Electrostatic launching of vibrating glass beads

Journal of

ELECTROSTATICS ELSEVIER

Journal of Electrostatics 42 (1997) 143-150

Electrostatic Launching of Vibrating Glass Beads Masayoshi Murayama, Koichi Fujibayashi, Mitsuru Matsui and Norio Murasaki Department of Electrical and Electronic Engineering, Faculty of Technology Tokyo University of Agriculture and Technology. 2-24-16 Nakamachi, Koganei-shi, Tokyo 184, Japan

When particles of insulating material are placed between parallel plate electrodes, they become polarized by the electric field, then charged by contact with the electrodes, and then jump due to Coulomb's force. To build a particle supply source a combination of a spherical mesh electrode and a vibrating spherical electrode has been used, with insulating glass beads as sample particles. The initiation voltage for launching of the glass beads and the launched height have been measured. The electric charge of the glass beads has been estimated from measurements of their launched height. The electrode system used in this study is able to concentrate the glass beads which are launched to a certain position on the outside of the mesh electrode. The initiation voltage for launching and the launched height have been measured for several size of glass beads.

1. INTRODUCTION Small particles can be launched upwards within a parallel plate air condenser which is arranged so that its plates are horizontal. The particles are polarized by static induction at the moment when high voltage is applied to the condenser. Each particle acquires a net electric charge through charge transfer, and since a Coulomb force acts on the charged particle due to the electric field between the condenser plates, the charged particles are torn from the contacting bottom electrode. This behavior has been well studied [Cho, 1964] for metal particles. Metal particles charged by similar two stages contact electrification have been accelerated to hypervelocities [Shelton, Hendricks, Wuerker, 1960]. Glass beads are adopted as the insulating specimen. Glass beads are an extremely good light reflectors, and are therefore widely used as the main component of the coating material for light reflecting adhesive tapes, background paint for traffic control sign boards, and road sign marking paint. This study deals with the launching of glass beads by electrostatic tbrce, which may be adapted to serve as a supply source for glass bead decoration for special effects Concentric spherical electrodes have been proposed, and the particle charges have been estimated from the dynamics of the launched particles based on the observation of the launched height of glass beads. 0304-3886/97/$17.00 © Elsevier Science B.V. All rights reserved. S0304-3886(97)00128-9

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M. Murayama et al. /Journal of Electrostatics 42 (1997) 143-150

[C~CALI.AT~] Figure 1 Concentric spherical electrodes ~ r launching glass beads.

2. P A R T I C L E L A U N C H E R Glass beads were spread on the bottom electrode of a horizontally parallel plate air condenser, whose upper electrode is made of fiat wire mesh. The beads were launched outside of the electrodes at the moment when high voltage was applied to the condenser. This effect is independent of the polarity o f applied voltage, and also independent of the choice of high voltage applied electrode, such as the upper wire mesh electrode or the bottom electrode, while the other electrode is earthed. Above the upper electrode, the launched particles dispersed due to Coulomb repulsive forces, so that the wire mesh fiat electrode has proved inadequate as a particle supply source. When the fiat wire mesh electrode is replaced with a concave wire mesh electrode, particles launched to the outside of the concave wire mesh electrode trace parabolic trajectories, whose vertices converge to a certain position above the upper electrode. A particle launcher employing a pair of concentric spherical electrodes is shown in Figure 1. A combination o f a spherical wire mesh electrode and a vibrating spherical electrode have been used. The mesh electrode was made of a piece of mesh of 0.2mm diameter stainless steel wire 16×16 strands per square inch. Several holes were enlarged by piercing with an awl. The mesh beaten out to take the shape of spherical dome, with a 111 mm radius of curvature. The bottom electrode is the concentric spherical electrode, made of a phosphor-bronze sheet of 0. lmm thickness, forming a spherical shell of 13 lmm radius and glued to a balsa disk with a pedestal. The electric field between the upper and lower electrodes is shown in Figure 2. To vibrate the glass beads, the bottom electrode was vibrated at a frequency of 100Hz with an audio speaker installed beneath the bottom electrode. Chladni's figures were not observed on the bottom electrode, To observe the trajectory of the launched particles, the space between the concentric

M. Murayama et al. /Journal of Electrostatics 42 (1997) 143-150

145

spherical electrodes was illuminated by a traversing light beam within a dark room. Commercially available lime-glass beads were selected as the insulating particles. They are classified into diameter ranges by sieves, as shown in Table 1.

...... EQUIPTOT ENTIAL UNE ELECTRIC LINE~ OF F O R C E

SPHERICAL E L E C T R O D E

Figure 2

Table 1

Nominal Diameter[Bm] 50 70 90 100 130 150 200 300 400 600 800 1,000 2,000

Electric field distribution.

Particle size of the sample glass beads.

Geom~ricalMeanDiam~er[Bm] 48 74 96 115 136 162 210 296 418 596 838 1,176 1,869

Diam~er Range[~m] 3763 6388 88- 105 105- 125 125- 149 149- 177 177- 250 250- 350 350- 500 500- 710 710- 990 990- 1,397 1,397- 2,5OO

3. MEASURED INITIATION VOLTAGE FOR LAUNCHING

The vertices of the trajectories of the launched particles were observed by reading a scale placed behind the particle-launching electrodes. The initiation voltage for launching, which is the minimum voltage applied to the spherical wire mesh electrode that can launch the glass beads up to the upper electrode, has been measured. The initiation voltage for launching each nominal-diameter group of particles is plotted in Figure 3. The initiation voltage for launching increases with the nominal diameter. However, it is independent of the charge polarity of the particle. The initiation voltage for launching resting glass beads is higher than the initiation voltage for vibrating glass beads. The initiation voltage for launching metal particles, which was calculated with the attainable

M. Murayama et al. /Journal of Electrostatics 42 (1997) 143-150

146

charge quantity q0 estimated by Eq. (1), is shown as the curve offl=l.0 in Figure. 3. =

(2/3) 36o,,2E,

(l)

where 60 is the permittivity [F/m] of vacuum, a is the radius [m] of the particle and E is the electric field strength IV/m]. In Figure 3, parameter fl stands for the ratio of the acquired charge q of the particle to the attainable charge q0, estimated by Eq. (1), for the metal particle of the same size, that is (2)

fl = q l q o .

The measured value of the initiation voltage for launching of resting, 70p.m glass beads agrees with the calculated value for ,8=0.4. Thus, the charge quantity of those particles is reduced to 40 percents of the charge attainable for the metal particle. The electrostaticvibrating feeder has decreased the required voltage to launch, compared to that of the electric feeder.

3 0 f~r--r--r-r-~

v

~.

• ,o-~-6

>

g

4

V--

•

• ELECTROSTATIC-VIBRATING FEEDER '~ I

I

I

II

40

I

I I

100

I

200

I

I

400

I

I

I

I

I

1000

I

2000

PARTICLE DIAMETER d [/zm]

Figure 3

Initiation voltage of particle launching.

I

4000

~

M. Murayama et al./Journal of Electrostatics 42 (1997) 143-150

147

4. MEASURED LAUNCHED HEIGHT The maximum launched height of particles belonging to each nominal diameter group is plotted as Figures 4 and 5 with applied voltage as a parameter. The larger the diameter, the higher the launched height attains. Therefore, the abscissas of Figures 4 and 5 are marked by the largest diameter of each nominal diameter group as listed in Table 1. The best height is attained for a nominal diameter of 200~tm. The electrostatic-vibrating feeder increased the number of launched glass beads compared to the electrostatic feeder, while it shows no increase in the launched height.

10o

,

,, .

.

.

.

,

,

E

I---

0

D

lOC

. . . . .

E

E ~_ 8c

O:10kV ~:12kV V:14kV 17:16kV

/~

80

z

6(1

4C

5

Q

6c

D

4(

/~

010kV Z& 12kV V 14kV D 16kV

5

~- 2c I-

e,-

40

100 200 400 1000 2000 PARTICLE DIAMETER d [/zm]

4000

Figure 4 Particle launched height from electrostatic feeder.

40

100 200 400 1000 2000 PARTICLE DIAMETER d[/zm]

4000

Figure 5 Particle launched height from electrostatic-vibrating feeder.

5. PARTICLE C H A R G E ESTIMATION The particle charge was estimated by the analysis of its motion based on its measured launched height L. The forces acting on the particle which passes through the mesh of the upper electrode are the viscous resistance due to the air and the gravitational force. The dynamic equation of the glass particle can be expressed as the following, assuming the positive direction is upwards, m ( d v I tit) = -rag

-

kv,

(3)

where, k = 6 x r l a, m is the mass of glass beads (=(4/3)xa3p [kg]), p is the density of the lime glass (2,480 [kg/m3]), r/is the viscosity of air (1.83× 10.5 [Pa-s], at 20C), v is the velocity of the particle [m/s] and g is the gravity constant [m/s2]. Integrating Eq. (3) with respect to the variable t, we obtain the following equation m g + kv = C e x p ( - k t / rag),

(4)

M. Murayama et al./Journal of Electrostatics 42 (1997) 143-150

148

where C is a constant. If the particle passes through the mesh at t=-0 with an initial velocity v0, then we have the following equation (5)

C = m g + kv o.

Thus Eq. (4) can be written as mg + kv = (rag + kv o) exp(-kt / m).

Let the position of the particle be Y, with an initial value Y=0 at t=0. (6) to obtain y = _ m g t + m (rag + kv o)~1 - exp(- kt / m~. k k~ ~ " "J

(6) We can integrate Eq.

(7)

When the particle comes to the vertex o f its trajectory, at the time T, its velocity v should be v=0. We can derive the following expression from Eq. (6), it'= - r a i n mg . k rag + kv o

(8)

Substituting the above value into Eq. (7), we can calculate the launched height H o f the particle as - .--:7m2g In mg + m vo H-k" mg+kv o k

(9)

Eq. (9) can be rewritten as an implicit function to determine the value of the initial velocity Vo,

meg, ] mg [ m f(vo) = --~ml--I + - - v o - H = 0. kL Img+kvol k

(10)

Using Newton's iterative method, we can estimate the value of v0 by the following formula, Vo(i + 1) = Vo(i ) - f {v°(i)}

J'{Vo(O}

(11)

Now, f'(vo) is derived from Eq. (I0) as f ' ( v o) -

mVo rag + kvo

(12)

M, Murayama et al. /Journal of Electrostatics 42 (1997) 143-150

149

Then the ratiof(v0)/f'(vo) in Eq. (11) can be expressed by

S{vo(#)} _ m g + k v o ( i ) ( m Z g l n

f'{v,,(i)}

mvo(i )

n_ig

\ k"

+ ~mv o ( i ) _ H

.

(13)

Img+Icvo(i)l

If the starting value v0(1) is enough close to the genuine value v0 in Eq.(10), the iterative calculation of Eq. (11) will rapidly converge to the genuine value vo. The starting value vo(1) may be approximated by the following equation (the gravitational energy is equal to the kinetic energy),

mgH = (1 / 2)m{v o (1)} 2 ,

(14)

Vo(1 ) = ~ - g H

(15)

Substitute the measured value of particle launched height (L+20 [mm]) for H in Eq. (10), and iterate the Eq. (11) to find the initial velocity v0. The particle charge q can be estimated by the motion dynamics of the particle accelerated by the voltage difference [" between the condenser plates

mv o / 2 :: qV,

(16)

q = m v 2 / 2V.

(17)

The particle charge q estimated by Eq. (17) is shown in Figures 6 and 7. 1000

1000

E ~ r i c charge calculated by Cho's equation

!Eleck~ charge calcu~tedbyCho's equation

q=(2/3)n~coa2E

:q=(213)~eea=E lOO

V=lOkV. V=12kV,~

j

V=14kV~\__

.~'/=~

100

~r

V=IOkV V=12kV V=I4kV V=16kV V=lSkV

~ lO -r

=, 0

j///~e f///="

01

o.o~ 01

0:10kv

100

.4f'///" w

,',.12kv V:14kv 0:lekV '~18kV

f///au e "W

200

400

lOOO

~

12kV

o

2000

4000

PARTICLE DIAMETER d [/.zm]

Figure 6 Electric charge of particle from electrostatic feeder.

0.01 40

100 200 400 1000 2 0 0 0 4000 PARTICLE DIAMETER d [.~'m]

Figure 7 Electric charge of particle from electrostatic-vibrating feeder.

150

M. Murayama et al. /Journal of Electrostatics 42 (1997) 143-150

6. THE INDUCED ELECTRIC CHARGE ON GLASS BEADS

The induced electric charge on a glass bead, which is calculated from the measurement of its launched height, has been compared the induced electric charge of a conductive sphere placed on an infinite plate electrode. When high voltage of 10, 12, 14, 16 or 18 kV are applied between the electrodes, the induced electric charge of a conductive sphere has been calculated by Eq. (1). The calculated values are drawn as five lines in Figures 6 and 7.

7. CONCLUSION The upper mesh electrode and the bottom electrode of the particle supply source are shaped as concentric spheres. The launched particles can be concentrated at a certain position outside of the mesh electrode. The initiation voltage of particle launching is proportional to the logarithm of the particle diameter. Vibration of the disk containing the particles decreases the initiation voltage, so that the particle supply source works at a lower voltage. The electrostatic-vibrating feeder is effective in increasing the number of launched particles, but has shown no increase in the launched height.

REFERENCE 1. Cho, A. Y. H. [1964], "Contact Charging of Micron-Sized Particles in Intense Electric Fields" J. Appl. Phys., 35(9), (1964) 2561-2564. 2. H. Shelton, C. D. Hendricks, Jr., and R. F. Wuerker [1960], "Electrostatics Acceleration of Microparticles to Hypervelocities" J. Appl. Phys., 31(7), (1960) 1243-1246.