  A simple model accounting for the ejection of heavy particles from the
vortical structures of a turbulent flow is introduced. This model involves a
space and time discretization of the dynamics and depends on only two
parameters: the fraction of space-time occupied by rotating structures of the
carrier flow and the rate at which particles are ejected from them. The latter
can be heuristically related to the response time of the particles and hence
measure their inertia. It is shown that such a model reproduces qualitatively
most aspects of the spatial distribution of heavy particles transported by
realistic flows. In particular the probability density function of the mass $m$
in a cell displays an power-law behavior at small values and decreases faster
than exponentially at large values. The dependence of the exponent of the first
tail upon the parameters of the dynamics is explicitly derived for the model.
The right tail is shown to decrease as $\exp (-C m \log m)$. Finally, the
distribution of mass averaged over several cells is shown to obey rescaling
properties as a function of the coarse-grain size and of the ejection rate of
the particles. Contrarily to what has been observed in direct numerical
simulations of turbulent flows (Bec et al., http://arxiv.org/nlin.CD/0608045),
such rescaling properties are only due in the model to the mass dynamics of the
particles and do not involve any scaling properties in the spatial structure of
the carrier flow.
