Fibrous Filter Efficiency and Pressure Drop in the Viscous-Inertial Transition Flow Regime

Fibrous filter pressure drop and aerosol collection efficiency were measured at low air pressures (0.2-0.8 atm) and high face velocities (5-19 m/s) to give fiber Reynolds numbers lying in the viscous-inertial transition flow regime (1-15). In this regime, contemporary filtration theory based on Kuwabara's viscous flow through an ensemble of fibers underpredicts single fiber impaction by several orders of magnitude. Streamline curvature increases substantially as air stream inertial forces become significant. Dimensionless pressure drop measurements followed the viscous-inertial theory of Robinson and Franklin (1972) rather than Darcy's linear pressure-velocity relationship. Sodium chloride and iron nano-agglomerate aerosols were tested to provide a comparison between particles of dissimilar densities and shape factors. Total filter efficiency collapsed when plotted against the particle Stokes number and fiber Reynolds number. Efficiencies were then modeled with an impactor type equation where the cutpoint Stokes number and a steepness parameter described data well in the sharply increasing portion of the curve (20%-80% efficiency). A minimum in collection efficiency was observed at small Stokes numbers and attributed to interception and diffusive effects. The cutpoint Stokes number was a linearly decreasing function of fiber Reynolds number. Single fiber efficiencies were calculated from total filter efficiencies and compared to contemporary viscous flow impaction theory (Stechkina et al. 1969), and numerical simulations of single fiber efficiencies from the literature. Existing theories underpredicted measured single fiber efficiencies, although comparison is problematic. The assumption of uniform flow conditions for each successive layer of fibers is questionable; thus, the common exponential relationship between single fiber efficiency and total filter efficiency may not be appropriate in this regime.