Diffusive Particles Travel Through a Tube in Less Time than the Flowing Fluid in Which They Are Suspended

This article presents a summary of recent theoretical investigations on the residence time distribution (RTD) of particles in laminar flow tubes, based on stochastic simulation of particles trajectories, and also a formerly unpublished comparison of the numerical simulation results with experimental data. The RTD depends on the flow velocity profile of the fluid. For the two extreme flow types, plug or uniform flow (UF) and fully developed or parabolic flow (PF), the RTD is a function of two dimensionless numbers: the particle diffusivity, D, and the tube aspect ratio, a. A third additional dimensionless variable, the Reynolds number, Re, should also be considered when the stationary fluid velocity profile gradually develops along the tube (steady transition flow, TF). The role of D can be split up into two contributions: one due to diffusion along the main fluid flow direction, the other to cross-stream diffusion; the first moment of the RTD depends on the product aD in the first case, but only on D in the second one. In the ideal case in which the fluid velocity is constant throughout the tube (plug flow) and particle axial diffusion is absent, the particle RTD coincides with that of the fluid. In any other circumstances the RTD of the particles shifts to smaller residence times in comparison with the RTD of the fluid: the mean particle residence time in the tube is smaller than that of the fluid. This surprising outcome is explained in terms of the particle survival probability, the mean particle radial coordinate and the mean axial displacement of the particles per unit time along the tube. In the last section of the paper, theoretical particle survival probability and residence time distribution are both favorably compared with the presently available experimental results.