Dispersion in residence time of particles with poly-dispersed size falling through a liquid

The residence time of a single, non-rotating spherical particle falling through a fixed distance in a stationary liquid is examined. The mass of the particle is taken to be a random quantity as a result of diameter being distributed according to the Log-Normal probability density function (particle density is assumed constant). In addition to weight, buoyancy and drag, the particle is assumed to be subject to random effects as it falls. The effect of both the dispersion in particle diameter and random disturbances in particle velocity on particle residence time are quantified. It is shown that the joint distribution in particle diameter and residence time can be approximated by a bivariate Log-Normal distribution. Such an approach permits the relative influence of systematic size dispersion and velocity fluctuations on residence time to be easily determined. It also permits the correlation between particle residence time and diameter to be expressed analytically. While the method is aimed at the motion of a single particle, it provides a fundamental basis to design systems based on falling particle-liquid interactions.