Cooperativity flows and Shear-Bandings: a statistical field theory approach

TL;DR

This paper develops a statistical field theory linking cooperativity effects and shear-banding in soft jammed systems, showing how non-local fluidity leads to inhomogeneous flow patterns stabilized by mechanical noise.

Contribution

It introduces a novel connection between non-local fluidity models and shear-banding via compacton solutions, incorporating the role of mechanical noise in stabilizing flow inhomogeneities.

Findings

Compacton solutions represent shear bands with finite support.

Mechanical noise stabilizes coexistence of flowing and non-flowing regions.

Fluidity acts as an order parameter for flow transitions.

Abstract

Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin \& A. Ajdari ({\em Phys. Rev. Lett.} {\bf 103}, 036001 (2009)), we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity), are intimately related to the emergence of shear-banding configurations. This connection materializes through the onset of inhomogeneous compact solutions (compactons), wherein the fluidity is confined to finite-support subregions of the flow and strictly zero elsewhere. Compactons coexistence with regions of zero fluidity ("non-flowing vacuum") is shown to be stabilized by the presence of mechanical noise, which ultimately shapes up the equilibrium distribution of the fluidity field, the latter acting as an order parameter for the flow-noflow transitions occurring in the material.