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

Abstract

This article presents a summary of recent theoretical investigations on the residence time distribution (RTD) of particles in laminar flow tubes based on the stochastic simulation of particles trajectories and on a formerly unpublished comparison of the numerical simulation results with experimental data.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. The role of D can be split 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 shorter residence times in comparison with the RTD of the fluid: the mean particle residence time in the tube is shorter 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 this paper, theoretical particle survival probability and residence time distribution are both favorably compared with the presently available experimental results.