Aerosol penetration through capillaries and leaks: Theory

Abstract

A general outline theory is constructed of aerosol penetration through small capillaries in which the gas flow is mainly laminar. The rate of particle transfer through a capillary is linearly related to the standard leak rate (SLR) of the capillary when no particle smapling or deposition losses occur, but the experiments of Mitchell et al. show that particle penetration falls sharply at SLR ≈ 10 −4 Pa m 3 s −1. The expected scaling of this possible cutoff in penetration with capillary dimensions and pressure changes is discussed, including the use of a laminar Stokes number to represent entrainment effects at the capillary entrance. A rigorous proof is given that, provided aerosol deposits remain in position and do not break off, the total aerosol transmission through a leak should be independent of initial aerosol concentration as long as it is not high enough to change the flow. If deposition occurs by impaction in a limited region near the capillary entrance, a scaling relation is postulated for this behaviour which relates the capillary length and external pressures. Experimental evidence supports the relationship, but does not give decisive results on the scaling of a penetration cutoff with changes to the capillary length and radius. Experimental results have been obtained by Burton et al. for aerosol penetration in capillary flows produced by varying the upstream pressure, and are shown to be consistent with an initial penetration efficiency close to unity in most cases. Exceptions occur where deposition is taking place at low pressure differences. The total mass deposited in a capillary is deduced for a case when aerosol penetration is cut off and the corresponding length of the deposit is 0.6 mm. Whilst considerable deposition in these capillaries is expected without any diminution in the gas flow, the very small reduction in flow in this case is difficult to reconcile with a deposit of this size.