Granular fluid in an arbitrary external potential: spontaneous convection, self-phoresis

The hydrodynamic stationary states of a granular fluid are addressed theoretically when subject to energy injection and a time-independent, but otherwise arbitrary external potential force. When the latter is not too symmetrical in a well defined sense, we show that a quiescent stationary state does not exist, rather than simply being unstable and, correspondingly, a steady convective state emerges spontaneously. We also unveil an unexpected connection of this feature with the self-diffusiophoresis of catalytically active particles: if an intruder in the granular fluid is the source of the potential, it will self-propel according to a recently proposed mechanism that lies beyond linear response theory, and that highlights the role of the intrinsic nonequilibrium nature of the state of the granular bath. In both scenarios, a state-dependent characteristic length of the granular fluid is identified which sets the scale at which the induced flow is the largest.