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International Journal of Chemical Engineering
Volume 2016, Article ID 2784584, 8 pages
Research Article

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

Fluid Mechanics Division, University of Huelva, Campus La Rábida, Carretera Huelva-Palos s/n, Palos de la Frontera, 21819 Huelva, Spain

Received 16 December 2015; Revised 15 February 2016; Accepted 28 February 2016

Academic Editor: Jerzy Bałdyga

Copyright © 2016 Urbano Sánchez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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, . 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 and its relationship with the elapsed time. We prove that the permanence time is of the order of (with particle diameter) and that the average settling velocity is of the order of 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.