Modelling the dispersion in residence time of size-dispersed particles with fluctuating axial velocity falling through a fluid

The residence time of a spherical particle falling in a stationary, Newtonian liquid is examined. The diameter of the particle is taken to be a described by the Log-Normal distribution which leads to a variation in residence time. Additionally, the complexity of the particle-fluid interaction introduces further dispersion into the residence time by causing particle velocity to fluctuate about its nominal value. Experiments were conducted at two ranges of Reynolds Numbers with a variety of particle-liquid systems to examine this phenomenon. The variability in velocity can be characterised by a dispersion parameter and a corresponding particle Peclet number. Using probability theory, a novel expression is developed that permits the effect of both the dispersion in particle diameter and the irregular nature of particle motion on particle residence time to be simultaneously quantified. Such an approach permits the relative influence of systematic size dispersion and fluctuations in motion on residence time to be determined. It provides new insights into settling behavior which can be used to promote greater uniformity in residence time.