Robustness testing of a free-fall triboelectric separation process for plastic waste recovery

Abstract

Among the separation techniques used in industries, the triboelectric separation of insulating particles using a rotary tube is an effective way employed in the waste recovery of plastic and mineral products. This process, also called free-fall triboelectric separation, is widely used for the sorting of granular mixtures resulting from industrial plastic wastes. Given that the robustness of such a separation process is an important issue, a standard procedure is used for determining the set point and for minimising the process sensitivity of sorting mixed particles of different polymers to changes in the values of some critical factors. The aim of this paper was to analyse the efficiency of the triboelectric separation process of polymers with respect to any slight variation in the values of the most significant factors. Experiments with a sample of high-density polyethylene and polyvinyl chloride plastic granules were carried out on a laboratory experimental bench. Several one-factor-at-a-time experiments, followed by two factorial designs (one composite and the other fractional), were performed based on the following experimental procedure: (1) determination of the variation limits of the input variables; (2) identification of the set point and (3) robustness testing of the process, i.e. testing whether the performance of the system remains high even when the factors vary slightly around the set point.

Keywords::

• triboelectric separator
• design of experiments
• particles of polymers
• robustness testing

1. Introduction

Recycling of polymers has become a hot issue due to the increasing quantities of obsolete information technology (IT) equipment that need to be processed every year (Haga 1995; Inculet, Castle, and Brown 1998). Landfill or incineration cannot be considered as end-of-life solutions for these materials, because of their negative ecological impact (Li et al. 2007). Plastics represent at least 30% in weight of IT wastes. The vast majority of such wastes are subject to a mechanical treatment involving shredding, granulation, magnetic separation and classification. Whenever possible, plastics must be manually sorted prior to mechanical recycling into polymer type and/or colour. Technology is being introduced to sort granular plastics automatically using various techniques such as X-ray fluorescence, infrared and near-infrared spectroscopy, electrostatics and flotation (Aizawa, Yoshida, and Sakai 2008; AI-Salem, Lettieri, and Baeyens 2009; Ongondo, Williams, and Cherrett 2010).

Electrostatic separation is a generic term given to a significant class of material processing technologies commonly used for the sorting of granular mixtures of polymers by means of electric forces acting on charged or polarised particles (Tilmatine et al. 2013; Crowley 1986; Brands, Beier, and Stahl 2001). A major application of these technologies is the recycling of metals and plastics from industrial wastes (Ralston 1961; Dascalescu 2001; Higashiyama and Asano 1998; Iuga et al. 2001). The quality of the recycled materials obtained using the electrostatic separation technique is better than that achieved by other conventional methods of waste processing, and the overall efficiency of this technique is also higher.

The use of a triboelectric separator has been recommended for processing granular mixtures made from various kinds of polymers (Lungu 2004; Yanar and Kwetkus 1995). Triboelectric charging occurs when any two different surfaces contact one another. This process is currently the subject of further research, especially for its optimisation using different mathematical methods (Dascalescu et al. 2005; Tilmatine et al. 2009; Medles et al. 2007a, 2007b). The resultant static charge is not usually noticeable unless it occurs in a system where the conductivity of the material surface is low, allowing the charge to build up to high levels. This static build-up, which is a significant burden in the handling of large amounts of fine dry powders such as flour or powdered chemicals and polymers, can be effectively employed for sorting differently charged particles in an electric field.

A descriptive schematic of a triboelectric separator is represented in Figure 1. First, the particles enter a rotating cylinder, where they undergo several ‘particle-to-particle’ and ‘particle-to-wall’ collisions. These collisions allow the granules to be charged, and thus they exit from the rotating cylinder by falling vertically into an intense horizontal electric field produced by two metal electrodes of rectangular form connected to two direct-current high-voltage supplies of opposite polarities. The particles charged negatively are attracted towards the positive electrode and the ones charged positively are attracted towards the negative electrode. The products are recovered in a collector that contains three compartments (material 1, mixed product and material 2).

Figure 1 Schematic representation of a free-fall triboelectric separation process.

A standard procedure, proposed by Medles et al. (2007a) which was applied for a role-type corona separation process of plastic/metal particles, was employed in the present study for determining the set point and for robustness testing of the triboelectric separation process of a granular mixture comprising high-density polyethylene (HDPE) and polyvinyl chloride (PVC) particles. In a free-fall-type separator (Figure 1), the factors influencing the outcome of the process are the feed rate, the granule size, the high voltage level, the angle of vertical electrodes, cylinder inclination and the speed of the rotating cylinder.

This paper considers four factors which are the high voltage level, the cylinder inclination, the speed of the rotating cylinder and the angle of vertical electrodes. Four ‘one-factor-at-a-time experiments’, followed by two factorial designs (one composite and the other fractional), were performed based on the following well-defined experimental procedure: (1) fixing the variation domain of the input variables, (2) searching the optimal set point and (3) analysing the robustness of the process.

2. Experimental design methodology

The methodology of experimental designs makes it possible to determine the number of experiments to be achieved according to a well-defined objective, to study several factors simultaneously, to reduce dispersion related to measurements, to appreciate the effects of coupling between factors and, finally, to evaluate the respective influence of the factors and their interactions (Frigon and Mathews 1996; Taguchi 1987; Eriksson, Johansson, and Kettaneh-Wold 2000).

Before the commencement of the experiments, it is necessary to set the best and suitable design that can model the process with the most possible precision. In this paper, the composite centred faces (CCF) design, which gives quadratic models, was adopted. It is possible to determine a quadratic dependence between the output function to optimise (response) and the input variables u _i (1, …, k) (factors):

(1) $y=f(u_i)=c_0+\sum c_i{u}_i+\sum c_{ij}{u}_i{u}_j+\sum c_{ii}{\displaystyle u_i^2}.$(1)

Given that $\Delta u_i$ and $u_{io}$ are, respectively, the step of variation and the central value of factor i, the reduced central values of the input factors may be defined by the following relation:

(2) $x_i=\frac{(u_i-u_{io})}{\Delta u_i}.$(2)

With these new variables, the output function becomes:

(3) $y=f(x_i)=a_0+\sum a_i{x}_i+\sum a_{ij}{x}_i{x}_j+\sum a_{ii}{\displaystyle x_i^2}.$(3)

The coefficients can be calculated or estimated using a data processing program, in order to have a minimum variance between the predictive mathematical model and the experimental results.

MODDE 5.0 software (Umetrics AB, Umea, Sweden), which is a Windows program for the creation and evaluation of experimental designs (MODDE 5.0, 1999), was used. The program assists the user for interpretation of the results and prediction of the responses. It calculates the coefficients of the mathematical model and identifies best adjustments of the factors for optimising the process. Moreover, the program calculates two significant statistical criteria that make it possible to validate or not the mathematical model, represented by R ² and Q ². The former is called the goodness of fit, which is a measure of how well the model can be made to fit the raw data; it varies between 0 and 1, where ‘1’ indicates a perfect model and ‘0’ no model at all. The latter is called the goodness of prediction, which estimates the predictive power of the model. As with R ², Q ² has the upper bound 1, but its lower limit is minus infinity. For a model to pass the diagnostic test, both parameters should be high and preferably not separated by more than 0.2–0.3.

3. Design of triboelectric separation experiments

The design of experimental methodology is useful for screening, optimisation and robustness testing. Screening experiments are designed in this paper to identify the variation domain of the four classical ‘one-factor-at-a-time’ experiments. The optimisation stage of an experimental procedure should enable the determination of factor values for which the middling fraction is a minimum and the rate recovery is a maximum.

The aim of robustness testing is to confirm that the response is not sensitive to small changes in the factors around the set point. As each factor is explored within a narrow range, a linear model is more suitable for robustness testing. Fractional factorial designs are recommended for robustness testing:

(4) $y=a_0+a_{1}U\#+a_{2}n\#+a_3\alpha \#+a_3\beta \#.$(4)

4. Materials and methods

The granular mixture to be separated is supplied at an adjustable feed rate into the rotating cylinder using an electromagnetic feeder. The feed rate of the vibrator, equal to 20 g/s, was constant for all the experiments. Actually, as the vibratory feeder is of electromagnetic type and the vibrations are of very small amplitude, it is expected that the electric charge will not have an influence on the tribocharging process of the cylinder.

The samples (200 g) of granular materials were composed of 50% HDPE and 50% PVC, which had an equivalent radius of 2 mm. The typical shape and size of the plastic granules are shown in Figure 2. The HDPE particles were spherically shaped, while the PVC ones were quasi-spherical. In triboelectric charging, the level of the electric charge is influenced by the size of the particles and less influenced by their shape. There would be no sensitive difference in tribocharging mechanism if PVC granules were spherical.

Figure 2 Shape and size of the PVC and HDPE particles.

Each sample was first processed in a custom-designed tribocharging device, as shown in Figure 3. The device consisted of a 10 cm-diameter, 100 cm-long PVC rotating cylinder that was inclined horizontally. The residence time of the tribocharging device was dependent on the inclination and speed of the rotating cylinder. A part of the charge acquired by the particles was due to their collisions with the walls of the device.

Figure 3 Experimental bench for triboelectric separation of polymers. 1, Rotating tube; 2, vibratory feeder; 3, command of the feeder; 4, driving motor; 5, DC power supply of the motor; 6, high-voltage electrodes; 7, collector; 8, hygrometer; 9, electronic balance; 10, tachometer; 11, high-voltage power supplies.

The charge of the particles was systematically neutralised before each experiment by grounding a metal plate on which the granular product was spread as a monolayer for at least 24 h. Measurements done before carrying out the experiments showed that the residual charge was negligible (i.e. less than 0.2 nC/g).

The charged granules were then separated in the electric field generated by two vertical plate electrodes (dimension 40 cm × 100 cm), and were collected in the following three compartments: two for the ‘pure’ products and one for the ‘middling’ products. The electrodes were separated in the top position by a gap of 20 cm, in order to have a high electric field. However, if the distance between the electrodes is small (less than 20 cm), then the electric field is sufficiently strong enough to ionise the air and the particles would acquire an unwanted charge due to the corona discharge.

In each compartment, the mass of the product was measured using a digital balance (precision 0.1 g).

The purity of the product was calculated as follows:

(5) $\text{Pur} (\text{\%})=\left(\frac{m_{\text{ic}}}{m_{\text{tc}}}\right)\times 100,$(5)

where m _ic is the quantity of product i that is collected in the compartment reserved for it and m _tc is the total mass (both products) collected in the same compartment. The recovery represents the ratio of m _ic to the total mass m _it of product i in the feed:

(6) $\text{Rec} (\text{\%})=\left(\frac{m_{\text{ic}}}{m_{\text{it}}}\right)\times 100.$(6)

In this paper, the experiments simulated the operation of a typical industrial triboelectric separator, which dealt successfully with the following four control variables:

1. high-voltage level, U (kV),

2. rotating cylinder speed, n (rpm),

3. slope inclination of the rotating cylinder, α (°) and

4. angle of the high-voltage vertical electrodes, β (°).

5. Results

5.1. Variation domain of the control factors

The variation limits of the aforementioned control factors are defined by the following four ‘one-factor-at-a-time’ experiments.

Experiment 1.1. Variable voltage U (10–35 kV) at constant values of n = 170 rpm, α = 5.6° and β = 8.5°.

Experiment 1.2. Variable cylinder speed n (120–320 rpm) at constant values of U = 30 kV, α = 5.6° and β = 8.5°.

Experiment 1.3. Variable slope inclination α (1.7–6.9°) of the cylinder at constant values of U = 30 kV, β = 8.5° and n = 170 rpm.

Experiment 1.4. Variable angle β (4.5–8.5°) of the vertical electrodes at constant values of U = 30 kV, α = 5.6° and n = 170 rpm.

The results of experiments 1.1–1.4 are given in Tables 1 2 3 4. The amount of middling particles and the recovery of PVC and HDPE particles were considered as significant for the evaluation of the process and are represented as functions of the four control factors in Figures 4 5 6 7. Although purity is a significant criterion to evaluate separation efficiency, in the majority of the experiments carried out in the present work, its value was higher for optimal conditions, ranging from 95% to 99%. That is why this response was disregarded, as it did not illustrate well the variation as observed for the recovery and amount of middling particles.

Table 1 Results of experiment 1.1 (n = 170 rpm, α = 5.6°, β = 8.5°).

	PVC product					HDPE product
U ( ±  kV)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)	Middling (g)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)
10	14.50	4.30	77.13	14.50	168.70	5.60	5.80	50.88	5.80
15	64.30	2.20	96.69	64.30	106.70	1.60	23.10	93.52	23.10
20	91.50	2.50	97.34	91.50	60.00	0.90	44.00	98.00	44.00
25	95.60	2.50	97.45	95.60	25.90	0.70	72.30	99.04	72.30
30	99.30	3.90	96.22	99.30	16.70	0.80	79.00	99.00	79.00
35	97.70	3.00	97.02	97.70	15.20	0.70	80.50	99.14	80.50

Table 2 Results of experiment 1.2 (U = ± 30 kV, α = 5.6°, β = 8.5°).

	PVC product					HDPE product
n (rpm)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)	Middling (g)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)
120	97.25	8.65	91.83	97.25	23.62	0.15	65.93	99.77	65.93
170	97.00	9.12	91.41	97.00	28.35	0.20	60.00	99.67	60.00
220	96.15	10.25	90.37	96.15	30.72	0.23	56.00	99.59	56.00
270	95.40	9.29	91.13	95.40	36.03	0.25	53.50	99.53	53.50
320	93.43	10.26	90.11	93.43	34.19	0.30	53.00	99.44	53.00

Table 3 Results of experiment 1.3 (U = ± 30 kV, β = 8.5°, n = 170 rpm).

	PVC product					HDPE product
α (°)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)	Middling (g)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)
1.73	93.00	2.60	97.28	93.00	15.80	0.50	76.80	99.35	76.80
3.03	95.50	5.10	94.93	95.50	16.20	0.70	77.70	99.11	77.70
4.33	97.20	2.80	97.20	97.20	16.40	0.60	80.00	99.26	80.00
5.62	97.90	4.30	95.79	97.90	30.10	1.00	61.80	98.41	61.80
6.91	97.60	4.20	95.87	97.60	25.30	0.30	66.40	99.55	66.40

Table 4 Results of experiment 1.4 (U = ± 30 kV, α = 5.6°, n = 170 rpm).

	PVC product					HDPE product
β (°)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)	Middling (g)	PVC (g)	HDPE (g)	Pur (%)	Rec (%)
4.5	85.30	3.90	95.63	85.30	40.20	2.40	62.80	96.32	62.80
6.5	89.70	2.10	97.71	89.70	28.10	1.20	74.60	98.42	74.60
8.5	87.30	2.80	96.89	87.30	42.50	0.90	63.00	98.59	63.00

Figure 4 Recovery of PVC and HDPE particles and amount of middling particles as functions of the applied high voltage (n = 170 rpm, α = 5.6°, β = 8.5°).

Figure 5 Recovery of PVC and HDPE particles and amount of middling particles as functions of the speed of the rotating cylinder (U = ± 30 kV, α = 5.6°, β = 8.5°).

Figure 6 Recovery of PVC and HDPE particles and amount of middling particles as functions of the slope inclination α of the cylinder (U = ± 30 kV, β = 8.5°, n = 170 rpm).

Figure 7 Recovery of PVC and HDPE particles and amount of middling particles as functions of the angle β of the high-voltage vertical electrodes (U = ± 30 kV, β = 8.5°, n = 170 rpm).

In this section, the results correlated with the definition of the variation domain of U, n, α and β. Thus, Figure 4 shows that in the conditions of experiment 1.1, the mass of middling particles represented more than 50 g for U < 20 kV. As the recovery of HDPE particles was also poor ( < 80%), U < 20 kV, U _min = 20 kV and U _max = 20 kV were retained as the limit values for the voltage. The trajectories of PVC and HDPE particles were affected by the combination of gravitational and electric forces. However, a certain number of granules remain not sufficiently charged, so even the voltage increases the separation efficiency remains constant.

In the conditions of experiment 1.2 (Figure 5), for n ≥ 220 rpm, the mass of middling particles exceeded 30 g, although the recovery of PVC particles remained sufficiently higher and that of HDPE particles decreased below 60%. On the other hand, the limit values for the cylinder speed should not be less than 120 rpm; otherwise, the overall efficiency of the process in terms of productivity would be uninteresting. After increasing the speed of the rotating cylinder, it was observed that due to the centrifugal force, the granules were ‘pinned’ to the cylinder wall and did not undergo particle-to-particle-type collisions, leading to a decrease in the electric charge. Consequently, the variation domain of the speed was defined as n _min = 120 rpm and n _max = 120 rpm.

In the conditions of experiment 1.3 (Figure 6), the results showed that the limit values for the slope inclination α of the rotating cylinder should not exceed 5.6°; otherwise, the recovery of HDPE particles would decrease below 70% and the mass of middling particles would reach 30 g, which was a considerable amount compared with the total feed mass. The overall efficiency was decreased when the slope inclination of the rotating cylinder increased, due to a reduction of the duration of the tribocharging process in the cylinder. This effect was more significant for HDPE granules which acquired an electric charge less than PVC particles. Therefore, the variation limits of slope inclination were defined as α_min = 1.7°, which was the lowest possible value obtained from the experimental bench, and α_max = 5.6°.

Furthermore, Figure 7 shows that the optimal outcome for the angle of electrodes was β = 6.5°, because the efficiency decreased for a high β value, causing diminution of the electric field, and also decreased for a low β value due to the impact of the particles on the electrodes. For a low β value, although the electric field was high, it was found that the granules had an impact on the electrodes and therefore their trajectories were modified. For a high β value, the electric field decreased, resulting in the decline of the overall efficiency.

5.2. Set-point identification

The set point (U _o, n _o, α_o and β_o) was identified using a central CCF design; the two levels ‘max’ and ‘min’ were the limits established in the previous section for each of the four control variables (U _min, U _max), (n _min, n _max), (α_min, α_max) and (β_min, β_max), with the central points (U _c, n _c, α_c and β_c) being calculated as follows:

(7) $U_{\text{c}}=\frac{U_{ min }+U_{ max }}{2}=\frac{20+35}{2}=27.5\text{ kV,}$(7)

(8) $n_{\text{c}}=\frac{n_{ min }+n_{ max }}{2}=\frac{120+220}{2}=170 r\text{pm,}$(8)

(9) ${\alpha }_{\text{c}}=\frac{{\alpha }_{ min }+{\alpha }_{ max }}{2}=\frac{1.7+5.6}{2}=3.65°,$(9)

(10) ${\beta }_{\text{c}}=\frac{{\beta }_{ min }+{\beta }_{ max }}{2}=\frac{4.5+8.5}{2}=6.5°,$(10)

The results of the experiment are given in Table 5.

Table 5 Results of experiment 2 (set-point identification).

Exp no.	Voltage, U ( ± kV)	Speed, n (rpm)	Slope, α (°)	Angle, β (°)	PVC recovery (%)	HDPE recovery (%)	Middling (g)
1	20.0	120	1.70	4.5	96.4	83.7	17.3
2	20.0	220	1.70	4.5	96.8	70.4	29.2
3	20.0	120	5.60	4.5	96.9	76.7	23.5
4	20.0	220	5.60	4.5	97.1	59.4	38.1
5	20.0	120	1.70	8.5	82.8	68.7	45
6	20.0	220	1.70	8.5	83.2	68.1	46.1
7	20.0	120	5.60	8.5	84.8	51.9	45
8	20.0	220	5.60	8.5	85.0	61.6	65
9	35.0	120	1.70	4.5	97.3	83.6	13.9
10	35.0	220	1.70	4.5	97.9	80.2	15.7
11	35.0	120	5.60	4.5	98.4	85.0	11.9
12	35.0	220	5.60	4.5	98.6	78.0	17.4
13	35.0	120	1.70	8.5	98.9	96.5	8.7
14	35.0	220	1.70	8.5	98.4	84.7	11.8
15	35.0	120	5.60	8.5	98.6	83.7	10.5
16	35.0	220	5.60	8.5	99.8	84.1	10.4
17	27.5	120	3.65	6.5	97.1	88.7	10.9
18	27.5	220	3.65	6.5	98.8	80.9	15.8
19	27.5	170	1.70	6.5	98.0	86.2	11.7
20	27.5	170	5.60	6.5	99.4	85.0	11.9
21	27.5	170	3.65	4.5	92.2	89.6	8.0
22	27.5	170	3.65	8.5	97.0	80.0	9.1
23	20.0	170	3.65	6.5	89.5	77.0	38.9
24	35.0	170	3.65	6.5	99.0	91.7	6.2
25	27.5	170	3.65	6.5	98.5	87.1	10.4
26	27.5	170	3.65	6.5	98.0	85.9	11.4
27	27.5	170	3.65	6.5	98.1	82.5	15.5

The mathematical model of the response considered for optimisation, which is the mass of middling particles, was obtained with MODDE 5.0 as follows:

(11) $y=97.5+4.1U\#+0.24n\#+0.5\alpha \#+2.4\beta \#-2.9U\#{}^2+0.8n\#{}^2+1.5\alpha \#{}^2-2.6\beta \#{}^2+0.06n\#\alpha \#-0.006n\#\beta \#+0.02n\#U\#+0.1\alpha \#\beta \#-0.1\alpha \#U\#+3.4\beta \#U\#.$(11)

According to this model, the optimal outcome of the process (i.e. the smallest amount of middling particles and the greatest values of recovery for both PVC and HDPE particles) should be obtained for speed (n = 166 rpm), slope (α = 5.6°), angle (β = 4.5°) and voltage (U = 32.0 kV). Figure 8 shows the iso-response contour plots obtained for the present model. Figure 8(a) shows the dependency of the mass of middling particles according to the variation of both separation unit factors (i.e. the applied high voltage level and the angle of positive and negative electrodes), while Figure 8(b) indicates the influence of the tribocharging unit factors (i.e. slope inclination and the speed of the rotating cylinder).

Figure 8 Response contour plots for middling.

5.3. Robustness testing

The robustness testing of the process was carried out using a fractional factorial experimental design. The levels min and max were chosen by considering the optimal set point (U ₀, n ₀, α₀ and β₀) determined in the previous section and the variations ( ± ΔU ₀ = 2 kV, ± Δn ₀ = 10 rpm, ± Δα₀ = 0.6° and ± Δβ₀ = 0.5°) that can occur in the set values of the control factors during the normal operation of the process.

The following central points were chosen for the experiment: U ₀ = 32 kV, n ₀ = 166 rpm, α₀ = 5.6° and ± Δβ₀ = 4.5°.

The results of the corresponding fractional factorial experimental design are presented in Table 6. The results of robustness testing for all the responses (recovery of PVC and HDPE particles and mass of middling particles) showed that the triboelectric separation process for this type of material was robust. There were no significant differences observed between the responses when the three factors varied slightly around the set point.

Table 6 Results of experiment 3 (robustness testing).

Exp no.	Voltage, U ( ± kV)	Speed, n (rpm)	Inclination, α (°)	Angle, β (°)	PVC recovery (%)	HDPE recovery (%)	Middling (g)
1	30	155	5	4	99.1	83	12
2	34	175	5	4	96	88.1	8
3	34	155	6.2	4	95.4	84.9	11.7
4	30	175	6.2	4	95	87.2	12.7
5	34	155	5	5	88.5	87.5	9.7
6	30	175	5	5	93.5	91.7	8.7
7	30	155	6.2	5	89.9	86.8	12
8	34	175	6.2	5	88.7	90	9.3
9	32	165	5.6	4.5	97	86.4	11
10	32	165	5.6	4.5	97.1	85.3	10.3
11	32	165	5.6	4.5	93.6	86.2	12.5

The models for the recovery of middling, PVC and HDPE particles were non-significant, which was the ideal outcome of a robustness test. Figure 9 shows that except for the slope inclination, the outcome of the process was not sensitive to the slight variation of the factors. Indeed, the plotted coefficients were not significant as they varied around the zero value; their mean value was around zero. Therefore, robustness testing confirmed that the response was not sensitive to small changes in the factors within a narrow range around the set point. The robustness of the process, i.e. the performance of the system, remained satisfactory even when the factors varied slightly around the set point.

Figure 9 Plot of model coefficients of robustness testing.

6. Conclusion

The triboelectric separation technique is a multifactorial process depending on several factors, and the methodology of experimental designs was effective to assess its robustness. Four factors that were considered as the most significant ones were analysed using an experimental procedure based on three strategic steps. For the free-fall triboelectric separator considered in this study, the four control factors were the high-voltage level U, the rotating cylinder speed n, the slope inclination α of the rotating cylinder and the angle β of the high-voltage vertical electrodes.