Scaling description of frictionless dense suspensions under inhomogeneous flow

TL;DR

This paper develops new scaling laws for predicting the behavior of frictionless dense suspensions under inhomogeneous flow, extending rheological models beyond traditional homogeneous assumptions.

Contribution

It introduces a novel dimensionless number based on particle velocity fluctuations, unifying rheological response in both homogeneous and inhomogeneous conditions.

Findings

Derived new constitutive laws for inhomogeneous suspensions

Unified rheological response using a combined dimensionless number

Predicted steady state velocity, stress, and volume fraction fields

Abstract

Predicting the rheology of dense suspensions under inhomogeneous flow is crucial in many industrial and geophysical applications, yet the conventional `$\mu(J)$' framework is limited to homogeneous conditions in which the shear rate and solids fraction are spatially invariant. To address this shortcoming, we use particle-based simulations of frictionless dense suspensions to derive new constitutive laws that unify the rheological response under both homogeneous and inhomogeneous conditions. By defining a new dimensionless number associated with particle velocity fluctuations and combining it with the viscous number, the macroscopic friction and the solids fraction, we obtain scaling relations that collapse data from homogeneous and inhomogeneous simulations. The relations allow prediction of the steady state velocity, stress and volume fraction fields using only knowledge of the applied driving force.