(85c) Granular Fluid Dynamics

Imagine a world where gravity is so strong that if an ice cube is tilted the shear forces melt the surface and water avalanches down at supersonic speeds. Further imagine that the ambient temperature is so low that the water re-freezes almost immediately. This is the world of granular flows. As a granular solid is tilted the surface undergoes a sublimation phase transition and a granular gas avalanches down the surface, but the inelastic collisions rapidly remove energy from the flow lowering the granular temperature (kinetic energy per particle) until the gas solidifies again. It is under these extreme conditions that we attempt to uncover continuum granular flow properties. Typical continuum theories like Navier-Stokes equation for fluids follow the space-time evolution of the first few moments of the velocity distribution. We study continuously avalanching flow in a rotating two-dimensional granular drum using high-speed video imaging and extract the position and velocities of the particles. We find a mixture of solid-like, gas-like behavior. In a companion experiment on a vibrated two-dimensional granular fluid under constant pressure, we find a steady-state first order phase transition between a gas and a crystal, which is characterized by a discontinuous change in both density and temperature. It shows rate-dependent hysteresis and obeys the Lindemann criterion for melting. Further, the measured equation of state both above and below the phase transition compares well with theory. The existence of a thermodynamic phase transition in a non-equilibrium system under steady-state conditions is a first step in a complete theory of non-equilibrium thermodynamics.