Pergamon J. Aerosol Sci. Vol. 28, Suppl. 1, pp. $653-$654, 1997 ©1997 Published by Elsevier Science Ltd. All rights reserved

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CHARGE DISTRIBUTION ESTIMATION FOR NON-SPHERICAL PARTICLES

YU-CHEN CHANG', JUI'CHEN LIN =, J.W. GENTRY"

' Yuan-Ze Institute of Technology, Chung-Li, Tao-Yuan, ROC = University of Maryland, College Park, Maryland, USA 20742

An important question is the determination of the electrostatic charging rates of aerosols from experimental measurements. An instrument was developed for determining the charging rate of non-spherical particles by Cheng. A key component in her analysis was a precipitator mounted directly after the charging section. Ideally the charge of aerosols should be determined by measuring the mobility of a collimated beam of charged particles. The configuration of the Cheng instrument precludes this analysis. In this paper we consider the development of protocols to determine the charge distribution of monodisperse particles.

The first set of experiments which she analyzed were for glass aerosols. The particle concentration before and after the precipitator was measured by an LAS-X.

AVERAGE 0.08-0.11 0.25-0.30 0.5-0.65

1 ,

i * * 40LPM 0.75 *

• • 4

Figure I Penetration As Function of Prggigitator Volta2e In Fig. 1 the penetration measured by an LAS-X instrument is plotted as a function of precipitator voltage for three different size classes. The solid line indicates the reading based on the total number of counts. The ion current in the precipitator was 2. E-6 Amperes and the flow rate in the precipitator section was 40 LPM. Assuming that trajectories are described by characteristics, the fractional penetration is linear with the number of charges and voltage.

The simplest algorithm is to assume that the particles of a given size have a mean charge. In this case the charge is given by the relation

"J = E J k fk o~ PiE=O C n g h m

where Dp is the particle diameter, Cnghm is the Cunningham correction, Pt is the

penetration, and J is the average number of charges. The number of charges were 6,35, and 60 for the results shown in the figure. In this paper we consider a number of options to have better estimates of the charge number.

$653

$654 Abstracts of the 1997 European Aerosol Conference

In the first set of simulations the particles were spherical and the penetration was obtained by direct measurements of the concentration leaving the precipitator.

~ 0 !° >

i

. . . . . . . . . . . . , . . 1 . . ,

t s l l

Ip •

; I I • I L : o.os c m I

PREcIPrrATOII VOLTAGE

IkV

3kV

SkV @

0 . . . . i , , , , i , , , . l . . . . i . . . .

0 $ 10 IS 20 DEPOSITION DISTANCE (CM)

Fiaure 2 Cumulative Probability As Functions of Downstream ]Distance and ]~recinitator yoltag¢ The data used in the inversion algorithm are similar to those shown in Figure 1. However the data were obtained by counting the fibers which deposited on the central electrode as a function of deposition distance. These data are for carbon fibers which are 500 ttm in length. They were obtained at an ion current of 2.5 x 10 -7 Amps. Measurements

were taken at six different precipitator voltages. The data were analyzed using a method similar to that for the spherical particles. Note that for these measurements all of the fibers are deposited before leaving the precipitator. This reduces the uncertainty in the inversion.

FREQUENCY 0.25

0.2

0.15

0.1

0.0S

Ion Current 2. e-7 I

l l l PLUG

N,2 7.0 3.0 2.0 2.0 0.9 0.14 14.4 5.1 3.2 2.3 1.0 0.4 0.05

CHARGES X 0.0001

Fi~a-e 3 Freauencv Distribution For Iron Fibers (2 Flow Models)

The raw probability data for deposition with the downstream distance can be inverted to give the histogram shown in Figure 3. Note that the intervals on the abscissa are not uniformly distributed. This plot indicates that the mean number of charges is near 25000 regardless of what the assumed velocity prof'de is. It is also clear that the model gives significant frequencies for large and small numbers of charges.

These data are for iron fibers which are 500 pm in length. They were obtained at an ion current of 2.5 x 10 -7 Amps. Four methods were used for processing the data. A mean charge approach similar to that used for the spherical glass particles was used. Next the distribution was assumed to be log normal and the parameters of the distribution estimated by regression. Thirdly the charge was estimated using the histogram approach for several different distributions entering the precipitator section. Agreement with theory is good.

Shu-Hui (Whitney) Cheng," Electrostatic Charging and Separation for Non-Spherical Particles" Ph. Dissertation, University of Maryland, (1995)