AIAA 92-01 17 A Method for Non-Contact Drop Charge Measurement K.C. Lin and T.G. Wang Center for Microgravity Research and A p p I icat io ns Vanderbilt University Nashville, TN

30th Aerospace Sciences Meeting & Exhibit

January 6-9/1992 / Reno, NV L For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 370 L'Enfant Promenade, S.W., Washington, D.C. 20024

RlffP1-92-OQ47 A METHOD FOR NON-CONTACT DROP CHARGE MEASUREMENT

K.C. Lin’ and T.G. Wang.’

Center for Microgravity Research and Applications Department of Materials Science and Engineering

Vanderbilt University, Nashville, TN 37235

Abstract A new approach for detecting point type of

charge has been developed. This system is based on the principle of reciprocal motion of a grounded conductor near a point charge. The current induced through such a process can then be used to determine the static field strength of the point charge, hence the quantity of the charge. Experiments were done to understand the characteristics of this new device. Test case indicates that the results are in good agreement with the theoretical prediction. This device shows extremely good linearity with respect to the strength of the input static field. The resolution of the system is better than 10 V/m, which is about two orders of magnitude in sensitivity higher than other types of field measuring apparatus. The high sensitivity of this system makes it possible to conduct charged drop experiments under microgravity conditions.

lntroduct ion

The dynamic behavior of a charged liquid drop has been a subject of investigation by scientists in chemical engineering, fluid dynamics, meteorology and materials science. However, under one G condition, the effect of gravity sometimes overshadows the surface charge effects. To eliminate the influence of gravity, the space environment provides an ideal place for the free drop study. The Drop Physics Module (DPM) under construction by Jet Propulsion Laboratory is to be used for studying drop dynamics on board the space shuttle. The drop experiments can be done by positioning and manipulating a free charged drop in the center of the DPM chamber through acoustic force.

There is one major problem facing the charged drop experiment, i.e., the determination of charge quantity on a liquid sample. Although charge detection and measurement is one of the oldest experiments, there has been little improvement in the mettiods used for static

measurement. The most frequently used instruments for non-contact charge detection are so-called field mill machines or generating voltmeters. Unfortunately, the resolution of this type of apparatus is on the order of 104 V/m and the measurement has to be done within a very short distance, typically less then one inch, while the drop charge experiment may require resolution as low as 20 V/m at a measuring distance of 6 inches. The primary objectives of this research are to address these technical challenges.

DPM Charaed D r w ExOeriment Analvsls

The critical part of charged drop

L J experiments is to determine the charge quantity precisely. To avoid the contamination and source loading problems, a non-contact charge measuring technique is preferred. From basic physics, there is only one way to determine the potential of a charged object by non-contact means and that is to measure the strength of the electrostatic field generated by the charged object. With precise calibration based on the geometry of the system and measuring distance, the field strength can be used to obtain the potential of the charged object.

In order to tackle the measuring problem more efficiently, various simplifications are made. The following analysis for charged drop experiment requirements does not consider the electrostatic field distortion problem in the DPM chamber, and the possible electronic interference is ignored.

The geometry of the charged drop experiment makes it possible to simplify the problem significantly. A free drop under no force will assume a spherical shape due to the surface tension. If some charge is introduced to the drop, the charge will distribute uniformly around the surface. The charged liquid sphere can then be easily transformed into an equivalent point

Aesearch Assistant Prolessor “Centennial Professor and Director, Member AlAA Copyright @J 1992 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1

charge. By measuring the strength of the E field, size of the drop, and the measuring distance, the potential of the drop can be obtained.

LJ The basic design criteria for charge measurement depends on the range of charge potential or strength of electric field. In the case of a charged drop experiment, the Rayleigh charge limit sets an upper bound for the amount of charge a drop may have. An ideal measuring apparatus for studying the dynamic responses of a charged drop is to detect the charge within such ranges while giving reasonable accuracy.

Various constraints exist for such a device. In general, the measurement must be performed at a distance while the disturbance Is kept to a minimum. For the DPM chamber (12.7 cm x 12.7 cm x 15.25 cm), the measuring distance from the drop to the sensor will be around 12 cm if the sensing probe is located in one of the corners of the chamber and the drop is at the center of the chamber. The weakness of the electric field at such a distance poses a great deal of challenge for any field measuring instrument. For example, a 1 cm water drop charged to 50% of the Rayleigh limit (6.3 KV) will generate a field strength of 2.2 KV/m at a distance of 12 cm. If 1 % accuracy is desired, the apparatus will need a resolution as low as 20 V/m. This is a formidable challenge. The above analysis shows that the isolation of the DPM chamber from outside interference is as important as the charge measuring apparatus. Without proper shielding, many background noises may be much higher than the field generated by the charge sample. To complicate matters further, the field distribution in the testing chamber will be severely distorted due to the chamber’s geometry.

”

Current Non-Contact C h a r m DetectioQ Technigug

The most commonly used instruments for non-contact charge measurement are field mill machines (generating voltmeters). The generating voltmeter was originally designed for field-strength measurements. Considered as a capacitive machine, it is an externally excited electrostatic generator. As in a permanent DC generator, the exciting field of a generating voltmeter delivers no energy (reciprocity theorem), and the energy consumed by the indicating instrument is supplied by the driving motor. The principle of a generating voltmeter is described as follows.

When a charge exists on an object, it sets up a related electrostatic field in the surrounding space. In the absence of other interference or at the near region of the object where the

‘4

interference can be neglected, the strength of this field may be used to determine the charge quantity of the object.

By Gauss’s law, a grounded conductor will acquire surface charge in an electric field. amount of surface charge depends on the geometry, field strength and surface area.

The

E . d S = Q 1 where the integration is taken over the conducting surface.

Any changes in these parameters will cause redistribution of the surface charge on the conductor. The charge flow can then be measured. Based on this principle, various types of field mill instruments1.2.3 have been constructed. The electric field is sensed through the sensing plate by applying a mechanical chopping device, i.e.. a segmented rotor, which is connected to the ground, to rotate in the front of the sensor. As a result, an alternating current is induced between the sensing plate and the ground. The measurement of this current enables one to evaluate the field strength. New devices such as that developed by Horensteind are also based on the same principle.

Unfortunately, this type of system has very limited resolution. For most of the field mill instruments, the resolution is around 104 V/m with a measuring distance of less than one inch. There are two factors affecting the resolution of such devices. One is the noise generated from the chopping process. The chopping frequency usually is a multiple of the driving motor speed. It is inherently difficult to filter out electronic noise when the sensing frequency is within a decade of driving frequency. The second reason is due to the system design. In the traditional design, the sensor is placed behind the segmented rotor and is surrounded by a guard plate. The purpose of this guard plate is to reduce the field mill sensitivity with respect to the distance. However, it was found out that under an extremely low electric field, the incident field is distorted to such an extent that the sensing plate is no longer able to detect any field change through the chopping process. As the sensor is behind the rotor, the field is also greatly distorted by the chopping rotor. There is also one drawback for such a device to operate in the DPM chamber. The high rotational rotor speed of the generating voltmeter will introduce air circulation, which is highly undesirable.

2

New ADDrOaCh for Charae Measurement

To solve the associated problems with the generating voltmeter, new design criteria were developed. The first consideration in designing the new system arises from the constraint of not allowing any disturbances inside the DPM chamber when performing a charge measurement. The sensing frequency must therefore be much lower than that of traditional generating voltmeters. To increase the signal-to-noise ratio, the frequency must also be selected so that the interference from other sources may be easily filtered, i.e., the chosen frequency must be at least one decade away from possible sources of interference. Secondly, the E field impressing on the sensor is to be maximized. That is, the chopping method has to be abandoned, i.e.. no guard plate and chopping rotor should be in the front of the sensor, and another method has to be developed to produce an alternating current flow.

There are a few ways to obtain an alternating current flow from an invariant electric field. The one used in most field mill machines is to change the exposed sensor area to the field. To achieve the area change without chopping it was decided to have the sensor rotate with respect to the center of the surface. The total charge on the sensor may be calculated from Equation 1, However, for test purposes it was done through a simple experiment.

1.5 cm bv 1.5 cm copper plate. Several clock The feasibility study was conducted with a

A new method to generate the current flow was attempted. Instead of changing the exposed area of the sensor, the sensor was set to motion. The electric field impressed on the sensor now depends on the position of the sensor. By providing a reciprocal motion, an alternating current will be generated.

A simple system was built for test. The motion of the sensor is rotational and is made of a metal wire. The wire is 4" long with a 1/16 diameter. The rotating radius is 0.75 and the speed is 20 rpm. The electric field is produced by connecting a high voltage power source to a 318" steel ball. The experiments were conducted in a metal screen cage to shield the effect of external field. A typical output from the chart recorder is shown in Figure 1, The test results are given in Figure 2 where the output indicates peak-to-peak value.

i . .~ motors with different'speeds ( 5 rpm to 60 rprn ) were used to provide the rotation. A 3/8" steel ball

produce an electric field. For determining the current amplitude, a current to voltage amplifier was built, and the outputs were measured through a digital multimeter and a chart recorder. Those tests were done with distance ranges from less than an inch to 5 inches, and voltage ranges from a few hundred volts to 7.5 KV, Le., the field

- 0 -~ .. . ~ j ~... . ~

~~ ~0~~ ~

was connected to a high voltage power source to i

Figure 1 : Typical Output From Sensor.

P0,.l ClldreD _. Illdl blll I0"iO, I/JV.<. coijm, *,,a N m I f oxm" Rm_.r(U,_ L 2a 10 "irn

strength is from a few thousand to more than a hundred thousand volts per meter. The results show that the current amplitude may range from 10-13 to 10-10 amps. To achieve a resolution of 100 Vlm or better through the whole range of interest, the amplifier has to be able to deal with current in the order of lO-15to 10-11 amps. With such a small current, it is very difficult to construct a stable system without sacrificing resolution. In particular, the dynamic range spans more than 3 orders of magnitude. It is obvious that the current amplitude

. Mln, D,, z 0 M.". ",# 3 0

* M " , " . % d W

has to be in the range of 10-1 1 to 108 amps for Y I 7 J 4 I 6 , d

such a system to be useful. I " W (Y"/

v Figure 2: Feasibility Test For Charge Detection,

3

For the purpose of preliminary study, the distance used in these experiments is defined as the closest distance between the sensor and the center of the steel ball. The results indicate that the output of the sensor is quite proportional to the input voltage.

The data were analyzed to determine the accuracy of the results. Surprisingly, the resolution of the system increases as the measuring distance increases. The following analysis gives a general ideal about the accuracy of this crude system. The noise from the amplifier is about 2 0.1 mV at the measuring frequency. The electric field strength generated from 1.25 KV potential input to the 3/8" diameter steel ball at a distance of 0 . 5 is about 37,000 V/m. The output voltage is around 32.2 mV peak to peak . The resolution at this condition is ?t20 V/m. At a distance of 4", the electric field is about 580 V/m, the output is around 2.5 mV , and the accuracy is about? 25 V/m.

measure extremely low electric fields with a very simple device. By using this non-conventional approach, the signal-to-noise ratio may be increased without sacrificing sensitivity. It is also found that the major problem is the disturbance from the external electric field, which is anticipated. The ability of this system to detect a very low field makes it vely sensitive to the outside disturbance. The shielding provided by the metal screen cage is no longer sufficient. For example, the charge carried by a person will indeed affect the measuring results. Fortunately, the effect is mainly caused by the transient response of the metal cage with respect to the outside field change. As long as the outside field is not variant, the measurement is repeatable.

obvious that further improvements are needed. The sensor used in the above experiments is large, 4" long with 1/16 diameter. A preferred size would be in the range of an inch or less. With the decrease of sensor size, the induced current decreases accordingly. To raise the output, the sensing frequency is increased to 60 rpm, i.e., 1 Hz, and, according to tests, the increase of electronic noise due to this increase of sensing frequency is negligible. At the current stage of study, optimal frequency has not been sought. It is expected that for earth-based experiments, 6 Hz may be the upper limit, which is only a decade away from the 60 Hz AC interference.

to boost the overall amplification while maintaining a higher signal-to-noise ratio. An electrometer OP Amp is used as the current to voltage stage and a low noise OP Amp is used for

The simple study shows that it is feasible to

"

From the results of preliminary study, it is

The electronic amplifier is also redesigned

t

the voltage amplification stage. A few low pass filters with corner frequencies of 1 to 2 Hz are implemented to eliminate high frequency components.

meoretical and E xoerimental Study

A. Theoretical Investlgatlon

To understand the characteristics of such a system, a simple image charge example was studied. A grounded conducting sphere was used as the sensor and placed near a point charge. The total charge induced on the sphere for this geometry is given as followss:

D Q = -aQ (2)

where Q is the induced charge on the sphere, Q is the point charge, a is the radius of the sphere and D is the distance between the point charge and the center of the sphere.

to the charge source, Equation 2 becomes As the sphere is set to motion with respect

Q=.dQ (D + 5 c o w )

(3)

where 6 and ware the oscillating amplitude and frequency.

By taking the derivative of Equation 3 with respect to time, the current is given as

Q (4) dQ' k w a s i n w t

dt (D + 5 cosot) I = - = -

2

With a, 5 and w fixed, the output voltage from a current to voltage amplifier will be proportional to the current I, i.e.,

v.. sinwt Q (D + tcoswtp

The peak-to-peak value of the output voltage can then be determined by Equation 5.

E. Experimental Results

A new charge detecting system (Figure 3) was built in which the motion of the sensor, a 1/2" steel ball, was rotational with a rotating radius of 11/32" at a speed of 60 rpm.

4

Figure 3: Schematic Diagram of Experimental Set Up, E Field (Vim)

Figure 6: Sphere Sensor Output vs. E Field. The electric field is produced by connecting

a high precision, high voltage power source to a 3/8" steel ball. The experiments were then conducted in a 2' x 2' x 3' solid aluminum cage to

300 I I I I . I Distance between poinl charge and .... .:-- ..~...

- minimize the effed of the external field. Tests $ 250 - were done with distances ranging from 2 to 7 inches (from the center of the charged steel ball to

L a 2011 - IY IAI I I IY CBllrei

the cenier of the sphere sensor). The applying voltage was from 100 V to 3 KV. Figures 4, 5. 6

reDresent peak-to-peak value. and 7 show the resulting data. Note that the data

VI IO0

20w

i7Y) DIsIan~e between

15w point charge and ,o,a,ing CB"l*,

12-

?OW

750

5w

250

0

. 2 0 - + 3". . 4 0 -

0 . 0 0.5 1.0 1 . 5 2.0 2.5 3.0 3.5 4 . 0

Input (KVI

Figure 4: Sphere Sensor Output vs. Charge Potential,

300

Distance beween point charge and

250 - - : 200 rotating Cenlsl - .3 . 50- 0 D

0

+ 80- . ,r . 150

VI 100

s * 50 = VI

0 0 . 0 0 .5 1.0 1.5 z.0 2.5 3.0 3.5 4.0

Input (KV)

Figure 5: Sphere Sensor Output vs. Charge Potential,

E Field ( V i m )

Figure 7: Sphere Sensor Output vs. E. Field.

The plots show that once the distance is fixed, the output is proportional to the input voltage. The linearity is within 1.5% for all the measurements. There are a few reasons for this error. First, the accuracy of the chart recorder used in these tests is on the order of 1 to 2%. Second, the amplifier generates about m.15 mV peak-to-peak noise when there is no outside disturbance. The third reason is the residual charge inside the metal cage. In general, the noise from the amplifier can be averaged out and has no significant effect on the data. However, the residual charge due to the insulating materials (i.e., high voltage wire and ceramic rods which were covered with aluminum foil) usually shifts the datum point. This shift can be controlled within about T0.4 mV when there is no input. From actual experimental data, the effect of this shift is seldom larger than f0.2 mV. If th i s shift of datum point has been taken into account, the overall linearity will be within 1% for all the data. The maximum error bar for this system is then estimated at about f0.4 mV.

L,

5

The data were compared with the value calculated from Equation 4. The results are shown in Figure 8 along with the curve I/@. Note that the results were normalized with respect to the value at 7 inches. It is obvious that at a far enough distance, the data are in good agreement with the prediction from Equation 4. At a CloSer range, the data show appreciable deviation. At 2 inches, the measurement is about 15% below the theory. However, at such a distance, the assumption of point charge is no longer true in the experiment and the finite size of the charge source must be taken into account. This deviation also explains the reason of the resolution change with respect to the measuring distance given in Figure 2. Equation 4 and Figure 8 also suggest that when D >> 5, 1/D2 may be used to approximate the ideal case.

a, 7"

\j Dlrlance (inches)

Figure 8: Sphere Sensor Experimental Data, Theoretical Curve and 1/12 Curve.

To further study the effect of geometry on the output of this system, a small metal wire sensor was used instead of the sphere sensor. The metal wire is 2 cm long, 1/32 inches in diameter, and the rotating radius is 1.5 cm. Figures 9, IO, 11 and 12 show the results of the measurement. Due to the geometry of this case , there is no known analytical solution. The data obtained from the metal wire case were used to compare directly with the 1W law, Le., E = I@. The results are shown in Figure 13. Note that the results were normalized with respect to the value at 6.5 inches. A comparison between Figures 8 and 13 indicates that similar characteristics exist for both sensors, Le.. the output has excellent linearity with respect to the input electric field and the relationship between output and distance shows identical patterns.

3.49 V/m per mV of sensor output at a distance of 6.5 inches and the resolution is about fl.5 V/m using the maximum error bar k0.4 mV. From Figures 9, IO, 1 1 , 12 and 13, any data between 2 to 6.5 inches can be obtained by interpretation.

The slope for the metal wire sensor is about

1 Om

5 QW

2 700 rotating centel

E Distance M t W B e n - BW - p i n 1 Charge and

I 3 . 2.5' 0 6W

$ 5W f 3.0" 5 1 3.5'

? 3W

:: 400 0 4.w

2 M

100

0 0 0 . 5 1.0 1 5 2.0 2.5 3 0 3.5

Input (KV)

Figure 9: Wire Sensor Output vs. Charge Potential.

s E -

350 I

Dtrlance between pin1 charge and rotating center . 4 , s

+ 5.0' * 5.5' 0 6.5'

. . . . . . 0:o 0 . 5 I O 1.5 2.0 2.5 3.0 3 5

Inpul ( K V )

Figure 10: Wire Sensor Output vs. Charge Potential.

I > E I

I 3 P = 0 I

z c VI

? s

1 OM

DiSlance between point c h a w and rotating center . 2,s

+ 3.0' . 3.5' n 4.0"

8W

6W

dW

2w

l o o 0 2000 3 0 0 0 4 0 0 0

E Field (Vim)

Figure 11: Wire Sensor Output vs. Electric Field.

6

Figure 12: Wire Sensor Output vs. Electric Field.

Distance (inches)

Figure 13: Wire Sensor Data and 1/r2 Curve.

Summarv of Study

A novel method and apparatus to perform non-contact point charge detection has been developed. By using this novel approach, the signal-to-noise ratio is significantly increased without sacrificing sensitivity. The experiment in the sphere case indicates good agreement with the theoretical prediction based on a grounded conducting sphere placed near a point charge. For other types of sensors, a l/r2 curve may be used for calibration.

The results for both sphere and wire sensors indicate that, at a given distance, nearly perfect proportionality through the whole range of interests can be obtained. The excellent linearity of this device makes calibration of the instrument possible by simply measuring the sensor's output at different distances with a given point charge. The output can then be used to construct a plot like Figures 8 or 13. Once calibrated, the device can be used to determine an unknown point charge by the sensor's output and measuring distance. Other devices using reciprocal motion with different shaped sensors were also developed which can be used to detect electric

fields along any direction.

The resolution of the current system is about two to three orders better than all other current non-contact charge measuring instruments. As demonstrated from the experimental results, the sensitivity of this type of device is able to satisfy the requirements in the DPM system for drop charge measurement.

u

Future Works

There are several issues which need to be addressed for DPM charge drop experiments. Some of them are as follows: 1) effects of DPM chamber geometry on the charge measurement; 2) apparatus calibration problems; 3) DPM electronic shielding problems; 4) residual charge contamination problems. All these issues will be studied in the future.

Acknowledae men1

The research described in this paper was carried out at Vanderbilt University's Center for Microgravity Research and Applications under a subcontract with the Jet Propulsion Laboratory.

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REFERENCES

. . Chalmers, J. A,, 2nd ed., Pergam-67). &u' Mapleson, W. W., and Whitiock, "Apparatus for the accurate and continuous Measurement of the Earth's Electric Field," J. Atmos. Terr. Phys. 7 , 61 (1955).

Schwab, A., Hiah Voltaoe Measurement -,,MITCambridge, MA, 141.146 (1 972).

Horenstein, M. N., "Peak Sampled Vibrating- Reed for The Measurement of Electric Field in The Presence of Space Charge." Rev. Sci. Instrum. 54 (5), 591-593 (1983).

D.R. Corson and P. Lorrain. Introduction to &Wmmg&ic Fields a d W a v a , W.H. Freeman and Company, San Francisco, CA (1962).

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