Rheology of granular liquids in extensional flows: Beyond the $\mu(\mathcal{I})$-law

TL;DR

This paper extends the GITT formalism to describe the rheology of granular liquids in extensional flows, revealing non-monotonous friction behavior and generalizing the $()$-law across flow types, with implications for Trouton ratio analysis.

Contribution

The work generalizes the GITT equations beyond simple shear flows to include extensional flows, providing a unified description of granular rheology across different deformation modes.

Findings

Effective friction coefficient $$ can vary non-monotonically with inertial number $$ in extensional flows.

The generalized $()$-law applies to all flow deformations, not just shear.

Trouton ratio behavior in granular flows resembles that in dense colloidal suspensions.

Abstract

The Granular Integration Through Transients (GITT) formalism gives a theoretical description of the rheology of moderately dense granular flows and suspensions. In this work, we extend the GITT equations beyond the case of simple shear flows studied before. Applying this to the particular example of extensional flows, we show that the predicted behavior is somewhat different from that of the more frequently studied simple shear case, as illustrated by the possibility of non monotonous evolution of the effective friction coefficient $\mu$ with the inertial number $\mathcal{I}$. By the reduction of the GITT equations to simple toy-models, we provide a generalization of the $\mu(\mathcal{I})$-law true for any type of flow deformation. Our analysis also includes a study of the Trouton ratio, which is shown to behave quite similarly to that of dense colloidal suspensions.