Estimation of the upper limit of aerosol nanoparticles penetration through inhomogeneous fibrous filters

The fully segregated flow model (FSFM) was formulated to describe filtration of aerosol nanoparticles in polydisperse fibrous filters made of fibers with different diameters. The model is capable of predicting significantly higher penetration of nanoparticles through polydisperse filters than it may be expected from the classical theory applied to a mean fiber diameter. The model was solved numerically in the case of the log-normal fiber size distribution, and a simple correlation between the actual penetration through a polydisperse filter and the one calculated for the geometric mean fiber diameter was proposed. Equivalent fiber diameter for deposition due to Brownian diffusion was determined and it was found to be dependent on particle size and filter’s polydispersity degree, being significantly greater than any mean fiber diameter. It was noted that it is impossible to select any one universal mean fiber diameter to describe penetration of nanoparticles with different sizes. It was also shown that in the case of a polydisperse fibrous filter the apparent exponent of the Peclet number based on the mean fiber diameter is greater than the expected value of −2/3 for diffusional deposition in a monodisperse filter. This prediction is in agreement with the available experimental data. The FSFM is expected to give the estimation of the upper limit of nanoparticles penetration in polydisperse fibrous filters.