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

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.