Dispersion/reaction model of aerosol filtration by porous filters

Abstract

Filter efficiency is rigorously calculated without ad hoc assumptions pertaining to aerosol distribution within the filter bed and even without the very concept of single-element efficiency. In particular, aerosol filtration processes are treated by formulating the particle transport problem at a pointwise (interstitial) level throughout the whole filter bed. These microscale processes ultimately govern aerosol transport and collection at the coarser Darcy scale. At the latter level of description the filter bed is viewed as a continuum in which aerosol propagation and deposition processes are characterized by three position-independent ‘global’ phenomenological coefficients: the mean aerosol velocity vector, dispersivity dyadic and mean volumetric aerosol deposition rate coefficient. Calculation of these three global aerosol coefficients is effected via a rigorous application of Taylor-Aris convective dispersion theory to a lattice model of a porous filter bed. The filter efficiency is easily and explicitly expressed in terms of these three transport coefficients, thereby completely eliminating evaluation of the single-element efficiency as an intermediate step in the calculations. Circumstances are outlined in which the coarse-scale aerosol diffusivity may be neglected and the concomitant aerosol collection rate uniquely characterized by Leer's filtration length parameter [Leers, R. (1957) Staub 17, 402.], relating filter bed thickness to total filtration efficiency. The scheme developed herein is illustrated by numerically computing the three Darcy-scale aerosol transport coefficients (via a finite element technique) for a fibrous filter subjected to typical filtration operating conditions. These coefficients are subsequently used to calculate the characteristic filtration length, whose values are then compared with existing theoretical results and available experimental data. The practical relevance of our theoretical development is outlined with respect to: (i) establishing the limitations of current filtration models; (ii) interpreting experimental data and (iii) optimal filter design.