An analytical solution for aerosol penetration in the slip flow regime

Feng Jia, Wei Huang, David Y.H. Pui, Chuen-Jinn Tsai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The classical theory for the diffusional loss of aerosol particles in a fully developed laminar flow through a circular tube derived by Gormley and Kennedy (1949) did not consider the slip-flow condition. However, the non-slip condition for the gas velocity boundary condition may not be appropriate for the gas flow in microgeometries such as microchannels and microtubes. This paper extends the work of Gormley and Kennedy (GK) to include the effect of slip-flow, which often occurs in the gas flow at low pressure or with a small characteristic length scale. In the present solution, the separation of variables was applied to solve the convection-diffusion equation, then confluent hypergeometric function was used to solve for the number concentration as a function of radial distance analytically. Eigenvalues were evaluated for Knudsen numbers ranging from 0.001 to 0.1. Finally, a simple power series correlation was developed to describe aerosol penetration in the slip flow regime as a function of the dimensionless deposition factor and Knudsen number (Kn). In the slip flow regime, the penetration decreases with increasing Kn. The correlation is reduced to GK's solution when Kn = 0. The present solution of aerosol penetration calculated at Kn = 0 shows good agreement with GK's solution and validates the applicable range of the approximate solution by Alonso et al. (2016).

Original languageEnglish
Article number105904
Pages (from-to)1-12
Number of pages12
JournalJournal of Aerosol Science
StatePublished - Jan 2022


  • Aerosol penetration
  • Confluent hypergeometric function
  • Eigenvalues and eigenconstants
  • Knudsen number
  • Microchannels and microtubes
  • Slip flow regime


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