Abstract
We provide 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.