The role of the Peclet number in the diffusion process of aerosols in a tube and correlations to estimate the mean particle residence time

The critical Peclet number above which particle axial diffusion is negligible has been determined for aerosols in a laminar flow tube. Two theoretical methods have been used: the numerical solution of the advection-diffusion equation (ADE), and a Monte Carlo (MC) simulation of particle trajectory. Two limiting velocity profiles have been considered for the fluid flow, namely, plug flow (uniform flow, UF) and fully developed flow (parabolic, PF). Two flow-related aerosol properties, particle penetration through the tube and its residence time distribution (RTD), have been studied. Three cases can be distinguished. (1) When there is no diffusion, penetration is one, and the dimensionless particle mean residence time is also one, the same as that of the fluid in either UF or PF. (2) When diffusion occurs only in the radial direction, penetration is less than one and decreases as the dimensionless particle diffusion coefficient increases; the mean particle residence time is also equal to one in UF but can be much less than one in PF so that, on average, particles in PF spend less time in the tube than the fluid, in spite that no external force is acting upon them. However, no particle can leave the tube in a dimensionless time shorter than 1/2. (3) When radial and axial diffusion are both important, penetration is still smaller than one, but larger than in case (2); the mean residence time in UF or PF is smaller than that of the fluid and, in contrast with case (2), it can be even smaller than 1/2 in PF. The critical value of the Peclet number depends on the specific flow-related aerosol property under consideration. Thus, axial diffusion does not affect particle penetration for Peclet larger than 10–20, and does not affect the mean aerosol residence time for Peclet larger than about 50; but the residence time distribution of the particles is affected by axial diffusion at values of Peclet as large as 6000. The mean aerosol residence time depends on its diffusion coefficient and on the tube aspect ratio (radius/length). Two practical correlations, one for UF and the other for PF, have been developed. Each correlation is the product of two factors which account separately for the contributions of radial and axial diffusion. • The Peclet number above which axial diffusion is negligible depends on the aerosol property under consideration. • The critical Peclet is ⁓10–20 for particle penetration, ⁓50 for mean particle residence time, and >1000 for RTD. • Correlations to estimate the mean aerosol residence time in a tube are proposed for uniform and parabolic fluid flow.