# Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows

## TL;DR

This study uses extensive simulations to unify the rheology of various granular flows, revealing a common scaling law that breaks down near flow thresholds, leading to a variable yield stress ratio.

## Contribution

It introduces a generalized rheology relation that applies across dry, wet, dense, and dilute granular flows, accounting for variable yield stress ratios.

## Key findings

- Mohr-Coulomb friction coefficient scales with the square root of Péclet number in most conditions.
- Scaling breaks down at low Péclet number and high temperature gradients, indicating a variable yield stress ratio.
- The results unify diverse granular flow behaviors under a common rheological framework.

## Abstract

Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient $\mu$ scales with the square root of the local P\'eclet number $\mathrm{Pe}$ provided that the particle diameter exceeds the particle mean free path. With decreasing $\mathrm{Pe}$ and granular temperature gradient $M$, this general scaling breaks down, leading to a yield condition with a variable yield stress ratio characterized by $M$.