Transition from viscous to inertial regime in dense suspensions

TL;DR

This paper investigates the transition from viscous to inertial regimes in dense suspensions through numerical simulations, revealing how different dissipation mechanisms dominate in each regime and unifying them via a single dimensionless number.

Contribution

It introduces a unified framework for understanding shear regimes in dense suspensions by linking viscous and inertial behaviors through dissipation analysis.

Findings

Identifies viscous and contact force dissipation as dominant in respective regimes.

Demonstrates the transition between Newtonian and Bagnoldian behaviors.

Proposes a single dimensionless number to unify rheological regimes.

Abstract

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behaviour at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This set-up is conceptually identical to the recent experiments of Boyer and co-workers [Phys. Rev. Lett. 107,188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.