Residence time distribution of ultrafine aerosol particles in a tube with transient and parabolic laminar flow

Abstract

This paper presents a theoretical investigation concerning the residence time distribution (RTD) of ultrafine monodisperse aerosol particles flowing in a circular tube in laminar flow regime. If a fully developed, parabolic flow (PF) velocity profile is assumed for the whole tube length, the convection-diffusion process undergone by the aerosol particles can be described by means of two parameters, the dimensionless particle diffusion coefficient D and the tube aspect ratio a (radius/length). An additional parameter, the Reynolds number Re, must be taken into consideration when the flow develops starting from a given velocity profile at the tube entrance, which we have assumed to be a uniform (plug) flow. The latter situation is referred to as transient flow (TF). The RTD has been determined using two different variations of a Monte Carlo (MC) technique to simulate the particle trajectory within the tube. The difference between the two MC methods is the assumed distribution of Brownian random displacements of the particles; in both cases the distribution had zero mean and variance 2DΔt, but the distribution was uniform in one method and normal in the other. The simulation results obtained with the two methods were almost coincident. In either PF or TF, even for relatively small values of D the aerosol RTD is quite different from that of the fluid where the particles are suspended. In particular, the dimensionless mean particle residence time, which initially decreases with D, soon attains an asymptotic value of 0.65 for D ≥ 0.3 (the mean residence time of the fluid is 1) in PF; a similar asymptotic value is attained for TF but in this case it depends on the particular combination of a and Re considered. The relative influence of axial diffusion on the RTD is insignificant unless the tube ratio a is of the order of 0.5 (tube with a length equal to its diameter).