Investigation of gas flow in micro-filters and modification of scaling law

In this study, important micro gas flow features including slip velocity, compressibility, and rarefaction effects for flow micro-filters are investigated. In this regard the compressible Navier–Stokes equations with wall slip and temperature jump boundary conditions are solved for a proper range of Knudsen numbers. For the filters, the ratio of the open orifice area to the total area is selected as 0.6 in order to compare the results with the literature. Considering that the filter holes repeat in a periodic fashion, gas flow is simulated through only one hole by imposing periodicity conditions. The simulation results are compared with the empirical scaling laws developed in the last works and a modified relation for the scaling law is presented. This modified relation predicts high-accuracy pressure drop through the micro-filters in the slip regime.