Rheological regimes in agitated granular media under shear

Agitated granular media have a rich rheology: they exhibit Newtonian behavior at low shear rate and density, develop a yield stress at high density, and cross over to Bagnoldian shear thickening when sheared rapidly -- making them challenging to encompass in one theoretical framework. We measure the rheology of air-fluidized glass particles, spanning five orders of magnitude in shear rate. By comparing fluidization-induced to Brownian agitation, we show that all rheological regimes can be delineated by two dimensionless numbers -- the Peclet number, $\Pe$, and the ratio of shear-to-fluidization power, $\Pi$ -- and propose a constitutive relation that captures all flow behaviors, qualitatively and quantitatively, in one unified framework.