The nature of Brownian motion and historical theoretical investigations of the phenomemon are reviewed. The feasibility of using a laser anemometer to perform small particle experiments in an orbiting space laboratory was investigated using latex particles suspended in water in a plastic container. The optical equipment and the particle Doppler analysis processor are described. The values of the standard deviation obtained for the latex particle motion experiment were significantly large compared to corresponding velocity, therefore, their accuracy was suspect and no attempt was made to draw meaningful conclusions from the results

Sastry, V. S.

English

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I
V/;A
b
(NASA-CR-163146) AN INVESTIGATION OF THE
	 N80-24575
MOTION OF SMALL PARTICLES AS BELATED TO THE
FORMULATION OF ZERO GRAVITY EXPERIMENTS
Final Report (Tennessee State Univ.,
	 Uncles
Nashville.) 17 p HC A02/11F A01
	 CSCL 20D G3/34 20940
School of Engineeringand Technology
Tennessee State University
Nashville, Tennessee
AN INVESTIGATION OF THE MOTION OF SMALL
PARTICLES AS RELATED TO THE FORMULATION
OF ZERO GRAVITY EXPERIMENTS
I
FINAL REPORT
NASA GRANT NO. NSG -8032
s
z
AN INVESTIGATION OF THE MOTION OF SMALL
PARTICLES AS RELATED TO THE FORMULATION
, OF ZERO GRAVITY EXPERIMENTS
FINAL REPORT
NASA GRANT NO. NSG-8032
V.S. SASTRY
MECHANICAL ENGINEERING DEPARTMENT
TENNESSEE STATE UNIVERSITY
NASHVILLE, TN 31203
May, 1980
t
AN INVESTIGATION OF THE MOTION OF SMALL
PARTICLES AS RELATED TO THE FORMULATION
OF ZERO GRAVITY EXPERIMENTS
1 NTRnnI IrTTnN
With the advent of a manned orbiting laboratory, many historically
fundamental experiments can potentially be performed where gravitational
effects are absent or minimal. Study of Motion of Small Particles is one
example of such an experiment. The motion of small particles in various
media is referred to as Brownian motion. Though Robert Brown did not
discover Brownian motion, his contribution was to establish Brownian
motion as an important phenomenon and to refute by experiment facile
mechanical explanations of the phenomenon [1] a . Albert Einstein
developed the full mathematical theory of the movements of the particles,
neglecting body forces [2J	 He deduced a formula which makes it possible
to calculate the magnitude of the Brownian displacements. Harvey
Fletcher proposed modifications to this formula and suggested a new method
for studying Brownian movements [3,4] . 	 Leopard Infeld conducted
theoretical investigation of Brownian motion [5] .
The theoretical formulations have, for the most part, neglected
gravitational body forces while the gravitational effects are unavoidably
included in the experimental results due to terrestrial testing. Pe -
forming small particle experiments in an orbiting laboratory would make
it possible to eliminate gravitational influence.
Laser Doppler Anemometer Techniques as described in Reference 6,
provide an excellent opportunity to conduct such experiments with greater
accuracy than ever before. The purpose of this project was to investigate
the feasibility and evaluate the scientific worth of experiments in space
by conducting earth based experiments,
a The numbers in the brackets refer to the list of references given
at the end.
1
THEORY OF BROWNIAN MOVEMENTS
Som, basic equations of interest are given here [3] .
The average absolute value of displacement of a small particle in
a gaseous medium with no outside forces is given by
x = f2
	 (X2) }^ 	(1)
n
where x 2 is the group average of the squares of the individial displacements.
The magnitude of Brownian displacement for a spherical particle
moving uniformly throu g h an incompressible gaseous medium can be written as
x	
2	 Et	 z	 (2)
= 	 (uaK 
where
	
E = average energy agitation of the gas molecule
t = time interval being considered
u = coefficient of viscosity
a = particle radius
K = a function of Z/a
z = mean free path
If the particle is moving under the influence of constant outside
force, assume that the particle displacement is composed of two components:
Xgravity - Vt
and
X	 = U ^ It
Brownian
where, U = displacement in one second due to Brownian movements
The total displacement is given by
b=Vt+UJt
U=bt1i-Vt^
E
2
i
3
The number n out of n events that will have the time of fall, through
a fixed distance, between t  and t 2 can be expressed as
t2
n _ -n(h
 ) l2	 (bt-'/2 + Vt
	
) exp (- r (b-Vt) 2 ) dt	 (3)
TT
t 
To obtain an expression of the distribution of frequencies, one utilizes
the equation for frequency shift...
W = ,^ f = t
substituting t = w
	
in equation 3,
„W2
__ n	 h ij 	 z	 _ 3^,	 h	 2n
^— (n )	 I (bc	 W	 + Vc w	 ) exp (- cW {wb-Vc) ) dw (4)
If the frequency due to gravity is (a g , then the average of the average
value of all frequencies below ,,g and of all frequencies above (J9 is g iven by
VC +
W = 2b	 8b^h
The first term on the right hand side is due to Gravity and the second
term is due to Brownian Motion.
EXPERIMENTAL SYSTEM
Laser Doppler Method
The Doppler effect is the fact that there is a change in frequency
with which energy reaches a receiver when the receiver and the energy
source are in motion relative to one another [6] . In the Laser
Doppler System, energy is transmitted to a moving scatterer (tracer)
which then becomes a source and the energy is transmitted to a
receiver. This technique is based on the fact that radiation passing
through a fluid is scattered by tracers in the fluid. In Laser
Doppler Systems small particles are suspended in the fluid and act
as tracers. The particles are assumed to move with the same velocity
as the fluid surrounding the particle (no-slip boundary condition).
The scattered radiation gives information regarding the velocity
of the particles. This information manifests itself by frequency
shifting the radiation striking the particles.
The amount that the source frequency is shifted,n f
	
, upon
striking the tracer and returning to a receiver is called the Doppler
Shift or Doppler Frequency.
DESCRIPTION OF THE SYSTEM
The experimental system is shown in Figures 1 and 2. 	 It is of a
dual beam-sinqle channel type utilizing forward scatter.	 It is easier
to obtain strong signals with forward scatter than with back scatter.
The main components of the system are described below:
Helium-Neon Gas Laser - 15 mW power and provides focussed and
coherrent light having a wavelength of
6.328 x 10
-7
 M.
Polarization Rotator - orients the polarity of the laser beam for
optimum efficiency.
f
4
5Transmitting Optics - consists of beam splitter and focussing
lens. The beam splitter splits the beam
into two parallel beams, each displaced
25 mm from the original beam.
Particle Container - contains the tracer particles suspended in
water.
Receiving Optics - consists of lenses to collect scattered light.
Photomultiplier - converts light energy received into proportional
electrical signal with a quantum efficiency of 130.
Particle Doppler Analysis Processor - measures the time period of
burst signals generated by
particles passing through
the test volume.
Data Sorter - forms histograms of signal time and prints the data.
The Laser and the optics were supplied by Thermo-Systems, Inc.
and the electronics were supplied by Spectron Development Laboratories,
Inc. The small diameter particles used as tracers were Dow Uniform
Latex Particles supplied by Dow Diagnostics.
TrT rVrTr\I
The laser beam is separated into two beams of equal intensity
and these beams are focussed at the measuring location as shown in
Figure 3. Where the two teams cross, the wave fronts interfere to
form alternate	 regions of high and low intensity light which causes
variations in the intensity of light scattered by the particles crossing
the measuring location.
6The scattered light is picked up by the photomultiplier and is
converted to an electrical signal whose frequency is proportional to
the rate at which the particle is crossing the interference fringes.
The following equations are applicable:
a
d f 2 —Si n
z
V = f d 
where	 a = wave length of incident light = 6.328 x 10 -7 m
f = frequency detected at Photomultiplier, Hz
V = velocity of flow perpendicular to fringes, m/s
d  = distance between fringes ( = 1.6 mm for 120 mm lens)
w = angle of the beam intersection ( = 250 for 120 mm lens)
The system is equipped with 3 sets of lenses of focal lengths, 120 mm,
250 mm and 600 mm. For lower velocities and lower frequencies, as in
the present application, shorter focal len g th lenses are preferable.
Therefore, 120 mm lenses were used.
The relationship between the velocity of particle and the frequency
aetected is shown in Figure 4.
DATA
The latex particles were suspended in water in a plastic container.
The particles were stirred wcll to make all the particles to be suspended.
Sufficient time was allowed for the fluid to become quiet so that the
particles can be considered to be moving freely. The collection of
data was started at this pint. A typical printout from the Data Sorta
is shown in Figure 5. The summary of data collected is shown in the
table below.
RUN N PARTICLE
SIZE
JIM
AVERAGE
VELOCITY
m/s
STANDARD
DEVIATION
m/S
14 0.085
0.085
0.2241
0.01415
0.01568
15 0.1015
16 0.085 0.02342 0.183
17 0.091 0.03965 0.2713
0.1027
0.1916
20 0.091
0.091
0.00624
21 0.0205
0.0707
0.06867
23 0.091 0.351
0.11330 0.176
0.17632 0.00289
0.05023
0.01296
0.0177335
36
38
0.176
0.176
0.176
0.09242
0.114258
0.1892
0.04211
7
CONCLUSIONS
The values of the standard deviation obtained in most cases are
significantly large compared to the corresponding velocity. Therefore,
their accuracy is suspect and no attempt is made to draw meaningful
conclusions from these results. The failure to obtain useful data
might have been due to the difficulty in keeping sufficient number
of particles suspended in water without settling down. It is
also possible that the instrumentation employed was not sophisticated
enough for the type of measurements.
ACKNOWLEDGEMENT
The author is grateful to National Aeronautics and Space
Administration for supporting this project.
8
REFERENCES
1	 Edward Nelson, Dynamical Theories of Brownian Motion (Princeton
University Press, 1961), p 9
I
f	 2. Albert Einstein, Annalen der Physik, 11 (1905), p 549
3. Harvey Fletcher, "A Verification of the Theory of Brownian Movements
and a Direct Determination of the Value of NE for Gaseous Ionization",
The Physical Review, V 33, No. 2 (1911), p 81
4. Harvey Fletcher, "A Determination of Avagadro's Constant N from
Measurements of the Brownian Movements of Small Oil Drops Suspended
in Air", The Physical Review, V 4, No. 5 (1913), p 440
5. Leopard Infelu', "On The Theory of Brownian Motion", University of
Toronto, Applied Mathematics Series, V 4 (1940), p 5
6. William C. Cliff, "Laser and Acoustic Doppler Techniques for
The Measurement of Fluid Velocities", NASA Technical Memorandum,
TM-X 64932 (1915)
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Figure 2. Details of Experimental Set-up
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Figure 4. velocity vs Frequency for 120 mm Lenses
I
14
^^^77-'--~-^-~-^----^------- ----'--------'--
^/\U^{'^^R	 ---' ^^0^---,---' 
	
— ''~--'	 Poon
-..' ^U^ J f^!
~	 ~-
5' 2 ^-&---^&^-'- --^ --------- ----------- --
FRING[ SPRC y9Yf3- '(MI C-'RUNq- -) --- 16009'. 104 ^--
NUMBER OF F5ERUNGS-^^---`^^~---' '------- --
[V[NTS^r-l562---- ' --'~~`-------'------~
TIME OF-RUN509RG^K-SEC ~---~--^--------- '--
LRRG[^T lBTN  COUNT --^~^^^^''---'----'-'-------- ~
YEL0C1TY'HIST0GRRM	
—
	
-RHNGE	 ----
	 HOM8[R--
(ME] ERS/S[C)	 (FRHCTIORl7Yr-TOTAL7'
0YER %	 0 0 - 02 -- %-. 14 	
-
1,600 ^2 T0 -441	 02	 -- 0.000-00
1.441	 02 TUI.280 02
- 0.000-08
1.280 0L T0 .120	 02 R 000-@0
.1CR0	 132 TO 9.609 01 0.-0110-00
9.609 0 T0 1 0.000-00
8.008	 0i TO/G.400 01
- Cl.
 0^0-00
6.480 0 T0 4 ' 801	 01 0000 80
-4.801	 01 TU J.200 01 1?.0P10-00
3.200	 01 T0 l.600 01 0.mg0-00
OY[R 599-0I 0 0q^^^^-
1.599-01 TO l'441-i!1
1.44-1-01 TO 1.279-01 000-@0
^.279-01 TC ^ ' ^20-01 0.80^-8^
120-@1 T8 9.609-02
9.609-02 TO ^ ' 999-02 2.9^1-04
99 TO .399-02 0.@00-^^
.39^-02 T0 4.800-02 0.000-00
4.800-02 TO J.199-02 0,000-00
3.199-02 TO 1.599-02 ^.u7P-^^
	
HV[RHGE VELOCITY = 6.867 02 HET R	 [C
° /D
STHN( , HPD P[YI AT! 0N = 1.1?1 m?
Figure 5 '
	Sample Printout of Data


An investigation of the motion of small particles as related to the formulation of zero gravity experiments

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