Ness, Chris

Beckett, Chris

Li, Xuan

2026-05-25T12:20:58Z

2026-05-25

Dense suspensions of solid particles in viscous liquid are ubiquitous in both industry and nature, and there is a clear need for efficient numerical routines to simulate their rheology and microstructure. Particles of micron size present a particular challenge: at low shear rates, colloidal interactions control their dynamics while at high rates, granular-like contacts dominate. While there are established particle-based simulation schemes for large-scale non-Brownian suspensions using only pairwise lubrication and contact forces, common schemes for colloidal suspensions generally are more computationally costly and thus restricted to relatively small system sizes. Here, we present a minimal particle-based numerical model for dense colloidal suspensions that incorporates Brownian forces in pairwise form alongside contact and lubrication forces. We show that this scheme reproduces key features of dense suspension rheology near the colloidal-to-granular transition, including both shear thinning due to entropic forces at low rates and shear thickening at high rates due to contact formation. This scheme is implemented in LAMMPS, a widely used open source code for parallelised particle based simulations, with a runtime that scales linearly with the number of particles, making it amenable for large-scale simulations. Building on this foundation, we study the rheology of dense suspensions comprising mixed colloids (smaller particles) and grains (larger particles). By systematically varying the volume fraction of the two species, we demonstrate a monotonic increase in viscosity when grains are added to colloids, but, conversely, a nonmonotonic response in both the viscosity and shear thickening onset when colloids are added to grains. Both effects are most prominent at intermediate shear rates where diffusion and convection play similar roles in the dynamics. We rationalize these results by measuring the maximum flowable volume fraction as functions of the P´eclet number and composition, showing that in extreme cases increasing the solids content can allow a jammed suspension to flow. These results establish a constitutive description for the rheology of bidisperse suspensions across the colloidal–to-granular transition, with implications for flow prediction and control in multicomponent particulate systems. Finally, we study the rheology of dense suspensions under inhomogeneous flow—that is, flows in which the shear rate, stress, or particle concentration varies spatially across the system, such as in pressure-driven channels, near solid boundaries, or around obstacles. Understanding inhomogeneous flows is critical because most real world suspensions in industrial and geophysical contexts are not subjected to uniform shear. Instead, they exhibit complex local flow phenomena that strongly influence macroscopic behaviour. Here, we focus on dense suspensions of non-Brownian particles, where thermal fluctuations are negligible and particle motion is governed primarily by hydrodynamic interactions and non-frictional contacts. Conventional constitutive laws, such as the μ(J) rheology, describe homogeneous shear flows effectively but break down under inhomogeneous conditions. To overcome these limitations, we employ Machine Learning (ML) to develop a data driven framework that bypasses constitutive formulations, our ML models are trained on constitutive model dimensionless parameters: the viscous number J, the total solid volume fraction ϕ, the regional solid volume fraction ϕloc, the macroscopic friction coefficient μ, and suspension temperature Θ, which together characterize the inhomogeneous, dense, non-Brownian suspensions [1]. In addition, we introduce an alternative descriptor, the relative velocity difference Δv, defined as the normalized difference between the average local particle velocity and the background fluid velocity. Our results show that ML models trained on (J, μ, ϕ, ϕloc,Δv) achieve nearly identical predictive accuracy to those trained on the full constitutive law parameter set (J, μ, ϕ, ϕloc, Θ). This demonstrates that Δv serves as a experimentally accessible, and computationally efficient descriptor of inhomogeneous, non-Brownian suspension flow. Overall, our framework extends the constitutive description of inhomogeneous flows while offering a computationally efficient and experimentally accessible approach to predicting dense suspension rheology.

https://era.ed.ac.uk/handle/1842/44738

https://doi.org/10.7488/era/7253

en

Simulating the rheology of dense suspensions using pairwise formulation of contact, lubrication and Brownian forces Li, X., Royer, J. R. & Ness, C., 15 Apr 2024, (E-pub ahead of print) In: Journal of Fluid Mechanics. 984, 22 p., A67

Dense Suspension Rheology

Computational Modeling

Machine Learning (ML)

ML

Shear Thickening

Inhomogeneous Flows

Computational modeling and machine learning approaches to dense suspension rheology

Thesis

Doctoral

PhD Doctor of Philosophy