Dust Control in Finite Air Volumes at Zero Gravity - Mean-Field Like Analysis

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We study a simple 1D model of dust rods, with mean size μ, passing through a parallel 1D alignment of pores as a problem of clogging of a filter by dust grains; μis kept less than the pore size, s. We assume that the filter is "sticky", characterized by some parameter 0 ≤ λ≤ 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, Ncl, grows in time as tₙclog ∝ Nclν, where ν= ν(μ,λ) is a non-universal exponent that depends upon the dust size distribution and filter properties.