~1~~ 1__~~_ ~~L
JUN 17 1964
LIBRAR1ES
CONDENSATION OF GASES ON A COLD SURFACE
by
AMIEL SHULSINGER
Submitted in Partial Fulfillment
of the Requirements for the
Degree of Bachelor of Science
at the
MASSACHUSLETTS INSTITUT: OF TECHNOLOGY
June,
1964
Signature of Author .
.
.
Department of Mechanical Engineering
u
-
Certified by
Certified by
.
-
May 29,
1964
*.
Thesis/upervisor
.
.
.
Accepted by
Chairman, Depart ent Committee on Theses
TABLE OF CONTENTS
Abstract
2
Acknowledgment
3
Introduction
4
Theory
6
Apparatus
10
Procedure and Description of Experiment
14
Results
17
Conclusions
19
References
20
Appendix
21
ABSTIRACT
The purpose of this thesis was to study the rate at
which gas molecules will stick on a cryogenically
refrigerated surface.
The goal was to complete the
building of apparatus that could be used to examine this
problem, and if possible, to obtain data as to a sticking
coefficient for various gases.
The method used was to measure the pressure change
in a gas after it was injected into an evacuated chamber
which contained a cold surface.
The gas that was tested
was carbon dioxide.
Due to many problems encountered during this work,
it was not possible to obtain the desired data.
the feasibility of the apparatus is discussed and
improvements are suggested.
However,
-3-
ACKNOWLEDGMENT
The author wishes to gratefully acknowledge the help
of the following people:
Prof.
Mr.
Robert Stickney
Michael Koskinen
The R.L.E.
Glass
Shop
This work was made possible
by a
grant from the
duPont Fund of the Mechanical Engineering Department.
The author wishes to thank the duPont Company and the
Mechanical Engineering Department for this grant.
The cooperation and support of the M.I.T. Research
Laboratory of Electronics is also gratefully acknowledged.
4
INTRODUCTION
The aim of this thesis is to study the condensation
of various gases on a cold surface.
It
is desired to
find out if the gas molecules, upon striking such a low
temperature surface, will stick to it by condensing.
There are two definite applications for such a
study.
The first is to help develop high speed gas
pumping methods.
Cryogenic pumping is being used today
to get low pressures, and in order to improve the
procedure, it is necessary to know at what rate the
remaining gas molecules will stick to the cold surface
so that the speed of pumping can be regulated and
increased.
The second area of interest is in simulating space
conditions (1).
For example, the gas molecules of the
exhaust of a rocket engine in space will continue to
move away from the rocket and will never return.
Thus,
when testing such an engine here on earth, it is not
enough merely to place it in a vacuum, for the exhaust
molecules will strike the containing walls of the vacuum
system and bounce back to the engine, thereby destroying
the space condition, for this could never happen in
space.
Therefore, some method must be found to prevent
these molecules from bouncing back; this can be
accomplished by cooling down the bounding surfaces to
-5.low temperatures, so that when the molecules from the
exhaust strike them, they will condense.
It is desired
that the molecules stick to the walls the first
time
they strike it, and therefore, this thesis will aid
in determining whether they will do so.
__ __~~_ ~
- 6 THEORY
The basic procedure consists of injecting a known
number of molecules into a known volume which contains
a cold surface, and then seeing how fast the molecules
condense; however, other techniques have also been
used (2j. The number of molecules at any given moment
may be determined by measuring the pressure of the gas
for, from the perfect gas law, the number of molecules
is directly proportional to the pressure.
PV = NRT
where
P = pressure of gas
V = volume of gas
N = number of moles of gas
R = gas constant
T = temperature of gas
Solving for N:
N=
.Y p = constant x P
RT
Finally,
Number of molecules = Avagadro's number x N
= Avagadro's nurmber x constant x P
= constant x V
______ _ __
_I_
I
- 7The basic equation which describes the experiment is:
----
Se
where
4V
t
P = pressure of gas
Pi = initial pressure of gas
A = area of cold surface
V = volume into which molecules are injected
5 = mean speed of molecules (at room temperature)
t = time
o = sticking coefficient (probability that a
molecule colliding with the area is pumped)
This equation is derived from the fdllowing equation
for the pumping speed of an orifice or condensing area,
which is based on kinetic theory:
dN9
I
Ns
N' = number of molecules
= LN
where L is
Avagadro's number.
From the perfect gas law,
RT
N = -RT
;1__ ____
____
-8-
Therefore
L PV
R T
Since R = kL, where k = Boltzman's constant,
PV
kT
and, .. ,
V dP
kT dt
dN'
dt
since V and T are constant.
Substituting back into the original equation,
dN'
dt
or
dP
P
V dP
1
P
- I i o<'lti cA
kT dt
A=
=
CWcV
dt
Integrating,
t
dP
p
f dt
4V
ep
0
results in
P
In -
Pi
or
P
Pi
=
Z-A
-o-oTv
-t t
4V
-IA
- 9 -
Thus, the purpose of the experiment is to determine
this sticking coefficient for different gases.
This can
be done from a graph of pressure vs. time, since all the
other terms are known beforehand.
This graph should
look something like this:
P
rnolecules condens'i7y
Injected
gas injected
It is desired that V be much larger than A, for
otherwise, the pressure will drop off too fast and it
will be difficult to get a meaningful graph.
Similarly,
Pi should be low enough, for otherwise, the molecules
will once again condense at too fast a rate.
-
10 -
APPAKATUS
A previous thesis student (3)
considered the methods
and partially built the apparatus, which I then completed.
The entire apparatus is made almost exclusively of glass.
Main system:
The pumping system is made up of a mechanical pump
and a diffusion pump (4).
diagram on page 12,
As shown in the schematic
the gas is
injected into a cylindrical
chamber, and the cold surface is the end of a hollow
metal rod which is cooled down by liquid nitrogen.
In
order to minimize heat conduction to the rod, the metal
plate is so constructed that it does not touch the rod.
However,
because of this, some of the injected gas would
be able to escape through the slight opening between the
rod and the plate, and therefore, the area above the
plate was enclosed so that the amount of escaped gas
could be measured.
The gas pressures are measured with
ion gauges.
Originally, it was planned to cool the surface with
liquid helium, and the apparatus was so constructed.
The liquid helium was to be put where the liquid nitrogen
is now, and around it was built an insulating pocket
which was to be filled with liquid nitrogen,
However,
_I;~ _ I _
~
-
11
-
the system as thus constructed did not have sufficient
strength to withstand the stresses when it was evacuated.
The glass kept on cracking, and therefore, the plan to
use liquid helium had to be abandoned; the system was
rebuilt to its present state and uses only liquid
nitrogen.
This severely limits the experiment, for many
of the gases which it was originally desired to test will
not condense at the temperature of liquid nitrogen (76 0 K).
Injection System:
As shown in the schematic diagram on page 13, the
pressure of the injected gas is measured by an oil
manometer.
An expansion chamber was introduced in order
that the injected gas would be at a low enough pressure
after it
expanded again into the main system.
A more
detailed description follows in the next section.
__ I_;~_ i~
1
- 12
-
Main System:
•/'
/d n/,troyen
metal plate
ball valve
surface
/'on gau es
injected
gases -
valve
-
13 -
Injection System:
steop cock v4/ve
mechanict/
V Cuum
Spt'mp
scale
orginal
unexpanded
9gas
ample
egpansion
chamber-
oil
expansion
system
injected
g8S
COR
4"o mai,
system
;ILPIID~ ;"Li~
- 14 PROCEDURE AND DiSCRIPTION OF EXPRIMENT
The pressure in the main system and in the expansion
system was pumped down to approximately 1 x 10-6 mm
g,.
The first gas chosen to be tested was carbon dioxide.
As stated before, the choice of gases is limited (5),
and furthermore, the vapor pressure of the gas chosen
had to be below 1 x 10 - 6 mm Hg at 76°K (See graph of
vapor pressure vs. temperature for some gases on page 16).
The procedure is as follows, with a more detailed
one in the appendix: the injection system
is evacuated
and the desired amount of carbon dioxide is inserted by
measuring its pressure with the manometer.
A sample of
the gas is then taken and expanded in the expansion
chamber.
A sample of the expanded gas is then taken
and injected into the main system.
The pressure
variation as the gas condenses is measured by the ion
gauge and recorded.
Due to the double expansion of the gas, the pressure
of the injected gas after it enters the main system, Pi,
is 6.5 x 10 - 6 of its original pre-expanded pressure as
measured on the manometer.
The manometer can measure pressures ranging from
1 inch of oil (1.7 mm Hg) to 24 inches of oil, and as
a result, Pi can vary from 1.56 x 10-4 mm Hg to
1.11 x 10-5 mm H.
-
15 -
Numerous difficulties were encountered during the
course of the experiment.
Many of them were due to the
fact that it was such a large glass system; for example,
several leaks developed.
The manometer also caused
trouble, as the carbon dioxide was apparently diffusing
through the oil into the vacuum side of the manometer,
and it was difficult to measure the pressure of the
carbon dioxide accurately.
i~l-i~Li
:i -~---;
~
_
4F
16
40
-
200
780
10-1
10-2
10-3
10-6
10-7
10-8
-IO1
I
FIG. I
2
5
50
20
10
TEMPERATURE OK
100
200
VAPOUR PRESSURE DATA FOR COMMON GASES
~L~
-
17 -
RESULTS
Due to the many problems in building the equipmnent
and running the experiment, there was not enough time
to obtain any data.
The only results which were obtained was in testing
whether the carbon dioxide would expand as calculated
(i.e.
without the cold surface in the main system):
Original pressure
in main system
Original pressure
Expected
Actual
(when evacuated)
of carbon dioxide
Pi
Pi
2 x 10 - 6
mm Hg
2 cm.
oil
1.lx10 - 5
mm Hg
1.2x 10 - 5
mm Hg
2 x 10 - 6
mm Hg
2 cm.
oil
1,1 x10 - 5
mm g
1.Ox10 - 5
mH Hg
In order to give some indication of what the
results should look like, curves were plotted for the
values
0( = i
o( = I
(1
(z,
time constant = 9.23 sec.) and
= 4.62 sec.) on the graph on page 18, with
Pi taken to be 10 x 10-6 mm Hg.
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-
CONCLUSIONS
One basic problem remains and that is the manometer,
as mentioned previously.
the oil with mercury.
A solution might be to replace
To make up for the fact that a
mercury manometer could not measure as low pressures as
an oil manometer could (the density of mercury is about
thirteen times the density of the oil), a second
expansion system could be built into the injection system.
Otherwise, it seems feasible that the experiment
could be run and the desired data obtained.
already indicated,
However, as
the scope would be very limited due
to the fact that liquid helium cannot be used.
i
mw
- 20
-
REFERNCES
i.
Chuan, Raymond L. "Rating Performance of a SpaceSimulation Chamber." Research/Development Magazine,
pp. 44-46, January 1964.
2.
Stickney, W. W., and Dayton, B.B. 'The Measurement
of the Speed of Cryopumps." Consolidated Vacuum Corp.
3.
Stokes, Andrew B. "The Measurement of Sticking
Coefficients of Various Gases to a Metal Surface
Cooled to Cryogenic Temperatures." M.I.T., B.S. Thesis,
Mechanical Engineering,
4.
1963.
Dushman, Saul. Lafferty, J. M., editor. "Scientific
Foundations of Vacuum Techniques." 2nd ed. New York,
John Wiley and Sons, Inc., 1962.
5.
Santeler, D. J. "Theory and Design of Cryogenic
Pumping Systems for Space Environmental Simulators."
Second Annual Symposium of Space Vacuum Simulation,
Arthur D. Little, Inc., June 16, 1961.
T-F
- 21 APPENDIX
Manometer Oil:
Octoil-S
specific gravity = 0.9103,
1 inch oil = 1.7 mm Hg
Expansion of Gas:
Volume of unexpanded gas sample = 8.0 cc.
Volume of injected gas sample = 7.6 cc.
Volume of gas after first expansion = 523.8 cc.
(Above two volumes plus volume of expansion chamber)
Volume of main system = 17,300 cc.
expansion expands the gas 67.5 times.
The first
The second expansion expands the gas 2,280 times.
The totnl expansion is therefore 1.536 x 105 times.
Area of Cold Surface:
0.326 cm.
2
-
22 -
Planned Detailed Procedure:
Aefering to the diagram on pale 13,
1)
Close valve 4, open valves 5, 6, and 7, and evacuate
expansion system through main system.
Turn valves
3, 6, and 7 until further turning does not affet the
pressure (but leave them open).
2)
Open valves 1 and 3, and evacuate rest of injection
system with mechanical pump.
3)
Close valves I and 3.
4)
Let in carbon dioxide very slowly by opening valve 2
very slightly.
This should force the manometer oil
all the way to the top.
5)
Open valves 2 and 3, and flood system with carbon
dioxide.
6)
Close valve 2 and evacuate once argain with the
mechanical pump.
7)
Let in carbon dioxide slowly by carefully opening
valve 2 until desired pressure is
8)
reached.
Take sample of unexpanded gas by closing valve 5
and opening valve 4.
9)
Expand gas by closing valves 4 and 7 and opening
valve 5.
10)
Close cut-off valve on main system (see diagram on
page 12).
_ ~_~_~ii;~
~
I
I -L--~enru~inEuB--
.
11)
23 -
Inject expanded gas into main system by closing
valve 6 and opening valve 7; record the pressure
variation.