An analytical model for aerosol filtration by nonuniform filter media

Filtration of submicrometer aerosol particles by nonhomogeneous porous filters is studied analytically. The effect of inhomogeneities is to cause nonuniform pressure gradient and concomitant curvilinear mesoscale air streamlines within the filtering material. A general equation governing change of aerosol filtration length along curved air streamlines is developed. Analytical analyses are performed for a homogeneous bulk filter material containing a small volumetric fraction, α, of spatial inhomogeneities (inclusions). An expression is derived for the effective filtration length of such a composite filter material, relative to the comparable length of the corresponding uniform matrix and the filtering properties of the inclusions. Calculations performed for spherical inclusions show that they tend to decrease the aerosol filtration efficiency when their porosity is less than that of the surrounding filter medium. However, the effect of inclusions with porosity exceeding that of the filter material is to decrease the aerosol filtration length, i.e. to enhance the aerosol collection rate. The model was tested by experiments performed for submicrometer aerosols, collected in a granular bed filter. It was composed of 1.4 mm spherical glass beads, forming a homogeneous matrix, and 15 mm balls, serving as impermeable inclusions. For such a medium the model predicts a nonmonotonic α-dependence of the effective filtration length, which qualitatively agrees with the experimental data.