The Single-Fiber Collision Rate and Filtration Efficiency for Nanoparticles I: The First-Passage Time Calculation Approach

Abstract

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 Knudse...