Efficiency of aerosol particle collection with filtering materials containing dispersed inclusions

During the flow around spherical inclusions in a homogeneous porous medium, the gas flow field is calculated using the Brinkman equation. The expression is derived for the effective permeability of the porous medium containing the rarefied ensemble of randomly arranged dispersed spherical particles of arbitrary sizes. It is shown that the Darcy approximation is applicable to the large-size inclusions. The influence of dispersed inclusions of spheroidal shape on both the pressure drop and the efficiency of aerosol particle collection with a filter is studied in the Darcy approximation. It is shown that dispersed inclusions can both increase and decrease the quality criterion of a filter depending on the values of parameters.