Recent Developments in Applied Electrostatics. Proceedings of the Fifth International Conference on Applied Electrostatics November 2~5, 2004, Shanghai, China

401 Pages·13.533 MB·English

by  Sun Keping and Yu Gefei (Eds.)

PREFACE
This proceedings contains papers presented at the 5th International Conference on
Applied Electrostatics held in Shanghai, China on November 2--5,2004. The ICAES
2004 Conference is of wide interest, as is shown by the contributions received from 11
countries and districts throughout the world. About 90 researchers attend the conference
and more than 100 papers were submitted for presentation in the proceedings.
The paper sessions covered following topics:
(cid:12)9 fundamentals and physics
(cid:12)9 applications (precipitation, pollution control, spray, separation, material, Ozone,
etc. )
(cid:12)9 hazards and problems
(cid:12)9 biology technology
(cid:12)9 electrets
(cid:12)9 measuring technology
(cid:12)9 electromagnetic compatibility and others
These papers demonstrated recent research level and developing trends of the entire
electrostatic field.
The objective of the Conference is to provide an opportunity for researchers from
all over the world to discuss various topics of electrostatic field at many levels, obtain
more information, absorb rich scientific nutrition and pick up the advantages from
varied researchers. New friends can be met and both the friendship and the cooperation
can be enhanced during the Conference.
The Conference is sponsored by the Commission on Electrostatics of Chinese
Physical Society, Shanghai Physical Society and Shanghai Maritime University. We
wish to thank all the authors for their cooperation and effort. We also thank Mr.
Christopher Greenwell, Publishing Editor, Control, Electronic and Optical Engineering,
Elsevier for his guide and assistance.
Prof. Sun Keping
Dr. uY Gefei
November ,1 2004
Shanghai, China
Paper Presented at the 5th International Conference on Applied Electrostatics (ICAES'2004), Shanghai, 2-5 November 2004
Elsevier, ISBN 0-08-044584-5
Charge behavior analysis in thin solid film by using simultaneous TSDC and LIPP
measurements
Tetsuji Oda, Koji Yamashita
Department of Electrical Engineering, the University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 Japan
Thermal Stimulated Discharge Currents (TSDC) analysis is very effective
technique to understand the charge stability and space charge behavior in a
charged thin film but the real position of those charges cannot be identified. For
that, a novel charge analyzing system has been developed. During TSDC
measurements, a Laser-Induced-Pressure Pulse (LIPP) method is applied to
observe the charge in-depth profile of the corona charged film ni that new system.
That system and new results obtained by that system are explained.
INTRODUCTIONS
Recently various kinds of excellent dielectric materials have been developed which are very useful for us.
However, such excellent dielectric materials are good insulators which may cause many unexpected
electrostatic accidents (named as electrostatic discharge: ESD and electrostatic over stress: EOS); such as
firing, explosion, device failure, computer misoperation etc. In order to prevent such trouble, the charge
analysis of the stored charge on/in the dielectric material. For the charge stability analysis, relaxation
process of the stored charge 1,2 in the dielectric material must be studied. Observation of the Thermally
Stimulated Discharge Currents (TSDCs)3 is one of analyzing methods of those relaxation processes.
The authors also started to analyze the charge by the TSDC at first for the fly ash 4, for PTFE and High
density Polyethylene (HDPE) films 5. The TSDCs are very sensitive to the charge stability and it is
easily to identify the different charge states. However, TSDCs cannot give us the information about the
charge position in the film.
Many researchers developed various space charge analyzing method. Thermal Pulse method 6 and
that modified Laser Intensity Modulation Method (LIMM) 7 are charge analysis by using thermal
conduction and expansion effects of the film. Pressure pulse traveling in the film can cause compression
of the film and the displacement current can be detected 8. Sessler groupe developed a very sensitive
and high special resolution method by using a picosecond laser 9. Other German group also developed
the space charge detecting method by using high speed piezoelectric device 10.The author also
developed a similar laser induced pressure pulse method 11 . Takada et al also developed a new system
by using a piezoelectric device12.
However, the reproducibility of TSDCs and LIPP methods is not so good and they must be observed
at the same time for the same sample. For that purpose, we developed a novel device that can observe
LIPP signal during TSDC analysis. That is, LIPP observation need only ten seconds or so and can be
done during TSDC analysis. Therefore at some temperature during TSDC analysis, a weak DC current
measurement is stopped about ten seconds and connected to LIPP measurement.
EXPERIMENTAL
TSDC and LIPP Observation
A newly developed TSDC and !:!PP measuring cell is shown in Figs.1 and 2. Laser beam can enter the
container from left side through a small window. The sample holder contains a charged sample film on
2
the detecting electrode (metal disk ) on right side and that electrode is connected to the BNC connector
with a straight wire. On that electrode, the charged surface of the sample film is pressed with a contacting
grease. A back side of the film is metalized by sputtering of aluminum before corona-charging and
connected with another ground electrode plate (aluminum). All materials are wounded by the electrical
heater and heated with a computer control. From that BNC connector, TSDC signal is transferred to
picoammeter (pA) and amplified signal is digitalized and stored in a personal computer as TSDC signals.
At some temperatures, Signal cable is switched to another low noise amplifier. The LIPP signal is
amplified and digitalized by the high speed digital oscilloscope connected with a personal computer.
elpmaS redloH
-, ...... :----- CNB retcennoc Temperature control
noitneter-taeH ,!~ol"
=.-lr-- J ,
/
:
resaL maeb a' 671r :~ ~'~QC I
,....
l e
j-~-.
Inlet of Lasel eB nsulationT hermal J 05 cable CSO
Oontainer
Fig.1 Simultaneous TSDC and LIPP Fig.2 TSDC and LIPP measurement switching circuits. LIPP measure-
for TSDC and OSC is for LIPP) ment and TSDC measurement (pA is measuring sample container)
Reproducibility of LIPP
To improve the data reliability, reproducibility of LIPP measurement was examined as shown in Fig.3
where the first shot means a laser ablation for the first time. ht001 shot means laser irradiation is repeated
001 times on the target surface and ht001 means the data is obtained by the last laser irradiation. From
Fig.3, about 20 % signal decrease from the ts1 to ht001 data can be recognized. That degradation must be
due to the increase of the surface roughness of laser irradiation target which coated with black special
paint for better laser absorption. The impedance matching grease is not used because of heating. All peak
values as shown X in Fig.3 are also shown in Fig.4 where the peak value gradually changes from -0.7 to
0.5 V during 100 laser irradiations. In Fig.4, 5 data are far from others indicating that the 5 % data are far
from the real charge profile. In other word, if the data is far from the estimated value, LIPP measurement
must be repeated.
number of shots (times)
0.4
0'2 04 0~( 0i~ b01
0.2 .f--%/ Y ~ 1 st shot
"~ 0.0 ,-- -0.2
-0.2
-0.4
o- 4
~_. ~e(cid:12)9 ~'0 o e (cid:12)9 ~ ,
-0.6 lOOth shot " ~_LJ 6.0- (cid:12)9 ....,~,-_,,~..-.-.-.'"- -~,%.B -- (cid:12)9 . . . . .
8:0- Lo ~
0~3 004 -0.8
4:~0
Time(ns)
.giF 3 LIPP signal egnahc neewteb eht ts1 resal Fig. 4 LIPP signals for 100 laser shots.
tohs dna ht001 laser .tohs
Sample Preparation
For our experiment now, 50 and 100 mxl PTFE Teflon sheet (Tomobo9001 supplied by Nichiasu ) and a
polyethylene terephthalate (PET) sheet are used as the sample. They are corona-charged where the grid
voltage is -5 kV where the corona voltage at the needle electrodes is about-30 kV at room temperature or
high temperature (50, 100 and 150 ~ In this paper, all data shown here are charged at 100 ~
RESULTS AND DISCUSSIONS
100 gm PTFE Sheet Charged at 100 ~
3
A typical example of TSDC spectra of 001 mt~ thick PTFE Teflon sheet corona-charged at 001 ~ is
shown in Fig.5. Two current peaks, b and g can be identified at about 250 ~ and 011 ~ Since the
charging temperature is 001 ~ there is no current peak below 001 ~ LIPP signal for that sample before
TSDC measurement (see Fig.5) is shown in Fig. 6 which is quite different from the TSDC spectra of
corona-charged at the room temperature [13] as shown in Fig.7. At 345ns(that time is from the laser beam
Fig. 5 TSDC spectra of corona-charged 100 6.giF LIPP signal of 001 ,mt.] PTFE thick mlif
mt~ PTFE thick thin .mlif degrahc-anoroc ta 001 ~ erofeb( .)CDST
irradiation and means the vertical position of the charge), a large negative charge (peak C) is observed
which may be negative charge in the sputtered aluminum back electrode and next peak B shows positive
charge maybe injected from the back electrode but that is not so sure. There are two other mechanisms
can be estimated. One is that the negative charges near the interface move from the PTFE to the back
metal electrode and positive charges remains near the interface. Another model is that the strong negative
electric field caused by the corona-charging induced the moving of the negative charge from the corona-
charged film (fight side) to the left side and accumulate near the metal-PTFE boundary which is shown as
peak C. That can well explained low negative charge peak A at the corona-charged surface. This model
can well explain that a large surface charge peak (A) is observed in Fig.7 but becomes very small in Fig.8
because high temperature increases conductivity of PTFE. However, that explanation cannot explain why
Fig.7 LIPP signal for 001 mm thick PTFE film Fig.8 LIPP signals at 100, 521 and 051 ~ during
charged atr oom temperature (before TSDC)[ ]31 TSDC measurement. Sample is charged at 001 ~
very sharp charge double layer as shown peaks B and C in Fig.6. More details will be discussed in near
future. During TSDC measurement, LIPP measurements can be done at some temperature range which is
shown in Fig. 8 and Fig. .9
By increasing the TSDC temperature, Peaks B and C are still very sharp but decrease with TSDC
temperature. On the other hand, peak A is pretty stable and does not decrease at about 200 ~ Therefore
those results suggested that Y peak in TSDC is strongly related with the charge peaks B and .C. TSDC
current peak a should be related with charge peak A because both peaks are stable at 200 ~ and other
apparent charge signal is not yet found. Off course, LIPP method is also not so highly sensitive for dipole
4
moment and there is a possibility that some new charges or dipoles are influenced TSDC a peak but not
yet detected in LIPP method. That fact is an experimental result.
.giF 9 LIPP at signals 571 dna 002 ~ of at charged PTFE 001 ~ during TSDC .tnemerusaem
50 mt~ PTFE Sheet Charged at 100 ~
Similar experiments are done for 50 mt~ thick PTFE film. In this case, the electric field in the film must
be double because the grid potential is the equal to -5kV which is the same for 100 mt~ PTFE film. The
typical LIPP data before TSDC analysis is shown in Fig.10 and the TSDC data is shown in Fig. .11 LIPP
signals at different temperatures during TSDC measurements are shown in Fig. 21 where the sample back
.giF 01 LIPP signals of 05 mt~ thick PTFE anoroc Fig. 11 TSDC of 05 mm thick PTFE film
degrahc at 001 ~ TSDC Before .sisylana degrahc-anoroc at 001 ~
electrode is at 305 ns and the corona-charged surface is at 400 ns, if the measuring temperature is 051 ~
When the measuring temperature increases, all peaks shift to larger time (fight side) in all data which is
due to the change of sound velocity, film expansion and elastic coefficient. From Figs. 11 and ,21 Y peak
at TSDC corresponds the back electrode interface charge which disappear at 200 ~ for both in Figs. 11
and .21 31 peak must .correspond surface charge (peak A). In other words, surface charge is trapped and
stable if the sample is heated up to 100 ~ The double peaks A in Fig. 01 are not sure but maybe surface
special configuration effect and will be disappear by heating.
One LIPP example is measured for the 50 mt~ thick PTFE film corona-charged at 160 ~ as shown in
Fig.13. A large amount of negative charge and counter positive charge are invaded inside the PTFE film.
The negative charge at the boundary is assumed to the induced charge in the back electrode by the
positive charge at the bottom of the film. That results suggest that various charge can move inside PTFE
if the PTFE temperature is more than 160 ~ Those phenomena are well-know as large peaks at about
100 ~ by TSDC measurement, if the corona-charging temperature exceeds 180 ~
Fig. 21 LIPP sinals of 50 mt~ PTFE at 150, 175, Fig. 31 LIPP signal of 50 mm PTFE charged at 061 ~
200, 522 and 250 ~ corona-charged at 001 ~ Before TSDC measurement.
CONCLUSIONS
The simultaneous TSDC (thermally stimulated discharge current) and LIPP (laser-induced pressure pulse)
measuring system is constructed for charge stability and charge position analysis. The position of charges
which cause some TSDC peaks is identified and charge behavior in the PTFE film is visibly observed.
Those results will explain various unknown electric current mechanisms near future by using that new
device.
ACKNOWLEDGEMENT
This work is partially supported by the Grand-in-Aid for Science Research by the Ministry of Education,
Culture, Sport, Science and Technology. The authors also thank Dr. Ono and Mr. Nakazawa for their
advices and assist.
REFERENCES
R.Chen ] 1 [ dna :hsriK.Y Analysis of Press, Pergamon Process," Stimulated Thermally New York )1891(
]2[ Braeurich, P.P. ed.: Relaxation Stimulated "Thermally ni Springer-Verlag, Solids," Berlin New Heidelberg York, (1979)
]3[ ,relsseS.M.G ed.: "Electrets," Springer-Verlag, Berlin New Heidelberg York, (1980)
]4[ T.Oda, S.Masuda dna T.Takahashi; "TSDC Measurements of Fly Ashes from Pulverized Coal Combustion," Proc.2nd
.fnoC.tnI ,.picerP.tsortcelE (1985) pp.540-547
]5[ T.Oda dna .S Wang; "Charging on HDPE Films eud to Surface Effects during Fabrication," .J pp.167- vol.35, Electrost.,
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]6[ A.Migliori dna J.D. Thompson, "A Electric Acoustic Nondestructive Field Probe," J.Appl.Phys., ,15 )0891(584-974.pp ]7[
gnaL.B.S dna ,atpuG-saD.K.D A Technique Method: Modulation "Laser-Itensity for Determination of noitubirtsiD laitapS
of noitaziraloP dna Space Charge ni Electrets," Polymer ,.syhP.lppA.J ,95 )6891(0612-1512
]8[ A.G.Rozno dna "Measurement V.V.Gromov, of eht egrahC-ecapS Distribution ni a Solid Dielectric," ,.tteL.syhP.hceT.voS
,5 )9791(762-662.pp
]9[ G.M.Sessler, J.E.West, R.Gerhard and H.von Seggem, Laser "Nondestructive Method for Measuring Charge Profiles ni
Polymer Irradiated Films," IEEE NS-29, Nucl.Sci., Trans. .pp !(9461-4461 )289
[ ]01 E.Eisenmenger dna "Observation M.Haardt, of Polarization Compensated Zones Films (PVDF) in Polyvinylidenfluoride
by cirtceleozeiP Step-Wave Acoustic Response," Solid .tS Comm., ,14 )2891(5772-9672.pp
[ 11 R.Ono, ] dna T.Oda, "Charge storage Polypropylene Corona-charged a im Film Analyzed by LIPP dna CST Method," .fnoC
.ceR 2002 IEEE-IAS pp.585-588 Ann.Meeting, )2002(
]21[ T.Takada dna T.Sakai",M easurement of Electric Field at a Dielectric/Electrode Interface Using Acoustic Transducwe
",euqinhceT IEEE Trans. EI-1I8n,s ul., )3891(826-916.pp
]31[ T.Oda dna K.Yamashita; "Charge Behavior Observation on/in Plasma Processed Thin Films by LIPP During Thermal
gnitaeH for TSDC IEEE/IAs Conf.Rec.2004 Analysis," ,gniteeM.nnA (2004) ot eb published
6
Paper Presented at the 5th International Conference on Applied Electrostatics (ICAES'2004), Shanghai, 2-5 November 2004
Elsevier, ISBN 0-08-044584-5
Induction Charging of Non-spherical Granular Materials: Size Analysis
Wu Y., Castle G.S.P. and Inculet I.I
.tpeD of lacirtcelE dna Computer ytisrevinU,.gnE of Western adanaC,oiratnO,nodnoL,oiratnO A6N 9B5
The charge and forces on a particle strongly depend on the particle size and shape. In
research studying induction charging of granular materials,, both the surface mean
diameter (D~) and the volume mean diameter (Dv) are needed to predict the theoretical
induction charge and determine the average charge per particle based on measured
values of average charge-to-mass ratios (Q/M). This paper describes a suitable way to
measure the particle size of irregularly shaped induction charged particles that
normally have a sampled mass of approximately 01 mg. The results of charge per
particle were found to be in good agreement with the theoretical predictions.
INTRODUCTION
An accurate measurement of particle size and shape is vital for determining the average induction charge
on each particle from the overall charge-to-mass ratio (Q/M) as measured in induction charging
experiments. Although there are different techniques to measure particle size, each technique has its own
limitations such as the required amount of the particle sample, the size range of the particles, the particle
density, etc. There is no single sizing technique that is superior in all applications. 1 To achieve a
reasonable result for the size of a group of particles, usually it is necessary to use several different
methods to get meaningful measurements. Thus the relationship between the results from different
methods needs to be considered. 23 Obviously particle shape takes a significant role in measuring
particle size. 45 Quantitative analysis of the effect of shape on particle size has been less investigated.
In this research efforts have been made to analyze particle size and shape and find a suitable way to
measure the effective particle size in terms of surface mean diameter (D~) and volume mean diameter (Dv)
of the collected induction charged samples which normally had a sampling mass of approximately 01 mg.
PARTICLE SIZE AND SHAPE
Particle Size
Particles can have many shapes such as a sphere, ellipsoid, wedge, irregular, etc. For a spherical particle it
is straightforward and unambiguous to use diameter to describe its size. It is also possible and useful to
define the size of a non-spherical particle in terms of an equivalent diameter as defined in terms of either
a circle or a sphere.
In practice different definitions of diameter are used for non-spherical particles depending upon the
property for which the particle size is required. For example, the properties of a particle considered in the
size definition include: surface area, volume, mass, sieve size, sedimentation rate, ete 145. In the
research reported here the surface diameter is used as the measure of particle size in induction charge
analysis because the charge is dependent on the surface area of the particles. The volume diameter is used
to calculate the mass of the particle to obtain the charge per particle from charge-to-mass measurements.
When a particle is observed under a microscope, a number of diameters may be defined to
characterize the particle based on its 2-Dimension projection 4. The diameter of a circle which has the
same property as the projected outline of the particle may be used such as the projected area, perimeter,
maximum diameter, minimum diameter, etc.
7
Mean Size
Almost all research deals with groups of particles instead of a single particle. Assuming that dsl, ds2,...dsn
are the surface diameters and ,~vd ,2vd ...dvn the volume diameters for n particles, two definitions of means,
surface mean diameter and volume mean diameter, are listed as follows 5.
/
~-7"
D. - av3~/n (2)
Particle Shape
The shape is an important property of the particle and is a critical factor in the correlation of size analysis.
There are many descriptive terms that are applied to particle shape such as angular, flaky, irregular and
spherical. It is necessary to incorporate a quantitatively defined shape factor into equations to analyze
particle properties. Generally it is assumed that in a group of particles considered in particle size analysis
each has approximately the same shape, which means that particle shape does not change significantly
with particle size.
The terms "shape factors" and "shape coefficients" are widely used in particle size analysis 4.
Shape Factors
Particle shape can be represented by a variety of quantitative shape descriptors from image analysis.
Particle shape factors primarily describe particle elongation, flakiness, roundness or angularity.
Heywood 5 developed Heywood ratios based on three mutually perpendicular dimensions of a
particle. Once the breadth (B), the length (L) and the thickness (T) are measured, the elongation ratio (RE)
and flakiness ratio (RF) can be obtained as follows.
R~ -L/B (3)
R F -B/T (4)
From the concept of elongation ratio a readily usable particle shape factor is the aspect ratio. Based
on the measured maximum diameter and minimum diameter the aspect ratio (RA) is defined as follows.
AR = xamD nimD/ (5)
In a similar manner one can define another useful ratio, the ratio of the mean surface diameter and
mean volume diameter, as .av~R
R,v d -D, /D v (6)
To estimate the appropriate value for R~va, it is necessary to observe and measure the shape of the
particle and find a similar geometric shape with the same aspect ratio and flakiness ratio.
Shape Coefficients
The other general method to indicate the particle shape is using shape coefficients. Shape
coefficients are defined as the relationship between the measured size and the particle surface or volume
diameter, for example, the volume shape coefficient, ~, shows the relation between the volume mean
diameter (Dv) and the mean projected area diameter (Da) 4.
gv - ~D3 /6D3
(7)
21
PARTICLE SIZE MEASUREMENT METHODS
Laser Diffraction
....
Laser diffraction has become the preferred standard in many industries for characterization and quality
control in particle size measurement 1 . Laser diffraction relies on the fact that the diffraction angle is
inversely proportional to particle size 4. A Malvem Mastersizer 2000 was used in this research. Samples
8
of 1-2 gram are necessary for accurate measurements. The results of laser diffraction give the size
distribution in terms of surface area diameter.
Microscopy
Microscopy is a method that allows the individual particles to be observed and measured. A digital
camera with a fixed magnification lens is used to take a picture of a sparse layer of representative
particles distributed on a microscope slide. An image analysis program is used to obtain measurements by
analyzing the number and shade of individual pixels. Only a small quantity of representative particles are
needed in the analysis. In this research an Olympus SZ-CTV microscope with a maximum magnification
of 40 and an imaging software program, Image-Pro Plus, were used to measure the particle size. A Nikon
digital camera DXM 1200 with a maximum magnification of 1,000 and a software program Automatic
Camera Tamer-1 (ACT-l) were used to observe the particle shape. The aspect ratio, flakiness ratio and
projected area diameter can be obtained from microscopic results.
Size and shape Analysis in this Research
In this research sieving was used to classify particles into fractions with a relatively narrow size range.
All the particles used in the induction charging experiments were sieved and were labeled with their mean
sieve diameters. These sieved particles were measured using laser diffraction and microscopy while the
samples collected from the charging experiments were only measured using microscopy due to the small
quantity collected. To illustrate the process of the measurements and calculations, an example of the
determination of the charge per particle and saturation charge for A1203 particles with a mean sieve
diameter )smD( of 390 l.tm is given as follows.
Step .1 Determination of dvsR from Sieved Particles
As described before, the aspect ratio and flakiness ratio for the particles can be measured using
microscopy. Applying these ratios to corresponding similar shaped objects (wedge for A1203 or ellipsoid
for aluminum particles), the ratio of the surface diameter and volume diameter, R~d, can be determined.
For A1203 particles (Dms = 390 l.tm) it was found that AR = 1.6 and RF = 1.5, hence R,vd = 1.29.
Note the projected area diameter (Da) can be also measured using microscopy. Here ~D = 559 .mt.l
Step 2. Determination of Volume Shape Coefficient
Laser diffraction results for sieved particles gave the surface diameter distribution. Based on these
results and R~d, the volume diameter distribution can be determined. Then the volume mean diameter (Dv)
and volume shape coefficient )vXt( can be determined.
,,D = ~ n,D 3 / N - 409 (l.tm)
~rc =~D 3/6D~ 3 = 0.2
Step 3. Determination of Size for Sampled Particles
The measurement results for the samples from the induction charging experiments were measured
using microscopy to give the mean projected area diameter, .aD Combining aD and the volume shape
coefficient we can obtain the volume mean diameter. The corresponding surface mean diameter can be
determined by multiplying ~D and R,vd for the samples.
In the example of the sample, aD = 468 mxI so:
~D - ~D tc6~3 v / lr = 143 (l.tm)
O, = d,,,RvD = 447 (l.tm)
Step 4. Application of vD and sD Size in the Charge Analysis
The above collected samples had an average charge-to-mass ratio of 39.0 (nC/g) in the induction
charging experiments. So the average charge per particle is:
ap = (Q / M) . mp = (a / M) . ~D~p / 6 = 3.2 (pC)
This may be compared to the saturation charge 8:
Q, = 1.18~0D~E ~ = 3.9 (pC)
A summary of the calculation results is shown in Table 1 below along with a comparison if one
simply assumes the mean sieve diameter as is normally used.
Table 1 Calculation results of charge per particle
sD vD M/Q pQ $Q
)mt~( dvsR )mt~( )g/Cn( )Cp( )Cp( sQ/pQ
447 92.1 143 0.93 2.3 9.3 8.0
093 1 093 0.93 4.4 8.2 6.1
It is reasonable that the charge per particle is a little less than saturation charge in Table 1 when the
above method is applied. If particle shapes were not considered, that is, mean sieve diameter is used to
calculate the charge per particle and saturation charge, it can be seen that the calculated charge is 60%
higher than the saturation charge, a result obviously in error. Similar errors occur when ~D or ~D is simply
used. For different experimental conditions these potential errors could often exceed 100%.
Analysis of results for the glass beads showed that the surface diameter and volume diameter were
identical, confirming that the beads were close to spherical and the simple measurement method was
adequate.
CONCLUSIONS
It is known that particle shape takes a significant role in size analysis. The ratio of surface diameter and
volume diameter can be obtained from shape analysis of similar geometries. A volume shape coefficient
can be determined by combining the measurement results from laser diffraction and microscopy. The
ratio of surface diameter and volume diameter can be used to determine the volume diameter from a
known surface diameter or visa versa. The volume shape coefficient obtained from sieved particles can be
used to determine the volume mean diameter for small samples measured with the microscope. Applying
this method in the study of induction charging for irregular and spherical particles the results of charge
per particle were found to be in good agreement with the theoretical predictions. Failure to properly
account for the effect of shape in determining the particle size can lead to significant errors in interpreting
results in induction charging experiments
ACKNOWLEDGEMENT
The authors would like to thank Mr. J.G. Lusk, Mr. B. Verhagen, Mr. D. Yin, Mr. P. Belej and Mr. R.
Harbottle, all of the Faculty of Engineering, UWO, for their help and advice. The authors would also like
to acknowledge NSERC for the financial support for Mr. Wu and the research and Saint-Gobain
Abrasives for the loan of equipment and provision of particle samples.
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