Study of charged particles trajectories in free-fall electrostatic separators Hakima Labair a , Seddik Touhami b , Amar Tilmatine a, * , Samir Hadjeri c , Karim Medles b, d , Lucian Dascalescu d a APELEC Laboratory, Djillali Liabes University of Sidi Bel-Abbes, Algeria b IRECOM Laboratory, Djillali Liabes University of Sidi Bel-Abbes, Algeria c ICEPS Laboratory, Djillali Liabes University of Sidi Bel-Abbes, Algeria d PPRIME Institute, CNRS-Poitiers University-ENSMA, F86962 Futuroscope, Poitiers, France article info Article history: Received 14 October 2016 Received in revised form 7 January 2017 Accepted 10 January 2017 Available online xxx Keywords: Electrostatic separation Electric field Electric charges Particles trajectory abstract The objective of this paper is to develop a mathematical model for computing the millimeter-sized particles trajectories in the free-fall electrostatic separator. The simulation involves the numerical so- lution of motion equations of the particles subjected to electric and gravitational forces. The air-drag force and the impact of the particles with the electrodes were also considered. The resolution algo- rithm is implemented as a MATLAB program that uses the results of electric field computation performed with COMSOL software. The model obtained is used to study the factors influencing the quality of the products recovered at the outlet of the separator. © 2017 Elsevier B.V. All rights reserved. 1. Introduction The free-fall electrostatic separators are widely used in sorting and purification of sub-millimeter size ores [1e4]. Currently, they are also successfully applied to the sorting of granular plastics from waste electrical and electronic equipment [5e8]. In these facilities, granular material sorting is produced by the electrostatic force acting on particles pre-charged in devices that use the triboelectric effect. The quality of products recovered at the outlet of the elec- trostatic separator is strongly related to the charge/mass (Q/m) ratios of the particles in the mixture [9,10]. Several triboelectric charging devices have been developed in recent years [10e13]. Currently, the fluidized bed is considered to be the best solution [14,15], as characterized by moderate energy consumption, as well as low operating and maintenance costs. Improving the tribocharging conditions by reducing the size of the treated particles is a way to increase the efficiency of the electro- static separations. However, particle size reduction is sometimes unnecessary and leads to an increase of the energy consumed for milling. Therefore, attempts were made to optimize the electrostatic separation of mm-size particles, by using numerical modelling techniques. Thus, Calin et al. [16] were the first to perform numerical modelling of particle trajectories in a free-fall electrostatic separator. However, the analytical method they employed for the electric field compu- tation was far from being accurate, especially in the proximity of electrode edges. Recently, Younes et al. [17] compared the outcome of free-fall electrostatic separation experiments with the results of numerical simulations of particle trajectories, but the computa- tional conditions were not very clearly described. This paper aims at validating an accurate numerical model of particle trajectory in a free-fall electrostatic separator. The model uses information on the geometrical and electrical parameters of the separation system and of the physical characteristics of the particles of the product under study. Thus, it relies on measures of Q/m ratio performed for the constituents of a mixture (ABS/PVC) recovered at the outlet of a laboratory separator (Fig. 1). The results obtained may be used to define the optimal values of the control variables of the separator that would give maximum gap between the collection points of two products, having different mass and charge distributions. * Corresponding author. E-mail addresses: amar.tilmatine@univ-sba.dz (A. Tilmatine), lucian.dascalescu@ univ-poitiers.fr (L. Dascalescu). Contents lists available at ScienceDirect Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat http://dx.doi.org/10.1016/j.elstat.2017.01.010 0304-3886/© 2017 Elsevier B.V. All rights reserved. Journal of Electrostatics xxx (2017) 1e5 Please cite this article in press as: H. Labair, et al., Study of charged particles trajectories in free-fall electrostatic separators, Journal of Electrostatics (2017), http://dx.doi.org/10.1016/j.elstat.2017.01.010