lattice Boltzmann method to simulate non-Newtonian fluids. Here, we present a comprehensive review of different lattice Boltzmann techniques used to solve non-Newtonian fluid systems, specifically dealing with shear-dependent viscosity, viscoplasticity, and viscoelasticity. In addition, we discuss various benchmark cases that validate these approaches and highlight their growing application to realistic and challenging complex flow problems. We further address outstanding issues in current lattice Boltzmann models, as well as future directions for numerical advancement and application.