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Journal of Electrostatics 67 (2009) 189–192

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Journal of Electrostatics

journal homepage: www.elsevier .com/locate/e lstat

Behaviour of charged insulating particles in contact with a rotating roll electrode

Subhankar Das a,b, Adrian Samuila a,c,*, Ciprian Dragan a, Lucian Dascalescu a

a University of Poitiers, Poitiers, Franceb General Electric, Bangalore, Indiac Technical University of Cluj-Napoca, Cluj-Napoca, Romania

a r t i c l e i n f o

Article history:Received 10 September 2008Received in revised form21 November 2008Accepted 31 December 2008Available online 20 January 2009

Keywords:Computational electrostaticsCorona fieldParticle charging

* Correspondence to: Adrian Samuila, DepartmenTechnical University of Cluj-Napoca, 15 C. DaicoviciuRoumanie. Tel.: þ40 264 401 429; fax: þ40 264 592

E-mail address: asamuila@iutang.univ-poitiers.fr (

0304-3886/$ – see front matter � 2009 Elsevier B.V.doi:10.1016/j.elstat.2008.12.016

a b s t r a c t

The overall economic efficiency of standard industrial roll-type separators for granular materials can beimproved by operation at higher velocities of the rotating roll electrode. The aim of this paper is toestimate how high this speed could be and still have a good separation. The answer to this questionimplied the calculation of the electric image force, which opposes the centrifugal force and sticks thecorona-charged insulating particles to the rotating roll electrode. This force depends on the residualcharge carried by the particles. By estimating the decay of this charge from surface potential measure-ments carried out on granular layers of insulating materials dispersed on grounded plate electrodes, itwas possible to simulate the particle lift-off from the rotating roll electrode under various operatingconditions. The results presented in the paper were obtained for fly-ash particles, but the numericalsimulation methodology employed by the authors can be successfully applied for the optimisation ofother electrostatic separation applications.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

The design of industrial roll-type corona-electrostatic separa-tors for granular materials [1–3] should be preceded by a thoroughanalysis of the various factors that might improve the efficiency ofthe process. Roll speed is one such factor. Indeed, low roll speedwould impose low feed-rates, as the two variables have to becorrelated, otherwise it would not be possible to ensure a mono-layer of particles at the surface of the roll electrode. But low feed-rates are not compatible with the criteria of economic operation ofthe separator. In response to customers request for higher feed-rates, the roll speed should be high, too. The question to whichnumerical simulations presented in this paper aim to give ananswer is: how high this speed could be and still have a goodseparation? The theoretical analysis performed in Section 2 of thepaper points out that the key issue for the accuracy of thesesimulations is the estimation of the electric image force, whichopposes the centrifugal force and sticks the corona-charged insu-lating particles to the rotating roll electrode. This force depends onthe residual charge carried by these particles. The decay of thischarge can be estimated from the surface potential measurements

t of Electrical Engineering,Street, 400020 Cluj-Napoca,

055.A. Samuila).

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carried out on granular layers of insulating materials dispersed ongrounded plate electrodes, as shown in Section 3 of the paper. Theresults of the numerical simulations of particle lift-off from therotating roll electrode under various operating conditions are dis-cussed in Section 4.

2. Theoretical aspects

The condition for an insulating particle of mass m to stick toa metallic roll electrode of radius R, rotating at an angular speed u

(Fig. 1), can be expressed as follows:

Fi > Fc � Fg cos b (1)

where, Fi is the image force, Fc¼mu2R is the centrifugal force, andFg¼mg is the gravitational force acting on the particle. In the aboveequation b is the angular position of particle on the roll electrode.

The image force Fi on a spherical particle of radius a can becalculated with the following formula:

Fi ¼ Q2ðtÞ=�16p30a2� (2)

where Q(t) is the instantaneous charge of the particle [4], and 30 isthe permitivity of free space.

The variation of Q(t) can be calculated from the surface potentialdecay curve V(t) that can be determined according to the experi-mental procedure presented in the next section of the paper, and

Fiβ

β

β

Fg

Fg

Fgt

Fg

Fc

y

x

Fc

Fi

FgtFgt

Fg

Fc

Fi

ν

Fg νFg ν

Fig. 1. Forces acting on insulating fly-ash particle in a roll-type corona separator.

Fig. 3. Potential decay of fly-ash particles at the surface of a grounded electrode,charged by corona discharge.

S. Das et al. / Journal of Electrostatics 67 (2009) 189–192190

taking into account that Q a V (providing that the capacitance of theprobe-electrode system is constant). Thus:

QðtÞ=Qm ¼ VðtÞ=Vm (3)

where Vm is the maximum potential measured by the electrostaticvoltmeter, Qm is the maximum charge carried by a particle. In thiscase, the particle is charged by corona and Qm is the saturationcharge, Qs given by Pauthenier’s formula [5]:

Qs ¼ 4p30a2E0½33r=ð3r þ 2Þ� (4)

with E0 being the electric field strength in the corona zone, and 3r

the relative permitivity of particle.With these in mind, it is possible to obtain the variation of the

charge with time Q(t), which can be easily converted into a Q(b)curve, knowing that:

b ¼ ut (5)

u ¼ ð2pn=60Þ (6)

where n [rev/min] is the roll speed.

DAQ

Trek 370Electrosta

voltmete

Granull

Fig. 2. Schematic of charge decay measuring

3. Surface potential decay measurements

The experiments were performed on 5-g fly-ash samples,uniformly dispersed on a square area of 25 cm2 at the surface ofa 20 cm� 20 cm grounded electrode (Fig. 2). The thin layer of fly-ash was charged by the corona discharged generated from a wireelectrode, located at 40 mm above the grounded electrode andenergized from a DC high-voltage supply, in ambient air (temper-ature: 20� 2 �C; relative humidity: 40� 5%).

Fly-ash being hygroscopic in nature, it absorbs moisture fromthe atmosphere and increases its surface conductivity [6]. A first setof experiments were performed on ‘‘dry’’ samples, that were heatedup to 100–120 �C for 10 min, prior to corona charging and surfacepotential decay measurements. Two other sets of experiments wereperformed on ‘‘medium dry’’ and ‘‘humid’’ samples after main-taining the fly-ash in contact with the ambient air of known relativehumidity (50% and 80%, respectively) and temperature (20 �C) forat least 24 h.

After 10 s exposure to corona discharge, the surface potential ofthe samples was measured with an electrostatic voltmeter (TREK,model 370, equipped with an electrostatic probe model 3450) [7,8].The measured potential was monitored via an electrometer(Keithley, model 6514), connected to a PC. The acquisition andprocessing of the experimental data were performed using an adhoc virtual instrument, developed in LabView environment [9].

The surface potential decay curves for the three types of samplesare given in Fig. 3 (the maximum reading of the electrostaticvoltmeter was 2300 V). The points of each curve were computed as

ticr

Potential probe

Corona electrode

e

U=19.5 kV

ar layer 2

20

s=70

experiment, all dimensions are in mm.

Fig. 4. Variation of the forces acting on ‘‘dry’’, ‘‘medium dry’’ and ‘‘humid’’ particles atconstant roll speed n¼ 200 rpm.

Fig. 5. Variation of the forces acting on a ‘‘dry’’ fly-ash particle at different values of theroll speed.

Fig. 6. Variation of the forces acting on a ‘‘medium dry’’ fly-ash particle at differentvalues of the roll speed.

Fig. 7. Variation of the forces acting on a ‘‘humid’’ fly-ash particle at different values ofthe roll speed.

S. Das et al. / Journal of Electrostatics 67 (2009) 189–192 191

average of at least five experiments. The standard deviation wasless than 10 V for the ‘‘dry’’ sample and less than 50 V for the‘‘humid’’ sample.

4. Results and discussion

The experimental curves V(t) in Fig. 3 were employed for thecomputation of the charge variation Q(t), according to (3). Theseresults served for the calculation of the electric image force Fi asa function of the angular position b. The radius of the particle wasconsidered to be 0.05 mm, for a mass density of 970 kg/m3. TheFi(b) curves obtained for the three types of samples, at low rollspeed (i.e., n¼ 200 rev/min) are shown in Fig. 4, together with theFc(b)þ Fgn(b) curve. The water content of an ash particle representsless than 1% of its mass. Therefore, the variation of humidity doesnot affect the centrifugal or gravitational forces exerted on it. Theintersections between the latter curve and each of the Fi(b) curvesgive the detachment angle of fly-ash particles at various relativehumidity values and n¼ 200 rev/min. It can be noted that at thislow value of the roll speed, ‘‘dry’’ particles, which are subjected tohigher electric image forces, as their residual charge diminishes ata slower pace, remain ‘‘pinned ‘‘ to the roll electrode, while the‘‘medium dry’’ and ‘‘humid’’ ones detach at respectively b¼ 256�

and b¼ 151�. The variation of the moisture content of the fly-ash cansignificantly modify the detachment angle and hence the electro-static separation conditions of this material. This observation

Fig. 8. Variation of different forces for different roll radii.

S. Das et al. / Journal of Electrostatics 67 (2009) 189–192192

should be taken into account in the design of the industrial processof fly-ash beneficiation. Thermal conditioning of the material seemsto be a vital requirement for a successful industry application of thistechnology.

The image force is proportional to the square of particle radius a,while both the centrifugal and gravitational forces are proportionalto the cube of a. Therefore, the larger the particles, the sooner theydetach from the roll electrode. Roll speed is a key factor that can beeasily adjusted in order to control the detachment angle of the fly-ash particle. With increasing the roll speed the centrifugal force (Fc)acting on the particle also increases. The effect of modifying the rollspeed can be examined in Figs. 5–7, for the three types of samples.In the case of the ‘‘medium dry’’ sample, the detachment anglediminishes from 256�, at 200 rpm, to 132�, at 400 rpm. Reducingthe roll speed is a way to compensate for higher moisture content ofthe sample. This solution is not always acceptable, as it impliesa reduction of the feed rate, which should be correlated to the rollspeed.

Roll radius is another parameter that should be taken intoaccount in the design of the corona separation process (Fig. 8).‘‘Humid’’ fly-ash particles, for instance, would lift-off at b¼ 151� foran R¼ 150 mm roll electrode, while b¼ 126�, for R¼ 250 mm.

5. Conclusions

The behaviour of the insulating materials in roll-type coronaseparators is significantly influenced by their moisture content,which is often correlated to the relative humidity of the ambient air.The higher the moisture content, the lower is the speed at whichthe separator can operate for achieving the selective sorting of theprocessed materials. Thermal conditioning of the materials isa solution for ensuring a good separation.

The results presented in the paper were obtained for fly-ash,which is a major industrial application of the electrostatic separa-tion method [10–13]. Nevertheless, the conclusions above are validfor no matter what other hydrophilic insulating material.

Acknowledgements

One of the authors (CD) benefited of ERASMUS Student Mobilityscholarships financed by the European Union. The authors aregrateful to Dr. Rainer Kohnlechner and Dr. Florin Aman, fromHamos GmbH, Germany, for fruitful discussions, as well as to M.Marc Gauthier, for his technical help with the experimental set-up.

References

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