Shocks in vertically oscillated
granular layers
Abstract:
We study shock formation in vertically oscillated granular
layers, using both molecular dynamics simulations and
numerical solutions of continuum equations to Navier-Stokes
order. A flat layer of grains is thrown up from an
oscillating plate during each oscillation cycle and collides with
the plate later in the cycle. The collisions produce layer
compaction near the plate and a high temperature shock front
that rapidly propagates upward through the layer. The shock is
highly time dependent, propagating through the layer in only a
quarter of the cycle. We compare numerical solutions of the
continuum equations to molecular dynamics simulations that assume
binary, instantaneous collisions between frictionless,
inelastic hard spheres. The two simulations yield results
for the shock position, shape, and speed that agree well. An
investigation of the effect of inelasticity shows that the
shock velocity increases continuously with decreasing inelasticity; the elastic
limit is not singular.
Phys. Rev. E 66,
051301 (2002).
Manuscript available in PDF and PS formats.