  We study a simple 1D model of dust rods, with mean size \mu, passing through
a parallel 1D alignment of pores as a problem of clogging of a filter by dust
grains; \mu is kept less than the pore size, s. We assume that the filter is
"sticky", characterized by some parameter 0 \le \lambda \le 1, which means that
dust grains slightly smaller in size than s can get trapped in the pores. Our
analyses suggest that the number of clogged pores, N_{cl}, grows in time as
t_N^{clog} \propto N_{cl}^{\nu}, where \nu = \nu(\mu,\lambda) is a
non-universal exponent that depends upon the dust size distribution and filter
properties.
