# Simulation of dense non-Brownian suspensions with the lattice Boltzmann method: Shear jammed and fragile states

## TL;DR

This study uses the lattice Boltzmann method to simulate dense non-Brownian suspensions, revealing shear-jammed and fragile states, and providing insights into their mechanical responses under different shear protocols.

## Contribution

First simulation of shear-jammed and fragile states in dense suspensions incorporating hydrodynamics and frictional contacts using the lattice Boltzmann method.

## Key findings

- Reproduced discontinuous shear thickening in 3D systems.
- Identified shear-jammed states with finite storage modulus.
- Observed fragile states with mixed fluid-like and solid-like responses.

## Abstract

Dense non-Brownian suspensions including both the hydrodynamic interactions and the frictional contacts between particles are numerically studied under simple and oscillatory shears in terms of the lattice Boltzmann method. We successfully reproduce the discontinuous shear thickening (DST) under a simple shear for bulk three-dimensional systems. For our simulation of an oscillatory shear in a quasi-two-dimensional system, we measure the mechanical response when we reduce the strain amplitude after the initial oscillations with a larger strain amplitude. Here, we find the existence of the shear-jammed state under this protocol in which the storage modulus $G^{\prime}$ is only finite for high initial strain amplitude $\gamma_0^{I}$. We also find the existence of the fragile state in which both fluid-like and solid-like responses can be detected for an identical area fraction and an initial strain amplitude $\gamma_0^{I}$ depending on the initial phase $\Theta$ (or the asymmetricity of the applied strain) of the oscillatory shear. We also observe the DST-like behavior under the oscillatory shear in the fragile state. Moreover, we find that the stress anisotropy becomes large in the fragile state. Finally, we confirm that the stress formula based on the angular distribution of the contact force recovers the contact contributions to the stress tensors for both simple and oscillatory shears with large strains.