Continuum description of finite-size particles advected by external flows. The effect of collisions.

The equation of the density field of an assembly
of macroscopic particles advected by an external flow
is derived from the microscopic description of the system. This
equation allows to recognize the role and the relative
importance of the different microscopic processes implicit in the
model: the driving of the external flow, the inertia of the particles,
and the collisions among them.
The validity of the density description is
confirmed by comparisons of numerical studies of the
continuum equation
with
Direct simulation Monte Carlo (DSMC)
simulations of hard disks advected by a chaotic
flow. We show
that the collisions have two competing roles: a dispersing-like
effect and a clustering effect (even for elastic collisions). An
unexpected feature is also observed in the system: the presence of collisions can reverse
the effect of inertia, so that grains with lower inertia are more
clusterized.