Multi-mechanism theory of aerosol capture by fibrous filters, including fiber diameter/orientation dispersity and particle morphology effects. Preliminary tests vs. data for mobility-selected submicron particles

Abstract

In Paper I (Sep. Purif. Technol. 257 (2021) 117676) we showed that a semi-analytic, multi-mechanism expression for the single-fiber capture fraction, ηcap,SF, (derived using asymptotically valid approximations: Ref<0.4, Pef≫1, R≪1, R⋅Pef1/3 arbitrary and Stkp≤Stkpcrit), facilitates a deterministic-, pseudo-continuum aerosol population-balance (PB-) approach to predicting fibrous filter performance. There we explicitly considered “deep” (Lf/df,g≫1), low solidity idealized fibrous filters (FFs) challenged by polydispersed aerosols—especially single-mode log-normal (LN) ASDs of modest spread captured by a spatially uniform array of fibers of a single diameter in crossflow. However, realistic fibrous filter media often possess a LN distribution of fiber diameters, as well as a near-Gaussian orientation distribution narrowly spread about normal incidence (θ=π/2). Moreover, even if this were not so, there would be meso-scale departures from a uniform average fiber solid fraction. We show here that our tractable aerosol PBE-approach to idealized FF performance (Paper I) can be generalized to incorporate these particular structural features of commercially available fibrous filter media. But, to clarify whether these generalizations are likely to be useful, if not fully sufficient, for practical circumstances, it is also necessary to compare such methods/predictions against selected sets of well-defined experimental results. We initiate this program here, having chosen the recent experiments of Kang et al. (2019) carried out using a commercially available fiberglass filter with Lf/df,g≃300, mean solid fraction of 0.039, and df,g=2.5μm, successively challenged by mobility-selected KCl(s) particles (with diameters between ca. 20 and 600nm) at the carrier gas velocities of 15 and 10 cm/s—capture conditions dominated by the transport mechanism of Brownian diffusion and convection, with “interception” (associated with non-negligible dp/df) becoming important above ca. dp=100nm. We conclude from these data that the effective interception diameter, dp,icpt,eff, of the particles studied is systematically larger than their stated mobility diameters—a situation which will deserve further attention in future studies. Encouraged by these preliminary but instructive comparisons, we expect that, for many current and future design purposes, our present class of semi-analytic/non-stochastic/multi-mechanism methods will provide a welcome complement, if not alternative, to much more computationally-intensive simulation methods for realistic fibrous media that have been described and implemented in the recent aerosol filtration literature. The consequences of including these structural features of fibrous filters in the presence of aerosol size- and shape polydispersity will be the subject of future studies, based on the generalized Population Balance Equation developed/proposed in Section 3.3.