Convective and diffusive dispersion of particles in laminar tube flow: Effects on time-dependent concentration measurements

In the measurement of transient particle concentrations, the effect of convective and diffusive dispersion in the sampling tube should be considered. Such dispersion, arising from the axial velocity distribution in the tube flow and the transverse diffusive particle flux, will produce a concentration at the outlet of the sampling line that has a modified temporal dependence from that of the inlet concentration. We have solved numerically the unsteady concentration equation for the fully-developed Poiseuille flow, yielding the temporal and spatial concentration distribution. The model was validated by comparison with the analytical solution for the case of convection-only, and through experiments performed for the combined convection-diffusion situation. Results are presented, for the case following a step change in the inlet concentration, in terms of the dimensionless parameter ξ (defined by LD/ u ̄r₀² where L is the length of the sampling tube, D is the particle molecular diffusivity, ū is the average flow velocity and r₀ is the internal radius of the sampling tube) and the dimensionless time t* (defined by t u ̄/L). Typically, the time for the outlet concentration to decay to 1% of its initial value varies from 2.8 to 5 times the convection transit time (defined by L/ u ̄) for ξ values between 2 × 10^-3 and 0, respectively. The procedure is highly relevant to the performance of aerosol measurement systems to rapidly-varying particle concentrations.