816 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012 Numerical Simulation of Tribo-Aero-Electrostatic Separation of Mixed Granular Solids Fatima Zahra Rahou, Amar Tilmatine, Senior Member, IEEE, Mihai Bilici, Student Member, IEEE, and Lucian Dascalescu, Fellow, IEEE Abstract—Numerical simulation can be a powerful tool in the research and development of any new electrostatic process. The aim of the present work is to introduce a simple mathematical model for simulating the outcome of a recently patented tribo- aero-electrostatic separation process for binary mixtures of gran- ular materials. The process is characterized by the fact that the charging of the granules is produced in a fluidized bed device, in the presence of an electric field. The mathematical model assumed that the probability of a granule to be separated can be expressed as a function of the number of impacts with granules belonging to the other class of materials. When this probability was given by a normal distribution law, the results of the simulations differed sig- nificantly from those of an experiment conducted with a granular mixture of polyamide and polycarbonate particles, in a laboratory tribo-aero-electrostatic separator. In order to improve the predic- tive capability of the simulations, a polynomial function derived from the regression of the experimental data was employed for expressing the same probability. Thus, it was possible to calculate the evolution in time of the mass of granules separated at the electrodes for various compositions of the granular mixture. The computed results were in good agreement with the experiments. Index Terms—Electrostatic separation, granular materials, numerical techniques, triboelectricity. NOMENCLATURE A, B Materials to be separated. C A ,C B Concentration of materials A and B. M Total mass to be separated. M A ,M B Mass of A and B in the fluidized bed. M As ,M Bs Mass separated of A and B. N Number of collision per unit time. P Probability function. Π Standard normal distribution function. PA Polyamide. PC Polycarbonate. X AB Number of collisions. Manuscript received June 7, 2011; revised August 4, 2011 and November 7, 2011; accepted November 28, 2011. Date of publication De- cember 22, 2011; date of current version March 21, 2012. Paper 2011-EPC- 250.R2, presented at the 2011 IEEE Industry Applications Society Annual Meeting, Orlando, FL, October 9–13, and approved for publication in the IEEE TRANSACTIONS ON I NDUSTRY APPLICATIONS by the Electrostatic Processes Committee of the IEEE Industry Applications Society. The work of F. R. Rahou was supported by a research scholarship from the Algerian Government for the completion of a Ph.D. thesis at the University of Poitiers. France. F. Z. Rahou, M. Bilici, and L. Dascalescu are with the PPRIME Institute, UMP 3346-CNRS-University of Poitiers-ENSMA, EHD Group IUT, 16021 Angoulême, France (e-mail: rahou.fatima@yahoo.fr; mihai_bilici@yahoo. com; lucian.dascalescu@univ-poitiers.fr). A. Tilmatine is with the University Djillali Liabes, 22000 Sidi-Bel-Abbes, Algeria (e-mail: atilmatine@gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2011.2181288 x AB Normalized number of A–B collisions. s xAB Normalized standard deviation. σ xAB Standard deviation. t 50% Time to the separation of 50% of the A granules. Subscripts av Average value. e Estimated value. exp Experimental value. I. I NTRODUCTION T RIBO-ELECTROSTATIC separation is a technology that has been actively promoted during the last two decades as an effective solution for the recycling of plastics from granular industrial wastes [1]–[5]. Identification of optimal operating conditions has been a crucial issue for each application [6]–[9], and the experimental design methodology has proved to be one effective way to address it [10], [11]. Numerical simulation could be a different way to achieve process optimization, as it has already been employed for the research and development of other electrostatic processes [12], [13]. In the case of corona and electrostatic separators for the recycling of metallic and insulating particles from cable wastes, for instance, numerical models have been proposed for esti- mating the charge acquired by the particles and for calculating their trajectories in an electric field [14], [15]. The simulations pointed out the effects of the various process control variables: high voltage, roll speed, etc. Tribo-charging is a much more complex phenomenon [16]– [19], and its mathematical modeling is still in progress [20]– [26]. The computation of particle trajectories, by taking into account all the mechanical, aerodynamic, and electrical forces is a very complicated and time-consuming task [27]. Both researchers and practitioners need a more user-friendly simu- lation tool for performing the feasibility studies that precede the development of a new application. Therefore, the aim of the present work is to introduce a simple mathematical model for simulating the outcome of a recently patented tribo-aero-electrostatic separation process for binary mixtures of granular plastics [28], [29]. The process is characterized by the fact that the charging of the particles is produced in a parallel-pipe-shaped fluidized bed device, in the presence of an electric field (Fig. 1). This horizontal field, perpendicular to the direction of the fluidization air, is generated by the metallization of two of the opposite vertical walls of the tribocharging chamber and connecting them to two dc 0093-9994/$26.00 © 2011 IEEE