Unifying Lengthscale-Based Rheology of Dense Granular-Fluid Mixtures

TL;DR

This paper introduces a unified rheological framework for dense granular-fluid mixtures that captures the transition from inertial to viscous regimes using a physics-based lengthscale ratio, linking stress and jamming behavior.

Contribution

It proposes a novel lengthscale ratio that unifies the rheology of dense suspensions across inertial and viscous regimes based on simple physics considerations.

Findings

The lengthscale ratio correlates with normal stress and jamming proximity.

The model captures the transition between inertial and viscous-dominated states.

Provides a consistent relationship between stress and system state across regimes.

Abstract

In this communication, we present a new lengthscale-based rheology for dense sheared particle suspensions as they transition from inertial- to viscous-dominated. We derive a lengthscale ratio using straightforward physics-based considerations for a particle subjected to pressure and drag forces. In doing so, we demonstrate that an appropriately chosen length-scale ratio intrinsically provides a consistent relationship between normal stress and system proximity to its ''jammed'' or solid-like state, even as a system transitions between inertial and viscous states, captured by a variable Stokes number.