Herschel-Bulkley rheology from lattice kinetic theory of soft-glassy materials

TL;DR

This paper demonstrates that a two-species lattice Boltzmann model can reproduce Herschel-Bulkley rheology, showing a power-law relation between shear stress and strain rate in soft-glassy materials, useful for computational studies.

Contribution

It introduces a mesoscopic lattice Boltzmann model that captures Herschel-Bulkley rheology in soft-glassy materials, enabling seamless transition between flow and non-flow states.

Findings

Supports Herschel-Bulkley rheology with power-law shear-stress dependence

Allows smooth transition from flowing to non-flowing behavior

Potential computational tool for soft-glassy material rheology

Abstract

We provide a clear evidence that a two species mesoscopic Lattice Boltzmann (LB) model with competing short-range attractive and mid-range repulsive interactions supports emergent Herschel-Bulkley (HB) rheology, i.e. a power-law dependence of the shear-stress as a function of the strain rate, beyond a given yield-stress threshold. This kinetic formulation supports a seamless transition from flowing to non-flowing behaviour, through a smooth tuning of the parameters governing the mesoscopic interactions between the two species. The present model may become a valuable computational tool for the investigation of the rheology of soft-glassy materials on scales of experimental interest.