Formulation of the Settling Velocity of Small Particles Initially Situated inside an Inclined Vortex

Abstract

Both the estimation of the time that small heavy particles remain inside a 3D vortex and the estimation of the average settling velocity of those particles are some important features in many practical situations. Previous works focused on the case of a horizontal 2D vortex. In this paper, we simulate the dynamics of heavy particles initially situated inside a three-dimensional vortex obtaining a formula for their average settling velocity. In a previous paper we obtained the trajectories of the particles and a formula that provides the time that they need to escape, Te⁎. This work simulates and analyses the escape process, and its main result is the obtaining, from numerical simulation, of a theoretical formulation of the average settling velocity Vz⁎ and its relationship with the elapsed time. We prove that the permanence time is of the order of dp⁎-10 (with dp⁎ particle diameter) and that the average settling velocity is of the order of Te⁎-1/5 for sufficiently small particles. Some applications of the settling velocity formula developed in this work would be the design of mixture devices, the design of particle separation devices, and the prediction of the settling of pollutant particles, seeds, and pollen.