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Lattice Boltzmann methods for simulating non-Newtonian fluids: A comprehensive review
Authors:
Vedad Dzanic,
Qiuxiang Huang,
Christopher S. From,
Emilie Sauret
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, toothp…
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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.
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Submitted 12 January, 2026;
originally announced January 2026.
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Jamming of Elastoviscoplastic fluids in Elastic Turbulence
Authors:
Christopher S. From,
Vedad Dzanic,
Vahid Niasar,
Emilie Sauret
Abstract:
Elastoviscoplastic (EVP) fluid flows are driven by a non-trivial interplay between the elastic, viscous, and plastic properties, which under certain conditions can transition the otherwise laminar flow into complex flow instabilities with rich space-time-dependent dynamics. We discover that under elastic turbulence regimes, EVP fluids undergo dynamic jamming triggered by localised polymer stress d…
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Elastoviscoplastic (EVP) fluid flows are driven by a non-trivial interplay between the elastic, viscous, and plastic properties, which under certain conditions can transition the otherwise laminar flow into complex flow instabilities with rich space-time-dependent dynamics. We discover that under elastic turbulence regimes, EVP fluids undergo dynamic jamming triggered by localised polymer stress deformations that facilitate the formation of solid regions trapped in local low-stress energy wells. Below the jamming transition $φ<φ_J$, the solid volume fraction $φ$ scales with $\sqrt{Bi}$, where $Bi$ is the Bingham number characterizing the ratio of yield to viscous stresses, in direct agreement with theoretical approximations based on the laminar solution. The onset of this new dynamic jamming transition $φ\geqφ_J$ is marked by a clear deviation from the scaling $φ\sim \sqrt{Bi}$, scaling as $φ\sim \exp{Bi}$. We show that this instability-induced jamming transition -- analogous to that in dense suspensions -- leads to slow, minimally diffusive, and rigid-like flows with finite deformability, highlighting a novel phase-change in elastic turbulence regimes of complex fluids.
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Submitted 17 March, 2025;
originally announced March 2025.
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Conserving elastic turbulence numerically using artificial diffusivity
Authors:
Vedad Dzanic,
Christopher S. From,
Emilie Sauret
Abstract:
To simulate elastic turbulence, where viscoelasticity dominates, numerical solvers introduce an artificial stress diffusivity term to handle the steep polymer stress gradients that ensue. This has recently been shown [Gupta & Vincenzi, J. Fluid Mech. 870, 405-418 (2019); Dzanic, From & Sauret, J. Fluid Mech. 937, A31 (2022)] to introduce unphysical artifacts with a detrimental impact on simulation…
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To simulate elastic turbulence, where viscoelasticity dominates, numerical solvers introduce an artificial stress diffusivity term to handle the steep polymer stress gradients that ensue. This has recently been shown [Gupta & Vincenzi, J. Fluid Mech. 870, 405-418 (2019); Dzanic, From & Sauret, J. Fluid Mech. 937, A31 (2022)] to introduce unphysical artifacts with a detrimental impact on simulations. In this Letter, we propose that artificial diffusion is limited to regions where stress gradients are steep instead of seeking the zero-diffusivity limit. Through the cellular forcing and four-roll mill problem, we demonstrate that this modified artificial diffusivity is devoid of unphysical artifacts, allowing all features of elastic turbulence to be retained. Results are found to conform with direct simulations, reducing the impact of artificial diffusivity from a qualitative scale to a quantitative scale while only requiring a fraction of the numerical resolution.
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Submitted 20 June, 2022; v1 submitted 24 March, 2022;
originally announced March 2022.