Investigation of the separation of conductive and insulating objects on a laboratory made electrostatic separator

Electrostatic separators are widely used to separate conductive and insulating objects up to some millimetres in size. Modelling of such equipment has been presented in several studies; laboratory and numerical models have been analysed. However, there are such situations, where larger samples of the order of centimetres have to be separated, as milling them into smaller size particles is not allowed or feasible. It was found that electrostatic separation can be used even in such cases but in a different arrangement than in the “traditional” constructions. This paper is a continuation of a previous study, in which the separation of a constructed laboratory separator was examined. The model was built in a circular plate arrangement with high voltage needle electrodes above the edge of cylinder’s mantle, where the discharges are generated. The slope of the circular plate is steadily decreasing, so the samples on the edge of the plate produce an increasing angle of inclination along the circumference. Charged samples stick to the plate, uncharged ones fall off. Some key parameters as rotation speed, electrode distance, voltage level and position of ionizer electrodes were varied.


Introduction
Several studies have been published on the separation of electric parts of objects using electrostatic charging [1].It is an important technology, because the production of plastics and other materials has increased significantly in the previous decades [2], and with an efficient and reliable solution, metals can be recycled, plastic can be collected in other places [3].Two major steps of the technologies that allow the recovery from waste: finely grinding of the material (if necessary) and separation of constituents [4].In this paper the separation is based on the differences in the electric conductivity of the objects.
Electrostatic separators (ES) are widely used for the separation of conductive and insulating objects up to some millimetres [5], [6] (or micrometres [7]) in size.Commonly used types of separators are the roll-type [8], plate-type [9], tribo-electrostatic [10] or belt-type [11] electrostatic separators (as can be seen in Fig 1 .).Modelling of such equipment was presented in several papers, and both laboratory and numerical models were analysed [12], [13].However, there are such situations, in which larger samples in the centimetres range must be separated, as milling them into smaller size particles is not allowed or feasible.
Although several alternative solutions exist, it was found that electrostatic separation can be used even in such cases but in a different arrangement than in the "traditional" constructions.Based on the measurements, a new design prototype model was built.It has four adjustable variables as delay of the rotation step-motor, DC voltage, location of the corona discharge ionizer and the distance between the ionizer and samples.

Samples and parameter relations
The geometry of the conductive samples is solid rectangular, as seen in Figure 2, where 'a' is the width, 'b' is the length, 'h' is the height of the conductive sample.The plastic samples are not solid but contain an interstitial space (into which air penetrates): continuing parameter lists will include 'hairgap' and 'hplastic' which is the height of the air gap and the height of the plastic body of the samples (parameter 'a' and 'b' is the same):

Rectangular metal sample
Plastic sample with a frame where 'a' is 1 centimetre, 'b' is 2 centimetres, 'hg' and 'hp' is 1 millimetre and 'h' is 2 millimetres.In the edges of the plastic samples can be found a plastic frame with the height of 'hairgap' which contains the air.We mention that there is also a capacitance between the high-voltage electrode and the sample surface, but it can be neglected.
The shape of the samples is not the result of grinding, but the residual part of the post-production output of the industrial plant.We do not plan to include a cutting unit for the grinding and after for the separation processes, so we designed a separator that matches this sample.We were looking for the optimum arrangement and parameter set-up where the metal and plastic samples are separated with one hundred percent.We were unconcerned with the intermediate results, as we sought the information needed for 100% separation.
Depending on the placement of the plastic samples, we can differ in two cases: when the plane surface of the samples is in contact with the grounded metal surface (case A) and when the frame of the sample is in contact with the grounded surface (case B).For a metal sample, it does not matter which way it lies on the ground from the geometrical point of view, it has a symmetrical body.The metal samples cannot keep charges if the sample holder is grounded, because they are conductive materials.The corona discharges charge the plastic samples which are placed on a metal sample holder.There is a capacitance between the upper surface of the plastic sample and the grounded sample holder, thus there can be a voltage difference between both sides of the plastic samples.We can estimate the capacitance 'C' of the plastic (Cp) part by eq (1) and the air gap (Cg) part by eq (2) The sum capacitance of the samples in case A: Ccase'a'=Cp because no other factors are involved (the geometric difference due to the frame is neglected because of the small surface area), but in case B two components connected in series: the air and the plastic.The resulting capacitance will be 'Cb' has always a lower value than 'Cplastic' if the plastic is a better insulation material than the air.The mass of the plastic samples was 0.998 g, the mass of the conductive samples was 4.962 g which was measured by a sensitive weighing instrument (but it can be also approximated knowing the volume and mass density of the materials).The gravity force can be calculated by the mass and acceleration constant, which is 0.00979 N.
In our studies, the samples will then slide, and the observation will be made at the location of the slip to determine if the samples are falling at different locations or not.The sliding requirements can be expressed by the main forces acting on the samples.There is an effect of gravity force, adhesionsfriction, and electrostatic force on the samples.The moment of sliding appears when the gravity force is higher than the adhesion-friction and electrostatic force.
Knowing the capacitances, and from various corona current and voltage measurements, we can calculate a theoretical adhesion-friction and electrostatic force, and compare this with the force of gravity.However, the aim was to build a working device rather than a theoretical derivation, so we will not go into the theoretical equations now.

Arrangement
Based on the preliminary calculations it was found that sliding of metal and plastic samples starts at significantly different bending angle () values.But if only one grounded metal plate is used in such a situation, the sliding metallic samples will collide and move the stuck plastic samples.To avoid collision, a new model was constructed (Fig 3 .).This model is composed of two different circular plates with different diameters (bottom, and upper plate with sample holders overhanging the edge), and a side wall that has different heights.Hence, the angle of the sampling holder changes from 0 [°] to 31.7 [°], and sampling plate can go back to original position (0 [°]) after one 360°circle.Upper plate is rotated by stepper motor 28BYJ-38 which is controlled by an Arduino board and can rotate continuously so the separation procedure can be done unceasingly.Positive polarity corona discharge produces less ozone than negative polarity corona discharge [3], so in this model from 0 kV to 25 kV of positive DC voltage was applied.Resonant feeders are considered to apply for placing samples one by one on the separator plate, as such feeders are widely used in the plastic industry.
The parameters of the model were: Length of sampling plate hitting the lowest height of side wall: 4 ~ 5 cm Sidewall of the model was scaled.The origin of the scale was at the position lowest height of side wall.Is marked as initial 0 cm, and every 2 cm away from this point, markers were placed both left and right side.Left side was marked from -2 to -16 and right side from 2 to 14 cm.31.67 ° 24.83 ° The code for the Arduino board was set.This code made the stepper motor rotate in a clockwise direction.Angular velocity can be controlled by changing the delay value.In this measurement, delay time of 1 ms, 1.5 ms, and 2 ms were used, which is the time differences between two successive positions of the stepping motor.The motor itself moves 5.625° in one step (360 degrees / 64), the gear ratio divides this by another 64.So, for example, if the time between two steps is 1 ms, the disc (and with that the upper plate) will make one complete turn in 4.096 seconds.
It was observed how many samples were falling down near a specific marker, and it was registered.To examine how different parameters influence the process, the following conditions were varied: • • Distance between Corona discharge ionizer and sampling plate on highest side wall.(hi) The location of the corona discharge ionizer above the samples (xi) was expressed using the markers on the sidewall, see Fig. 3.The Distance between the corona discharge ionizer and the sampling plate on the highest side wall was measured by a ruler.A minimum distance between the ionizer and the highest sampling plate was set as 5 cm, and the DC voltage was applied up to a maximum of 25 kV DC to avoid breakdown [14].
Number of samples for this measurement was 50 for both metal and plastic cases.In the case of plastic sample measurement, only CASE A (┏┓) was put on a sample plate because CASE B (┗┛) will have the strong electrostatic force to stay on a plate even at -180 ° (always 100% of the separation rate during some test measurement).
Depending on the result, it is possible to set a separation zone for metal and plastic samples.In these zones, only metal and only plastic samples are situated, respectively.Between them, there is a mixed sample zone from which samples can be put back into the feeder for the subsequent separation step.However, the separation is easier when there is no mixed zone, and the distance between separation zones for metal and plastic is as high as it is possible.

Results
The effects of the above parameters on the separation rate are illustrated in the following figures (Fig 4-6.).The metal samples are always signed as light-blue colour in the diagrams, and the plastic samples are signed as dark-blue, orange-red, green, and purple (in the function of parameter set-up, can be seen on the diagram's right part).shows the number of samples falling at a given marker in case of different ionizer distances and different time delays of the stepper motor.The time delays were set to 2, 1.5, and 1 ms, while the ionizer distances were set to 27, 18, 12, and 6 cm.In such cases, the time of one complete turn of the rotating plate is 8s, 6s, and 4s, respectively.27 and 18 cm showed a long mixing zone for all three cases, especially xi = 27 cm experiment, where it was practically impossible to separate the samples (as we can see in all figures that the darkblue signed plastic samples fall down in every 2 cm range distance slot).For 2 and 1.5 ms time delay and 12 cm ionizer location, significant mixing can be observed.In case of a 1 ms delay, the separation zones were not overlapping.The reason is interesting: at high speed, the "jumping" of sample holders on the uneven parts of the edge of the sidewall becomes so intensive that it "shakes" down the metal samples from the sample holders earlier.
When the ionizer location was set to xi = 6 cm, the separation was much better, no overlapping of metal and plastic zone was observed at lowest and highest speed at a charging voltage of 25 kV.
Looking closely at the diagrams, we can see that adding the values for the columns gives different sums (e.g., in Fig 4, the sum of metal samples is much more than plastic samples at -18 cm ionizer distance).This is not because fewer samples were tested but because the samples stayed in the holder all along!As a summarization, for all three-time delays, the separation shows better efficiency when the ionizer is located near the separation slope, so the location of the ionizer is a significant variance when designing a separation model.Effect of charging voltage was also examined.As it was expected, when IOP Publishing doi:10.1088/1742-6596/2702/1/0120107 voltage level was set higher, the area of mixed samples reduced, even 100% separation could be reached.
Further parameter relations for the separation factor are shown in Figure 7-14.For each test, the short conclusion can be found in the figure caption.For the different measurements, the fixed parameters are marked at the top of the diagrams, and the voltage variations (Fig. [7][8][9][10][11][12] or ionizer distances (Fig. 13-14) are shown in colour on the right.The 'x' axis shows the side wall markers for the distances and the 'y' axis shows the number of samples dropped.
Figure 7 When the time delay is 2 ms (T = 8 s), and the ionizer location is xi = 6 cm, some plastic and metal samples fell to the same area.In this time delay, the last metal sample fell down to the separation area between 4 cm ~ 6 cm, and 17 kV case had plastic samples fall down from 4 cm.Meanwhile, the 25 kV case has plastic samples falling down in an area between 10 cm ~ 12 cm.It means that the arrangement can separate the metal and plastic with a separation rate of 100%, and there was a distance slot between (6-8 and 8-10) cm where none of the samples fell.Figure 8 The measurement was too homogeneous, metal samples fell in every point of the arrangement, so metal and mixed collection area can be formed only.
Figure 9 When the time delay was 1 ms (T = 4 ms) and ionizer location was 6 cm, the border of 100% separation rate can be found at 8 cm if we used 15 kV or 25 kV.Using 13 kV we got a wide mixed area.
From the diagrams above, we can conclude that a more significant part of the metal samples separates until the range of 6-8 cm, while some plastic samples are gathered in the same area (which is mixed so that we can take back to the input).Using higher voltage, we give the chance to minimize the mixed area and get a totally separated area, as we could see in 3 cases.
Figure 10 With the ionizer location of 12 cm, a time delay of 8 s, the separation rate cannot reach 100%.The metal samples fell until 6 cm, but there was a wide mixed area between the (-4 and 6) cm range.With an ionizer location of 12 cm, the separation rate becomes better and better if we increase the supply voltage.In general, we got worse results than the xi = 6 cm case, because the mixed area was more extensive; many plastic samples fall between the range of 2 -10 cm, too!So, the charged samples quickly lost their charges, thus reducing the adhesion at the points of higher slope.Figure 13 With an ionizer location of 12 cm, a time delay of 4 s, and a supply voltage of 25 kV, there is a huge difference if we increase the height (distance) of the ionizer.The metal samples fell until the 6 cm location, and the plastic samples started to fall at 8 cm or 14 cm when the ionizer height was set to 5, 8, and 10 cm.The separation rate can reach 100%; the model works in all three cases.Figure 14 Similar to the previous measurement with T = 8 s, the 100% separation rate can be reached when the ionizer height is 5, 7.5 and 10 cm.Fig. 13. and 14. shows that when the distance between the ionizer and the highest sampling plate is between 7.5 cm and 10 cm, more plastic samples are gathered after the sampling plate angle is recovered to 0°.When the distance between the ionizer and the highest sampling plate is more than 10 cm, some plastic samples fall in the separation area.When corona discharge appears, ionization of gas is made; during this procedure, gas gets momentum from Coulombic force, which makes an ionic wind.Ring shape anode with 25 [kV] can make 4 [m/s] ~ 6 [m/s] ionic wind [8][9].
This result indicates that a shorter distance between the sampling plate and the ionizer does not always make a better result, so it is required to find an optimal distance for each condition.

Conclusion
From the examined parameters the distance between the corona electrode and the sampling plate was very important, as the corona electrode was closer to the sampling plate due to the corona wind caused by the corona discharge, and this corona wind exerted additional force on the plastic samples.In order to avoid this, it is recommended to increase the distance between the corona electrode and the sampling plate.However, this distance should vary with the voltage level, and further measurements are needed to find the optimal distance for each voltage level.The delay time of the stepper motor measurement showed a correlation between speed and separation rate, with shorter delay times (higher showing better results compared to other delay times.This also indicates that better separation rates can be achieved when using shorter delay times.In general: electrostatic separation gives a solution for the presented task, but it is still a question whether in industrial construction it is competitive with other existing solutions or not.

Figure 2
Figure 2 Structure of the metal (left) and plastic (middle) samples, and the model of corona resistivity (right).
CASE A Case A, where the plane-side of the plastic sample has contact with the ground (or support structure) CASE B Case B, where the frame-side of the plastic sample has contact with the ground (or support structure)

Figure 3
Figure 3 laboratory model for separation of the metal and plastic samples.
Delay time of stepper motor.(Thus resulted in different speed w [revol./sec])• DC voltage level.(Supply voltage of ionizer U [kV]) • Location of Corona discharge ionizer (xi).

Figure 4 - 6
Figure 4-6 Number of samples falling down at a given marker at different ionizer distance and different time delay of stepper motor.

Fig 4- 6
shows the number of samples falling at a given marker in case of different ionizer distances and different time delays of the stepper motor.The time delays were set to 2, 1.5, and 1 ms, while the ionizer distances were set to 27, 18, 12, and 6 cm.In such cases, the time of one complete turn of the rotating plate is 8s, 6s, and 4s, respectively.27 and 18 cm showed a long mixing zone for all three cases, especially xi = 27 cm experiment, where it was practically impossible to separate the samples (as we can see in all figures that the darkblue signed plastic samples fall down in every 2 cm range distance slot).For 2 and 1.5 ms time delay and 12 cm ionizer location, significant mixing can be observed.In case of a 1 ms delay, the separation zones were not overlapping.The reason is interesting: at high speed, the "jumping" of sample holders on the uneven parts of the edge of the sidewall becomes so intensive that it "shakes" down the metal samples from the sample holders earlier.When the ionizer location was set to xi = 6 cm, the separation was much better, no overlapping of metal and plastic zone was observed at lowest and highest speed at a charging voltage of 25 kV.Looking closely at the diagrams, we can see that adding the values for the columns gives different sums (e.g., in Fig4, the sum of metal samples is much more than plastic samples at -18 cm ionizer distance).This is not because fewer samples were tested but because the samples stayed in the holder all along!As a summarization, for all three-time delays, the separation shows better efficiency when the ionizer is located near the separation slope, so the location of the ionizer is a significant variance when designing a separation model.Effect of charging voltage was also examined.As it was expected, when marked of side wall [cm] location of ionizer : -27 cm location of ionizer : -18 cm location of ionzier : -12 cm location of ionizer : -6 cm metal sample T = 1/w = 8 s; U = 25 kV; h i = 5 cm; x i = see marked of side wall [cm] location of ionizer : -27 cm location of ionizer : -18 cm location of ionizer : -12 cm location of ionizer : -6 cm Metal sample T = 1/w = 6 s; U = 25 kV; h i = 5 cm; x i = see below marked of side wall [cm] location of ionizer : -27 cm location of ionizer : -18 cm location of ionizer : -12 cm location of ionizer : -6 cm metal sample T = 1/w = 4 s; U = 25 kV; h i = 5 cm; x i = see below International Conference on Electrostatics 2023 Journal of Physics: Conference Series 2702 (2024) 012010 w = 8 s; x i = -6 cm; h i = 5 cm; U = see below w = 6 s; x i = -6 cm; h i = 5 cm; U = see below w = 4 s; x i = -6 cm; h i = 5 cm; U = see below

Figure 11
Figure 11  With the ionizer location of 12 cm, a time delay of 6 s, the separation rate cannot reach 100%, and give similar results nearly independently by the supply voltage.

Figure 12
Figure 12  With an ionizer location of 12 cm, a time delay of 4 s, the separation rate can reach 100% with a voltage of 25 kV.With other supply voltage, the separation rate is reasonable, and the range of mixed area is smaller than the previous parameter set-up.

Table 2
shows angle of sampling plate () for each marked location of side wall.Values are symmetrical to 0, thus only negative positions are used.Angle of sample holder plate for each marked location of side wall. TableI