Determination of dynamic dispersion coefficients for passive and reactive particles flowing in a circular tube

Abstract

Using the moment analysis method and the Green’s function, mathematical formulations valid across the full-time scale have been derived to determine dynamic dispersion coefficients for passive and reactive particles flowing in a circular tube with fully-developed laminar flow under different source conditions. The newly proposed formulations were verified through agreements with both analytical solutions and random walk particle tracking (RWPT) simulations. The relationship between particle size and dispersion coefficient for passive particles varies with time and they are positively correlated if Peclet number is larger than its critical value; otherwise, they are negatively correlated. Furthermore, the critical Peclet number decreases as time increases. Compared to an instantaneous point source, the critical Peclet number for a volumetric planar source is much smaller. At a small size ratio, size-exclusion effects on passive particle dispersion can be neglected across the full-time scale for both instantaneous point and volumetric planar sources; whereas, at a large size ratio, its significance needs to be considered, depending upon time and source condition. Using Dre_diff=0.02 (Dre_diff=(D−Dnon_ad)/D, where D and Dnon_ad are dispersion coefficients with and without axial diffusion, respectively) as the critical value, axial-diffusion effects on dispersion are negligible for passive solutes at long times if Peclet number is not smaller than 50; however, due to size exclusion this is not applicable for passive particles. At early times, reaction rate, center-of-mass velocity, and dispersion coefficient are not sensitive to Damköhler number for reactive particles. At long times, reaction rate and enter-of-mass velocity increases in magnitude as the Damköhler number increases, while the dispersion coefficient decreases with increasing Damköhler number. Consequently, reaction at the tube walls greatly affects concentration distributions.