Correction for sampling errors due to coagulation and wall loss in laminar and turbulent tube flow: direct solution of canonical ‘inverse’ problem for log-normal size distributions

Abstract

Aerosol sampling from industrial environments (e.g. combustion engines) or natural environments (e.g. the troposphere) frequently involves conveying the sample to a downstream (‘sheltered’) instrument via an upstream tube or duct. While the instrument may be capable of characterizing, say, the particle size distribution (PSD) of the aerosol actually presented to it, the investigator is, of course, usually more interested in the PSD of the aerosol entering the upstream sampling tube. Invariably, this differs from that measured because of several systematic phenomena—perhaps the two most obvious of which are particle size-dependent losses to the tube walls (i.e. incomplete ‘penetration’) and PSD distortion due to suspended particle-particle coagulation when the particle concentrations are sufficiently high. We show here how recent research on the use of ‘moment methods’ to predict the effects of size-dependent walls loss and/or Brownian coagulation in flow systems can now be brought to bear to conveniently solve this ‘inverse’ problem by numerically integrating the quasi-one-dimensional coupled moment equations in the upstream direction, using downstream (measured) aerosol properties in the definitions of all dimensionless dependent variables and parameters. Illustrative ‘universal’ graphs are presented here for the sampling of log-normally distributed ‘inertialess’ (Brownian) aerosols in long straight adiabatic ducts for both commonly encountered extremes of particle Knudsen number Kn p ⪢ 1(free molecule) or Kn p ⪡ 1 (continuum), as well as convenient rational approximations derived from the leading terms of a Taylor series expansion of the above-mentioned dimensionless moment equations.