'"

. *

AIAA ELECTRIC PROPULSION, . . CONFERENCE ... .. .: , . ir

BROADMOOR HOTEL, COLORADO SPRINGS, COLO. MARCH 11-13, 1963

THRUST MEASUREMENTS OF COLLOIDAL PARTICLES AS AN INDICATION OF PARTICLE SIZE AND THRUSTOE OPERATION

w Daniel S o Goldin and Carl T o Norgren National Aeronautics And Space Administration Cleveland, Ohio

63050-63

First publication rights reserved by AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS, 500 Fifth Ave.. New York 36, .e, N. Y. ~ ''

i W 1 Abstracts may be published without permission if credit is given to the author and to AIAA.

THRUST MFsSIJREfGNTS OF COUOIDm PARTICLES AS AN INDICATION

OF PARTICLE SIZE AND THRUSTOR OPERATION

By Daniel S. Goldin and C a r l T. Norgren

Lewis Research Center National Aeronautics and Swce Administration

Thrust measurement and its cor re la t ion t o the opera t iom1 characteris-

t i c s of an experimental col loidal-par t ic le thrustor a r e discussed.

ments were made on a previously designed condensation col loidal-par t ic le

e lectroStat ic t h rus to r with mercurous chloride as the propellant. Thrust

measurements of t h e order of 1 t o 10 m i l l i @ a m s were made with a modified

e l e c t r i c microbalance cal ibrated t o a s e n s i t i v i t y of lo-* t o

anticipated from t h e c l a s s i ca l liquid-drop theory of nucleation, no th rus t

was observed u n t i l a viscous flow regime and subsequently a c r i t i c a l nuclea-

t i o n r a t e had been obtained i n the nozzle.

vaporizer temperature of 485' K.

l o ids , it was determined t h a t a mean p a r t i c l e s i ze of 1 . 2 ~ 1 0 ~ mu would be

required t o account fo r measured t a rge t def lect ions at a vaporizer temperature

of 490' K.

operating conditions, a mean p a r t i c l e s i z e of 1.71X106 m u was indicated.

Measure-

gram. As

This condition corresponds t o a

With t h e assmpt ion of s ingly charged co1-

From a n electron photomicrograph of t he co l lo ida l beam at similar

IN'IRODUCTION

For optimum performance of e l e c t r i c spacecraft, t he e s sen t i a l require-

ments of the t h r u s t o r are: operation through a specif ic impulse range of

2000 t o 40,000 seconds and high thrustor e f f ic iency throughout t h i s range

of specif ic impulse (refs. 1 and 2 ) . The col loidal-par t ic le t h rus to r

-" .

offers many possible advantages over other types.of e l e c t r o s t a t i c thrustors

i n meeting the aforementioned mission requirements i f operated a t high va l t -

ages ( r e f s . 1 and 3).

high power efficiency i n the lower specif ic impulse range ( Z o o 0 t o 6000 set),

integrat ion with proposed high-voltage space-power supplies over t he e n t i r e

specif ic impulse range ( r e f . 4), variable p a r t i c l e charge-to-mass r a t i o , and

a higher r e l i a b i l i t y due t o t he lower mechanical tolerances required.

though at the present time a col loidal-par t ic le t h rus to r appears very

promising from a theo re t i ca l standpoint, many problems have yet t o be solved

i n order t o develop a r e l i a b l e high-performance device.

The major theoret ical advantages offered are: very

Al-

In order t o approach a high theoret ical value of t h rus to r performance,

it is necessary tha t the propellant u t i l i z a t i o n efficiency

The propellant u t i l i z a t i o n efficiency as defined herein f o r t he colloidal-

p a r t i c l e thrustor is the product of t he pa r t i c l e formation efficiency q f ,

and the pa r t i c l e charging efficiency qc. The p a r t i c l e formation efficiency,

defined by the pa r t i c l e mass flow

indicates how effect ively vapor is being converted in to par t ic les .

p a r t i c l e charging ef f ic iency indicates how ef fec t ive ly the pa r t i c l e s a r e

being u t i l i zed i n the charging chamber of the th rus to r and is defined by

the charged pa r t i c l e mass flow $,c divided by the t o t a l pa r t i c l e mass

flow %. w i l l have different exhaust veloci t ies . This e f f ec t is accounted f o r i n

the power efficiency as derived i n reference 5.

qu be very high.

divided by the t o t a l mass flow ri+,

The

Of comse, if the pa r t i c l e s have a s i z e d i s t r ibu t ion , then they

These efficiency parameters a r e ref lected d i r e c t l y i n the actual t h r u s t D

t ha t is produced by the col loidal-par t ic le thrustor . Since the t h r u s t i s % great ly affected by the p a r t i c l e s i ze and its inherent dis t r ibut ion, it is - ij

.i- c c

i

very important that an understanding of the particle formation process be

obtained. As predicted by the classical liquid-drop theory of nucleation,

particle formation in a nozzle condensation process is dependent primarily

on reaching a critical nucleation rate in the flow.

of the supersaturation, temperature, and physical properties of the propel-

lant in the stream. Once this critical nucleation rate is reached, the

growth of particles by condensation onto these nuclei can be completed.

This rate is a function

TO evaluate thrustor performance requires a knowledge of particle forma-

tion and charging efficiencies, pazticle mass distribution, charge-to-mass

ratios, beam thrust, and current.

these quantities are not highly developed. Measurements of the particle

charge-to-mass ratio in the range of interest is difficult as is measurement

of thrust at present obtainable levels.

a quadrupole mass spectrometer to indicate qualitatively charge-to-mass

ratios of a stream of colloidal particles.

Experimental methods of obtaining most of

One investigator (ref. 6) has used

"ust sensors have been successfully wed in conjunction with relatively

lov-thrust systems such as the instrument described in reference 7 and that

used by Kerslake and Pawlik in an unpublished investigation at Lewis Research

Center. Houever, these instruments have a maximum sensitivity of 1x10-2 gram,

and therefore are not satisfactory for measuring ranges of thrust (on order of

milligrams) produced by present colloidal-particle thrustors.

method for gaining insight into the thrvstar characteristics is a simulta-

neous measurement of beam thrust and current. These measurements would

yield an indication of average particle size, utilization efficiency, and

correlation with particle formation theory. Measurements of beam current

Another

are obtained with little difficulty, but thrust measurement requires a

i

device with a sensitivity of at least lX10-4 gram.

that measurement of thrust is the primary subject of this paper.

It is for these reasons '

A

B

ce

c

a

e F

3; g

H

3

Kn

k

1

M

m

16

NO

SYMBOLS

cross-sectional area, cm2

vapor monomer molecule

concentration of monomer B in equilibrium with bulk (infinite)

condensed phase.

actual concentration of monomer

diameter, cm

electrostatic forces, newtons

conductance, cm3/sec

deflection force, newtons

number of molecules in embryo

perimeter, cm

current, 5 p

B molecules in system

Knudsen number, mean free path per dimension of flow passage (e.&,

width of nozzle throat)

Baltmann constant, 1.38~10-16 erg/'%

nozzle length, cm

molecular weight, m u

mass, grams

mass flow, kg/sec 8 6 c

Avogadro number, 6.025~10~~ particles/gram-mole I: N(r.) nuclei having radius r, number

n number of atoms

R

P

S

T

t

V

V -

a

r

1

K

P

0

T

pressure, m of Xg

total charge, coulombs per electronic charge x number of electronic

charges

nucleation rate, particles /(cm3)/(sec)

drop radius, cm

degree of supersaturation, (p/pe)T=constant, dimensionless

thrust, newtons

time, sec

velocity, m/sec

average velocity, cm/see

accommodation coefficient

Edtvos constant, dimensionless

efficiency

constant, equal to total number of molecules

density, grams/cm3

surface tension, dynes/cm

temperature, absolute OK

0 energy of formation, ergs

9 accelerator potential, Y

Subscripts :

a molecular

c charged

e vapor phase equilibrium

f formation

g cluster containing g-molecules

p particle

T total

t. nozzle

u utilization

Q gaseous phase

p liquid-drop phase

T temperature

m bulk phase

Superscript:

critical

THEORY

In this investigation, measurements were made of the thrust and current

from accelerated Charged particles produced by the colloidal generator of

reference 3.

vapor as it passes through a supersonic nozzle. Mercurous chloride was used

as the propellant to provide cosparison with previous experimental data when

applicable.

table I, and the vapor pressure as a function Of temperature is giva in

figure 1.

This generator produces parricles by condensation of pmpellant

The physical properties of mercurom chloride are given in

Particle formation is a highly complex process and is governed by a

critical nucleation rate, which, in twn, is dependent on the degree of

supersaturation attained in the nozzle. Theoretically, to predict the con- 6\

g F

ditions conducive to pazticle formation in the nozzle flow m&es it neces- - sary to consider the factors governing the propellant mass flow and nuclla-

tion rates.

c

c i

Flow Rate

The flow regimes obtainable in the colloidal senerator range from free

molecular to viscous a8 beat is applied to the vaporizer.

number (based on the smallest dimension of the nozzle throat) can be used

as an indication Of the Plow regime within the nozzle.

in this investigation, the leaet dimension at the nozzle throat was the

width of the rectangular nozzle (0.273 cm). When the Knudsen number is

less than 10-2, viscous flow is predominant; whereas, when the Knudsen

number is greater than 1, free-molecular flaw is present (ref. 8 ) .

criteria are used to establish the flow regime in the colloidal generator.

In figure 2(a), the Knudsen number is plotted for free-molecular and viscous

flow as a function of vaporizer temperature.

The Knudsen

For the nozzle used

These

The theoretical mass-flow rates for the free-molecular flow regime were

calculated by the following equation (ref. 8 ) :

m = F p t (1)

where 4 - 3 . 3

2

- v Ft =

and

A numerical method Of integration vas used to evaluate the integral

The mass-flow rate in the viscous f l o w regime is calculated from the

perfect gas laws and the continuity equation applied at the nozzle throat.

One-dimensional isentropic flow was assumed from the vaporizer to the nozzle

throat.

for comparison with the theoretical rates.

the conditions for free-molecular and viscous flow are established at vapor-

i ze r temperatures of 400° and 503' K, respectively.

free-molecular to viscous flow includes the intermediate and the slip-flow

regions.

Experimental flow rates from reference 3 are shown in figure 2(b)

These flow rates indicate that

The transition from

Nucleation Rate

The nucleation rate is dependent on the particle concentration, which,

in turn, is dependent on the supersaturation that is controlled by expansion

in the nozzle. The nucleation rate is considered as the controlling step in

particle formation. Condensation shock waves, which result from supersatur-

ation of the stream, have been described by Stever (ref. 9), and the result-

ing particle formation explained by the classical liquid-drop theory of

nucleation (ref. 10). More recently, Courtney (ref. 11) has published an

analysis of the kinetics of condensation and has shown that experimental

results for the condensation of Water vapor could be explained by the clas-

sical liquid-drop theory of homogeneous nucleation together with the

collision-frequency growth kinetics.

collision-frequency kinetic and macroscopic thermodynamic models to explain

the formation of a new solid or liquid "P-phase" amidst a supersaturated

metastable vapor "a-phase." The P-phase is in the form Of Bg embryos,

which are merely clusters containing a number g of molecules of the p

The theory applied to this case uses

G,

e

a-phase and are considered as very small l i qu id drops.

t he 8-phase embryos of rad ius

The nmber N ( r ) of

r i s given by t h e Gibbs formula (ref. 10):

where m(r) is t h e energy of formation of a drop of radius r given by

A0 = - ( 0 - 0 ) g + 4nr'o (3) a b

where g the number Of molecules i n a drop i s given by

4 nr3M 3 ",$_

g = - -

Subs t i t a t ing equations ( 3 ) and ( 4 ) i n to equation (2 ) y ie lds

( 4 )

If t h e i n i t i a l vapor phase happens t o be i n a supersaturated s t a t e , t he

vapor a-phase is i n a metastable condition because i t s thernodynamic poten-

t i a l 0, i s grea te r than t h e thenodynamic po ten t i a l OB of t h e liquid-drop

phase.

sketch ( a ) as a function of drop radius.

The drop fomat ion energy, as expressed by eguation.(3), is shown in

( a )

From t h e sketch it i s obvious t h a t A@ reaches a m a x i m u m at a ce r t a in

radius, denoted as t h e c r i t i c a l radius. m e number of nuclei of radius 1,

therefore , reaches a minimum value at the C r i t i c a l rad ius , Since N ( r ) i s

proportional t o

i l l u s t r a t e d in sketch ( b ) .

exp(-fM), as shown by equation ( 2 ) . This var ia t ion is

I* I-

( h )

Beyond t h e c r i t i c a l rad ius , t he "potential ba r r i e r " t h a t l i m i t s t h e forma-

t i on of t he new P-phase is passed, and t h e number of drops increases at a

tremendous rate (ref. 10). The drop s i z e at Ammax i s defined as t h e

c r i t i c a l nucleus, and any s ize smaller than t h i s w i l l not a l l o w drop forma-

t i o n t o t&e place at an appreciable rate.

The nucleation r a t e R can be expressed in the form of a steady-state

r a t e equation as derived by Courtney (ref. 11):

where

and

g* = (-T

( 7 )

If t h e supersaturation S i s defined by t h e miompson equation (ref. lo),

t he c r i t i c a l radius at any point is given by

d. t A

and equation ( 6 ) can be wr i t ten

Assuming the aocomodation coefficient equal t o 1 and subst i tut ing the

physical p roper t ies of mercurou6 chloride, y ie ld the folloving equation

To obtain t h e nucleation r a t e s of mercurous chloride, and therefore t o

get an insight i n to the pa r t i c l e formation process, it i s necessary t o know

the surface t ens ion of t he propellant. Since there Were no measured values

of swface t ens ion available, an approximation discussed i n the appendix wa6

used. The ca lcu la ted values of Surface tension were then used i n equa-

t i o n (12) t o determine nucleation r a t e s .

i n f igure 3 as functions of supersaturation and l o c a l temperature.

t he c l a s s i ca l liqurd-drop theory use6 a continuum approach i n its derivation,

it fails when t h e r e are approximately less than 10 molecules per drop

( r e f . 9).

reached, the nucleation rate is very slow, and t h a t at higher degrees of

supersaturation the nucleation r a t e becomes so great t h a t condensation must

take place almost instantaneously.

These nucleation r a t e s are shown

Because

F r o m f igu re 3 it is evident that u n t i l a given supersaturation i s

It was assumed for these calculations that surface tension was indepen-

dent of p a r t i c l e s i ze ; howsrer, it is apparent that pa r t i c l e s i ze must a l s o

influence surface tens ion ( i . e . , the number of molecular bonds experienced

by a surface molecule w i l l change with t h e radius of curvature of t he sur-

face) .

(ref. 13), has shown t h a t t h i s effect tends t o increase the nucleation rate .

Head ( r e f . 1 2 ) , using a radius dependency calculated by Tolman

Since the values of surface tension for mercurous chloride were e n t i r e l y

empirical and since surface tension influences the nucleation r a t e as an

exponent cubed, t he nucleation r a t e (as shown i n f i g . 3) is only intended

t o serve as an approximate indication of the region i n which nucleation can

O C C W .

Thrust

If the proper conditions i n the generator have been established t o form,

charge, and accelerate p a r t i c l e s , t heo re t i ca l estimates of t h r u s t are pos-

s ib l e .

charge, an average v-ue can be assigned t o represent t h e mass of an indi-

vidm.1 pa r t i c l e .

most probably take on only one electron charge (ref . 14) .

of the Pa r t i c l e s i zes expected ( r e f . 3) are i n t h i s range, t h e assumption

seems reasonable.

If the assmpt ion i s made tha t each pa r t i c l e t ransports only one

Pa r t i c l e s of t he order of 0.10-micron diameter or l e s s w i l l

Hence, s ince most

The thrust w a s calculated from the following relat ion:

(13) T = iV = 1 . 4 & 1 0 - 4 ~ / 2 $f2

and i s Plotted i n the form O f a nomograph i n f igure 4.

t o be equal t o 10 ki lovol ts , M

t i c l e ) , and J equal t o smpere, t he th rus t is 5 . 7 5 ~ 1 0 - ~ newton.

This example indicates t he range t h a t w i l l be required of an instrument t o

measure t h r u s t from the col loidal-par t ic le thrustor being investigated.

If & is assumed

equal t o lo6 am" ( a t yp ica l co l lo ida l par-

The space-charge l imited current for t he col loidal t h rus to r used i n the

present investigation (with Child 's Law and s ingly charged p a r t i c l e s assumed)

is shown i n f igure 5. D

Three acce lera t ing potent ia ls (5, 10, and 20 kv) a r e $ indicated for a range of col loidal-s ize pa r t i c l e s . From t h i s c u r ~ e . it is c 5

evident t h a t Only a f e w microamperes of beam current would be expected with

t h i s th rus tor f o r a lo6 mu par t i c l e .

APPARAWS

Thrustor

The experimental co l lo ida l -par t ic le th rus tor i n s t a l l a t i o n is shown i n

f igure 6.

convergent-divergent supersonic nozzle t o expand and condense t h e propellant,

a negative corona discharge t o charge t h e par t ic les , and a pa i r of accelerator

electrodes. An e l ec t ron t r a p was used t o prevent back streaming O f t he elec-

t rons from t h e corona. A wide range of mass flow rates was used i n t h i s in-

vestigation; and, consequently, t h e vaporizer was loaded with up t o 10 grams

Of propellant.

mately 2 p a s of propellant.

adjusting power input t o the e l e c t r i c a l l y heated vaporizer. High propellant

mass-flow rates at most operating conditions regilired modification of t he

or ig ina l configuration, since t h e lava insu la t ing blocks became conductive

due t o surface and impregnated contaxination. Consequently, a l l components

were insulated from each other and from t h e facepla te by means of cemented

g lass sandwiches (as shown i n f i g . 6(a)) .

additional advantage of being r ead i ly cleaned between test runs.

p l i e s and meters were connected as shown i n f igure 6(b).

The t h r u s t o r (fig. 6(a)) cons is t s of a propellant vaporizer, a

The System was o r ig ina l ly designed (ref. 3) t o handle approxi-

The control on the propellant flow was made by

The glass sur faces offered the

Power sup-

Thrust Indicator

In considering a t h rus t sensor fo r t h e co l lo ida l th rus tor , a highly

sens i t ive ind ica to r i s required because t h e maximum t h r u s t i s i n t h e m i l l i -

gr3m range. With t h e thrus tor exhausting ve r t i ca l ly upward, a beam balance

pan was a log ica l choice t o serve as the th rus t t a rge t . The t a rge t was

attached t o a modified comerc ia l Cahn microbalance ( r e f . E ) , which was in-

s t a l l e d i n the vacuum system and operated by remote cont ro l ( s e e f i g . 7) . A

torque YBS applied t o the balance arm by a s m a l l torque motor.

determined from a measwement of t h e power required t o maintain a reference point.

The torque was

This arrangement offered a number of advantages i n operation: (1) t he

balance had a s e n s i t i v i t y of t o @em (depending on operational

procedure), which i s w e l l within t h e range of in t e re s t ; ( 2 ) t he th rus t t a rge t

(balance pan) is always returned t o the same reference point; and (3) t h e

Cahn microbalance can operate accurately i n a r a the r severe environment

( i . e . , mechanical v ibra t ion and temperatui.e var ia t ions , within limits, do

not i n t e r f e re with its operation i n a vacuum).

several modifications were required t o adapt t he microbalance fo r use with

the thrus tor . A potent, ial of 10 ki lovol t s o r more is placed on t he CoroPa

wire.

balance and b u n out t h e torque motor.

balance a t ground po ten t i a l (negative pa r t i c l e s accelerated t o ground poten-

t i a l ) extra pound wires were i m t a l l e d from t h e case, t h e motor, and the

beam balance m t o ground t o protect t he meter fur ther ( s e e f ig . 7 ) .

hole was dr i l l ed in to t h e case so t h a t t h e t a rge t Could be suspended from

the m a x i m m beam load posit ion.

insu la t ing nylon thread t o the balance am.

was inSta l led in t ac t i n t h e vac~um system, a la rge hole was d r i l l e d i n t h e

top t o f a c i l i t a t e degassing. A chimney with an of 6 vas used with an e external baffle t o prevent back s t r e m i n g of ~ X C ~ S E propellant, which c o u l d j

deposit on the in t e rna l balance surfaces.

To measure thrust, nowever,

Under cer ta in conditions, an arc could propagate t o the grounded

Since it is necessary t o keep t h e

A

The t a rge t itself w a s then suspended by an

Since t h e weighing compartrtent

g" l/d

c,

c Targets

The microbalance s e n s i t i v i t y depended on the weight of the t o t a l t a rge t

assembly:

s ens i t i v i ty .

t a r g e t s were used; (1) a 0.25-mil aluminum-coated Mylar t a rge t , (2) a 1.0-mil

aluminum t a rge t , (3) a % m i l s ta inless-s teel target , and ( 4 ) a 0.3-mil t i t a -

n i m t a rge t .

7.5 cm)

was cyl indrical w i t h a sl i t t o accept t he col loidal beam. This t a rge t was

designed t o minimize t h e e f f ec t of e l a s t i c co l l i s ions from t he t a rge t sur-

face.

microammeter.

pa in t or was crimped.

as applied t o the balance, t he l i gh te r t h e target t he higher t h e

During the course of the investigation, four lightweight (mg)

Three of t h e t a rge t s were f la t and rectangular (approx. 1 by

formed on a 3 - m i l tungsten-wire frame. The s ta inless-s teel t a r g e t

The t a r g e t was grounded by a 1 - m i l tiangsten wire connected through a

The wire was fastened t o the t a rge t e i ther by conducting s i l v e r

PROCEDURE

Thrustor Operation

The co l lo ida l -pa r t i c l e thruBtor was operated with a negative accelerating

poten t ia l o f 9 t o 13 k i l o w l t s t o maintain a s t ab le corona current.

focusing electrode po ten t i a l s were selected t o provide minimum impingement

currents on the ground accelerator and no impingement current on the t r ap .

A 1.5-volt ba t te ry heater vas connected t o heat t h e 3-mil corona wire during

vaporizer m u p t o prevent condensation of propellant on the wire.

ers were disconnected during thrustor operation (high yoltage supplies on)

since a leakage path could be s e t up between e i the r the thermocouples or t he

heater power supply t o p o u n d . m e heat capacity of t he col loidal generator

w a s suff ic ient t o maintain constant propellant flow for apmoximately 10 min-

u t e s even though no addi t iona l power was supplied.

,Trap and

A l l heat-

The col loidal generator

vaporizer and nozzle temperatures were independently controlled by two radia-

t i o n heating coi ls .

vacuum chamber walls.

Two radiation shields suppressed heat losses t o t he

The propellant, mercurous chloride, was selected primarily t o enable

d i r ec t comparison with previous data. I n ac tua l operation, a quantity of

mercurous chloride was loaded into the vaporizer and the thrustor was as-

sembled.

temperature was reached. The vaporizer and nozzle operating temperatures ranged

between 350' t o 510' K. A t temperatures above 510' X, t he propellant mass

flow was so high t h a t t he he l l - j a r presswe could not be maintained by the

&inch oil-diffusion pump. A t vacuum pressures above millimeter of

mercury, a glow discharge would take place i n the system shorting out a l l

components; thus, t e s t s were possible only below t h i s pressure level .

The vaporizer ana nozzle were then heated u n t i l a desired operating

Thrust Sensor Operation

I n the operation of the th rus t sensor, a t a r g e t i s suspended from the

The t a rge t was located balance arm by means of a nylon insulat ing thread.

approximately 4 mill imeters above the pound accelerator electrode. A s

previously mentioned, t he s e n s i t i v i t y of t he microbalance peading i s depen-

dent on the t a r g e t weight. The microbalance is equipped w i t h a continuously

adjustable range control, re fe r red t o as the "x-scale." The s e n s i t i v i t y was

Selected by balancing t h e beam with t a rge t attached and c0unierwei;hted with

the range selector se t on the x-scale.

required t h a t a cal ibrat ion be determined fo r each run. This ca l ib ra t ion

was made by adding known weights t o the t a rge t and noting the deflection.

A 1 - m i l tungsten wire w a s attached from t h e t a rge t t n a m i c r o m e t e r .

Since the x-scale was used, it was

F F a

This

w i r e influenced t h e ca l ib ra t ion of t h e t a rge t . A nonlinear cal ibrat ion was

obtained when t h e wire attached t o t h e t a rge t was i n t he form O f a coiled

sp r ing ( s e e sketch (c)).

0 r-' L-- 1

Target

( C )

This problem w a s eliminated and a l i n e a r ca l ib ra t ion was obtained by using

a r 'elatively a t r a i g h t wire (see sketch ( d ) ) .

0 r -dLi I I I Balance I

L-- I -J iu--@+'' No spring

Target

(d )

Once t h e ca l ib ra t ion was obtained, it was assumed tha t no changes occurred

during the run.

is 1/1000 of ful l scale , f o r example, with the t i tanium t a r g e t and a system,

as indicated i n sketch ( a ) , t h e m a x i m m sens i t iYi ty was

When t h e balance is Operated i n t h i s manner, the Sens i t i v i ty

pa.

Since def lec t ions a r e proportional, t he torque can be determined i n

terms of th rus t . With the t a r g e t i n place, t he balance i s counterweighted

and adjusted t o balance at about 30 percent of t he fu l l - s ca l e reading.

operation, as t h e t a r g e t weight increased due t o the deposition of mercurous

During

chloride, the balance usually maintained a readable range.

was placed under high vacuum

any data were taken.

The thrust sensor

m Hg) fo r approximately 4 hours before

The deflection force 9 of the balance m is

9 = 1.44xl0-4Jb$/~ &I2 + &v(n,nionized particles)

(14) dm e -9.81 - A t + (hV) dt (sput tered)

To obtain r e l i ab le thrmt readings required the second t o f i f t h terms i n equa-

t i o n (14) t o be minimized or eliminated ent i re ly .

neutral pa r t i c l e momentum a t the experimental mass-flow r a t e is insuff ic ient

t o de f l ec t t he t a rge t (second term i n eq. (14 ) ) .

however, impose a more severe problem ( t h i r d term i n eq. (14 ) ) . These ef-

f e c t s were eliminated by grounding the t a rge t so t h a t a charge could not

accumulate on the t a rge t surface.

grounded. In t h i s manner, t h e t a r g e t was a l so made t o seme as a col lector

t o measwe the colloidal-beam current.

a t a given posit ion without propellant flow and no def lec t ion was noted as

power was applied. During ac tua l operation with propellant flow, the t a r g e t

vas returned t o i t s i n i t i a l r e l a t i v e position; and t h m any nonuniform f i e l d

effects should cancel out. The effect of t a rge t weight increase due t o con-

densation of the material on the t a rge t surface (fourth term i n eq. ( 1 4 ) )

vas minimized by l imit ing the

"Off power" readings t o a f e w seconds. Finally, t he e f f ec t of a sput te r ing

lo s s ( last term i n eq. (14 ) ) from the t a rge t s was minimized by using e i the r

titanium with i t s inherent l o w sput ter ing r a t e o r a cyl indrical s t a in l e s s - E

s t e e l target with a s l i t t o accept the col loidal beam. A t h r u s t reading was

It can be shown tha t

The e l e c t r o s t a t i c forces,

The f i n a l accelerator was separately

As a t e s t , the t a rge t was maintained

At o r time in t e rva l hetween "On power" and

g 9

c t

taken with the corona, accelerator, and electron-trap power supplies on; then,

t h e power was h e d i a t e l y shut off and the zero reading taken as soon as pos-

s ib l e .

co l lo ida l -par t ic le thrustor .

The difference i n these two readings was t h e effect ive thrust of t he

RESULTS AND DISCUSSION

The t h r u s t measurements obtained are shown i n figure 8. I n t h i s f igure,

t he th rus t readings a r e plot ted fo r a range of vaporizer temperatures from

300' t o 510' K.

current and acce lera t ing voltages between 0 t o 6 micromperes and 9 t o 13

ki lovol ts , respectively.

These readings were taken a t a few different values of beam

The various t a r g e t materials used are a l so shown.

Thrust Evaluation

From f i w e 8 it is apparent t h a t t h e onset of recordable t h r u s t

newton) occurred abruptly at a vaporizer temperature of 485' K. If

t he flow through t h e nozzle had been made up en t i r e ly of charged molecules

( r a the r than p a r t i c l e s ) for the complete range of vaporizer temperatures, a

continuous increase of th rus t would be expected with increasing vaporizer

temperature. Final ly , due t o the charging and acceleration processes, space-

charge-limited current would be reached ( see sketch (e)).

Lq = constant /-----

Thrust 1 ,// Vaporizer temperature

( e )

Operating at space-charge-limited current conditions, t he charged mole-

cule flow would he constant and can be expressed as a mass-flow r a t e as

follows:

J = m ( E G 1 molecule)

Under these conditions, t h e charged molecule ve loc i ty would be much greater

than the thermal ve loc i ty of t h e neutral molecules, so the e f f ec t O f neu t r a l

molecules on the th rus t readings would be negligible.

of mercurous chloride (236 m u ) at a typ ica l operating point of 485O K

vaporizer temperature, 10 k i lovo l t s acce lera t ing voltage, and beam current

of 4 microamperes, a theo re t i ca l value of 8 . 7 ~ 1 0 - ~ newton of t h r u s t i s oh-

ta ined (see f i g . 4).

It is concluded, therefore, that a charged-particle beam ra the r than a

charged-molecular beam exis ted at these conditions.

For a moleculer beam

Measured thrust at these conditions was 5.5~10-5 newton.

The mode of flow (free molecular, intermediate, s l i p , or viscous)

through the nozzle as determined by the vaporizer temperatwe was plo t ted i n .

f i gu re 2. From t h i s f igure, it is observed t h a t t he vaporizer temperature

at which t h e flow regime becomes e n t i r e l y viscous is approximately 500' K.

Since experimental detection of p a r t i c l e s d id not take place u n t i l a temper-

ature of 485O K was a t ta ined i n the vaporizer, a conclusion may be reached

t h a t t he onset of recordable th rus t and consequent p a r t i c l e formation doe8 i

not take place u n t i l the flow regime through the nozzle approaches a viscous

s t a t e . This is consistent with theo re t i ca l expectations. For p a r t i c l e

i

:I formation i n a homogeneous condensation process, as i n t he expansion i n a

nozzle, it is necessary t h a t a c r i t i c a l nucleation r a t e must be reached a8

predicted by the c l a s s i c a l liquid-drop theory of nucleation (see THEORY 8ec-

. t i o n ) . F Since t h e expansion and consequent Supersaturation must be negligible

i n the free molecular and intermediate flow regimes, t he c r i t i c a l value of

supersaturation cannot he a t ta ined u n t i l t he flow approaches a viscous regime. - 0

The values of critical nucleation rate necessary for condensation are

uncertain at the present time, althou8h investigators have estimated that it

must lie between LOo and LO8 nuclei per cubic centimeter per second (ref. 9).

Plotted in figure 9 are lines of constant nucleation rate obtained from a

CroSSplot of figure 3.

ical nucleation rates. In addition, a one-dimensional isentropic expansion

for the test nozzle at a vaporizer temperature of 490° K is shown plotted

across these lines of constant nucleation rate. From this figure it is ap-

parent that the critical supersaturation necessary for condensation lies

between 15 and 38 and is located in the legion of the nozzle throat. If the

nucleation rate during the isentropic expansion had not approached the crit-

ical region (10' - lo0 nuclei/( a n 3 ) ( s e c ) ) , particle formation would not he

expected. It appears, therefore, that the prticle-formation process in a

condensatior\-type nozzle is at least partly explained by the classical liquid-

drop theory of nucleation.

The crosshatched region indicates the range of crit-

Particle Size

The average particle size was expected to he nea r 0.01 micron from pre-

vious particle size measurements Of mercurous chloride with photomicrographs

(ref. 3). In figure 10, a typical photomicrograph and particle distribution

for mercurous chloride for a vaporizer temperature of 490° K are shorn. The

distribution factor is an indication of the relative abundance of a given

particle size.

within a given diameter range were counted.

to normalize the distribution.

It is necessary, however, to consider the particles on a mass hasis (mu)

One hundred typical particle.? were selected and all particlea

The diameter range was then used

rather than by diameter (microns). The curve Shown in figwe 11 can be used

to convert the particle diameter of mercurous chloride to atomic mass units.

This curve was calculated by using the hullt density of mercurous chloride as

the particle density and by assuming that all particles were spherical. For

small particles in the range of interest, a spherical particle would he ex-

pected because of the surface tension and energy considerations.

An estimate of the average "effective" particle size in the colloidal

beam can he made by application of equation (13) with a knowledge Of the

thrust, current, and certain assumptions, namely,

(1) That each particle has one electronic Charge

(2) That particles were accelerated through the voltage represented by

the corona potential to ground

An average particle size of 1.2~106 amu (76 coulomb/kgj was obtained for a

vaporizer temperature of 490' K by this method of calculation.

weighted value of particle size is determined f o r the distribution in fig-

ure 10, a value of 1.71~10~ mu (53 coulomb/kg) is obtained.

If an average

mese two values

agree well within experimental error.

Target Materials

As previously mentioned, four types of target materials were used. The

basic chmacteristics of each target are given in the following table:

Stainless steel

Titanium

Thick- Weight (less

0.250 0.0274

2.000 .lo98

2.000 .6420

.0549

c c

i

. -

Some observations on the performance of these targets are as follows:

Target A burned out readily from stray sparks; even though it was light-

weight, it was not satisfactory.

Target B did not burn out from sparks, but propellant attacked the metal

causing excessive corrosion and lass of electrical continuity.

Target C (cylindrical) had no corrosion problans and the electrical

continuity remained excellent throughout the run. Tho major disadvantage

was that this target was very heavy (reduced sensitivity) and the deposit

was not firmly attached to the surface.

Target D was selected on the basis of its lightweight (higher sensi-

tivity) and low-sputtering material characteristics. Electrical continuity,

however, was difficult to maintain. The propellant formed a tenacious coat-

ing an the target, the adherence of which was not observed with any previous

target material. The target weight enabled the microbalance to operate with

a maximum sensitivity of gram. It is possible that the electrical

connections to the titanium, can be improved in future PUIIS. It was concluded

that titanium could be worked into a successful target suitable for operation

with the colloidal thrustor.

CONCLUDING RFhlARKS

A modified electric microbalance was used to measure the thrust of an

experimental colloidal-particle thrustor. It was shown that an electric

microbalance could measure thrust with a maximum sensitivity Of !&ram.

Since the thrust from an experimental colloidal thrustor operated at rela-

tively low voltages (10 kv) is Of the order of millipms, the electric

microbalance gave desirable accuracy in thrust measurements.

hraluation of the experimental thrust and beam-current data revealed a

dependence of particle formation on a critical supersaturation. This critical

value of supersaturation was attained by increasing the flow through the

nozzle until it approached a viscous flow regime.

was shorn that the particle-formation process can be partly explained by the

classical liquid-drop theory of nucleation.

From this evaluation it

It was determined that a mean particle mass of 1.2x106 amu would be

required to account for thrust deflections on the electric microbalance at

a vaporizer temperature of 490' K. The mean particle mass determined from

an electron photomicropaph of the colloid beam was 1. 7U1O6 amu at similar

operating conditions.

experimental error.

These values are considered to be in agreement within

At the present time, a means of defining completely the operating param-

eters in a colloidal beam by reliable experimental techniques has not been

perfected. Simultaneous measurement of beam thrust and current (as reported

in this paper) is a step t o w d this goal. Further definition of the beam

will be possible with a measurement of the distribution in charged and un-

charged particle size. As a step toward accomplishing this, an experiment

is being prepared to measure charge-to-mass ratio distribution of the colloi-

dal beam by means of a quadrupole mass spectrometer. These measurements i n 0

conjunction with the thrust and current measurements will &e it possible

to define precisely the utilization efficiency of the colloidal thrustor. F - e

REITRENCES

APPENDM - APPROXIMATION OF -ACE TENSION VALUES

The surface t ens ion of mercurous chloride was estimated from an empir- 1. Mickelsen, W i l l i a m 3.: NASA Research on Aeavy-Particle Elec t ros ta t ic

i c a l equation obtained by assuming that surface t ens ion is a function of t e m -

pera ture only.

Shie lds , i s as follows (ref. 16):

Thrusters. Pwer 63-19, In s t . Aero. S c i . , 1963.

This equation, derived by E'dtvos and modified by Ramsay- 2. Mickelsen, W i l l i a m R . : Comparative Performance of Elec t ros t a t i c Rocket

Engines. Paper 62-74, In s t . Aero. Sci. , 1962.

3. Norgren, C . T . : On Board Colloidal Pa r t i c l e Generator f a r E lec t ros t a t i c ct)2'3 = r(rcritical - 6 - T )

Engines. Paper 2380-62, Am. Rocket Soc., 1962.

4. Low, Charles A . , and Mickelsen, W i l l i a m R. : An E lec t ros t a t i c Propulsion The c r i t i c a l temperature ~~~~~~~~1 was obtained from Guldberg's rule

( r e f . 17) : System with a Direct Nuclear Generator. Paper presented at Ins t . Aero.

Sei. Nat. Prop. Meeting, Cleveland (Ohio), M a r . 9, 1962. 'cr i t ical = 'b

where T~ is t h e absolute normal boi l ing point of t h e material. The Eatvos

constant

5. Lockwood, D. L . , Mickelsen, W. R . , and Hamza, V. : Analytic Space Charge

r was assumed t o vary as follows for a given composition (ref. 16): Flow and Theoretical E lec t ros ta t ic Rocket Engine Performance. Paper

r = 1.90 + 0.011 n+

Surface tension calculated for mercurous chloride by using these expressions

is given i n t h e following table:

105.0

110.0

115.5

400 120.7

2400-62, Am. Rocket Soc., 1962.

6. Krohn, Victor E . : Glycerol Droplets f o r E lec t ros t a t i c Propulsion. Paper

2398-62, Am. Rocket Soc., 1962.

7. Nelson, L. A . , and Hansen, S.: Sensit ive Ion-Engine-Thrust Measuring

Device. Rep. 246, Hughes Res. Lab., June 1962.

8. Dushman, Saul: Sc ien t i f i c Foundations of Vacuum Technique, ch. I. John

Wiley,& Sons, I n c . , 1949.

9. Stever, H. G. : Fundamentals Of Gas Eynamics. Vol. 111. Princeton Univ.

Press, 1958, p. 526.

10. Frenkel, J.: Kinetic Theory of Liquids. Dover Pub., Inc. , 1955. E C I

11. Courtney, Welby G.: Kinetics of Condensation from the Vapor Phase.

1M-1340, Texaco Experiment, Inc., Ju ly 15, 1962.

c

12. Head, R. M.: Investigations of Spontaneous Condensation Phenomena.

Ph.D. Thesis, C.I.T., 1949.

13. Tolman, Richard C.: The Effect of Droplet Size on Surface Tension.

Jour. Chem. Phys., v01. 17, 1949, pp. 333-337.

14. Loeb, Leonard B.: hdamental Frocesses Of Electrical Discharge in

Gases. John Wiley & Sons, Inc., 1939, p. 149.

15. Cahn, Lee, and Schultz, Harold K.: Vacuum Microbalance Techniques.

Vol. 2. Plenum Press, 1962, p. 7.

16. Glasstone, S : Textbook of Physical Chemistry. D. Van Nostrand Co.,

Inc., 1946, p. 492.

17. Reid, Robert C., and Shervood, Thomas K.: me Properties of Gases and

Liquids. McGrav-Hill Book Co., Inc., 1958, p. 7.

18. Lange, Norbert A . : Handbook of Chemistry. Fifth ea., Handbook Publ.,

Inc., 1944, p. 210.

19. Hcdgaan, Charles D., ed.: Handbook of Chemistry and Physics. Thirty-

eighth ed., Chem. Huhber pub. Co., 1956-1957, p. 550.

20. Anon.: A cmprehensive treatise on inorganic and theoretical chemistry.

Ionmans Green and Co., London, England, 1946, p. 802.

21. Perry, John H.: Chemical Engineers Handbook. Second ed., McGrav-Hill

8ook Co., Inc., 1941, p. 633.

Molecular weight BmU

TABLE I. - PFXSICAI PROPERTIES OF MERCUROUS CHLORIDE

236.07 18

Property j Units Value IReferenceI -. .-

Melting point

Sublimation point

Boiling point

OC 302 18

OC 373 19

OC 382.5 18

Density I grams/cm31 7.15 I 18

Latent heat of vaporization at-

16' C

180 c

I gram-cal 20

131

127

i I I I I

I I I Specific heat ratio I r = c,/c..l 1.33 I 21

CROSS-SECTION **".IS

COLLOIDAL - PARTICLE NOZZLE

TEMP-' . I / 'K x 103

T H R U S TI

I d

EXAMPLES

-COLLOIDAL PARTICLE 1 n d = IOKV: \

up = 1060m", 1 1 , J = 4 X AMP 1

1 T 1 5.75 X 10.' NEWTONS

T = 8.7 x IO-' NEWTONS

J

VAPORIZER TEMP, O K

~. . . . , . . , . . " _ . I . .", . . - .. . . ~ ,,*. .~ ,. ,.,,. . . I : , .! ..,,. . ,., . 1, ,- . II. .,... ,.,. ...

PARTICLE DIAMETER, MICRONS - - - -

0 0 0 - 0 z m

5 w w

DISTRIBUTION FACTOR

h

c