Hydrodynamics of granular gases with a two-peak distribution

Vibrating walls, frequently employed to maintain the temperature (i.e., average velocity) in a granular gas, modify the system strongly, rendering it dissimilar to a molecular one in various aspects. As evidenced by microgravity experiments employing a quasi-two-dimensional (quasi-2D) rectangular box and by 2D simulations, the one-peak velocity distribution is split into two, rendering the stress both nonuniform and anisotropic-without a shear flow and in the absence of gravitation. To account for this, granular hydrodynamics (as first proposed by Haff and later derived employing the kinetic theory) is generalized by introducing two additional variables, with one accounting for the distance between the two peaks and a second for the difference between the average velocities along different directions. The hydrodynamic theory thus generalized relates the velocity distribution to the stress, yielding results that agree with experiments and simulations.