The single-fiber collision rate and filtration efficiency for nanoparticles i: The first-passage time calculation approach

We describe an approach to filtration-efficiency calculations as an alternative to the traditional depth filtration theory. The new approach involves linking the single-fiber efficiency to the collision rate coefficient/kernel between nanoparticles and fibers, and correspondingly inferring the collision kernel via dimensionless mean first-passage time (MFPT) calculations. This method has the advantage of easily incorporating the influences of particle diffusion, inertia, and particle size; therefore, all filtration mechanisms can be considered simultaneously. Through non-dimensionalization of the equation of motion for a particle in MFPT calculations (the Langevin equation), it is shown that both the single-fiber efficiency Ef and dimensionless particle-fiber collision kernel, H, are functions of the ratio of particle radius to filter-fiber radius, R, the solid volume fraction in the filter, Vf, the ratio of particle persistence distance to the particle-filter collision distance, KnD (the diffusive Knudsen number), and the ratio of the particle translational kinetic energy to the thermal energy χf. Using a Kuwabara flow-cell model to define the geometry and flow field, MFPT calculations are used to determine H and Ef for nanoparticles in atmospheric pressure systems, i.e., when particle inertia is negligible but when diffusion and interception act in tandem to collect particles. From MFPT results, regression equations for both H and Ef are developed. A comparison is made between MFPT results and commonly invoked depth-filtration single-fiber efficiency relationships, experimentally measured values, and H equations derived from Sherwood number correlations based upon measurements of heat transfer from a fluid flowing perpendicular to an array of cylinders. Good agreement is found with both measurements and previously developed equations over a wide range of parameter space.Copyright 2014 American Association for Aerosol Research © 2014