The pumping theory of diffusion pumps - Pennsylvania State...

THE PUMPING THEORY OF DIFFUSION PUMPS By

G. T£

PHu IN$TITUTE, UNIVERSITY FOR TECHNICAL SCIENCES, BUDAPEST

(Presen ted b y A. K£ - - Rcceived 19. I . 1965)

Theories on the pumping effect of diffusion pumps assume an ideal gas t r anspor t by the jet , and so the diffusion sectas to be essential in the performance of pumps. To a t t a in correet numerieal results secondary effects ate supposed. Other theories t r y to examine the pumping effect on the ground of the collisions be tween gas and vapour molecules, bu t with the help of the "mean- f r ee -pa th" theory, which is not very easy to survey in this case, and not quite of universal val idi ty. This paper tries to handle the pumping effect wi th the aid of the kinet ic theory of nonuni form gases. On this ground ah equat ion is obta ined, which will be solved for ah ideal case. Thus ir will be possible to unde r s t and the pumping effect in a deeper manner , to verify the exper imenta l resul ts and to critically evaluate previous theories.

1. Introduction

The diffusion pump is one of the most important instruments to produce high-vacuum. Great advantage is its comparatively simple apparatus, robust- ness, its easy handling and economy.

Diffusion pumps have been developed over the past fifty years. In spite of this the theory of pump performance is not satisfactory. So diffusion pumps are designed and eonstructed with trial methods.

The sketch of a diffusion pump is shown in Fig. 1. Mercury or oil of high molecular weight are boiled in the boiler (a) and the vapour streams at high speed across the nozzle (c) into the pump chamber. Gas molecules having entered the pump from the container to be evacuated across inlet (e) interaet with the vapour molecules and by the vapour beam pass downwards towards the forepressure outlet and on the forepressure side (f) the backing pump exhausts them across (h). (For brevity the vapour of the pumping fluid will be called "vapour" and the material to be removed "gas", remarking, that the diffusion pump is suitable to remove vapours.)

2. Experimental results

Essential characteristics of pump performance are: forepressure toler- anee, pumping speed and ultimate vacuum. (Recently the backstreaming has been taken into aecount in pump performance, but this paper studies only

7* Acta Phys. Hung. Toro. XX . 1966

1 ~ G . T ~ H

the working principle of diffusion pumps, and the backstreaming can be neglected in this respect.)

The vapour pressure in the boiler is of the order of mmhg. To obtain a suitable jet one needs a forepressure under certain threshold. This threshold can be characterized b y the forepressure tolerance.

r161

_ " ' 11 II -~

Fig. I . Single-s tage diffusion p u m p

I

I Speed of the purnp [

ii ~oreprea~ure /o/emnco /or a given /e~

t/ea/inpuf (Arbifmr# unit~ )

Fig. 2. Effect of ehange in heat input on performance of diffusion pump

Forepressure tolerante is specified as the forepressure at which the inlet pressure increases 10 per cent at maximal throughput. The decrease of the forepressure tolerance with decreasing heat input at the boiler was found experimentally (Fig. 2).

Diffusion pumps ate able to sustain certain pressure drop between the pump inlet and forepressure outlet. Accordingly the inlet pressure depends on the forepressure (Fig. 3).

The ultimate pressure is the smallest pressure attainable by a pump. Practically the vapour pressure of the pumping fluid in the given circumstances will be the ultimate pressure because of the pump ability to hold

Ada Phys. Hur~. Toro. XX. 1965

THE PUMPING THEORY OF DIFFUSION PUMPS 101

a great pressure ratio, so a low forepressure. In practice thus baffles or cold traps are needed. The uhimate pressure and pressure ratio are shown in Fig. 4 for helium and nitrogen. According to former and the latest experiments the pressure ratio and so the attainable uhimate pressure are worse for gases of low molecular weight [2], [6], [14], [18]. To increase the pressure ratio a muhi-stage pump is applied.

r

t

~1o-7

1o-�91 f , , i J , r r

Forepreasure - mm h 9

r , l 10-1

Fig. 3. Forepressure tolerance characteristics for different heater power with oil diffusion pump DO-501 for hydrogen [14]

A significant characteristic of diffusion pumps is the speed defined by S ~ Q/P, where Q is the quanti ty of molecules streaming across the pump inlet per second, and P i s the pressure at the same place. Because of using always a known gas at a given temperature Q can be given in the forro Q = = PV, so S = 11, namely, the volume of gas streaming across the pump inlet per second [23].

The speed of a pump depends on the heat input (Fig. 2). The speed, because of being independent of pressure in a wide pressure range, (Fig. 5), is a characteristic of the pump at the smallest pressures as well. The peculiar pressure range is affected by the hcat input and the nozzle cross section (Fig. 6). The speed of a pump in given circumstances depends on the molecular weight of gases to be removed. There is a wide discrepancy in the data of literature in this rcspect. GmsoN [9] obtained for hydrogen the one third of the speed of air. SETLOW [18] obtained the speed of air for hydrogen but

1 1 only at high heat input; at normalhea t input he measured only-~ to~- of the

Acta Phys. Hung. Tom. X X . 1966

102 G. T‰

speed of air. NOELLER [14] and HENDERSON [10] obtained twice the speed of air for hydrogen using baffles and liquid nitrogen refrigcrations at the high vacuum side. FLUCKE [5] found in bis measurements ah increase of the speed

10-5

10"8

lO 7

10"9

10-~

1 0 J 1~ NRC HP ~ iO "7,

Einne• 1000F 10-8

CEC MHG gO0 / __

CEC PMC 1~40 ~" lO-S

~RC HP 1O

/,ooy...

10 -10 , , ~ J ~ ~ 1 0 4 0 i j i , ,

0 50 100 150 200 250 300 0 50 100 150 200 260 800 Forepres~ure - m/cron~ Forepres~ure - microna

eh b)

Fig. 4. a) Forepressure tolerance r for nitrogen; b) Forepressure tolerance characteristics for helium [10]

3000

2500 r

~ 2000 t

~ 1500

~ 1O0O

500

, , , , l . . . . I . . . . I . . . . I

lO-S lO-S 10-7 10-s i0-~ Partial pre~~ure o/ m/e/ oir - mm hg

Fig. 5. Speed of oil diffusion pump DO-8001 with baffle and co]d trap, pumping air [14]

at the tate I / M d2, where M i s the molecular weight: in the experiments he used liquid air refrigeration at the high vacuum side. According to DAYTO~ [2] the tate of speeds for hydrogen and air for a pump may be various, depend- ing on the design of pump the pumping fluid, the heat input and the fore pump capacity.

Pumps of different sizes have different speeds. The efficiency of a pump is estimated by the Ho-coefficient. The Ho-coefficient of speed factor is

.4cta Phys. Hunjg. Toro. XX . 1966

THE PUMPINO THEORY OF DIFFUSION PIYMPS 103

def ined as the ra t io of the speed measured at the inlet to the nozzle chamber to the ideal speed as calculated b y the kinet ic theory for the pump mouth . The ideal speed is identical with the speed of the perfect vacuum.

In the pressure region of diffusion pumps the behaviour of gases is molecular , thus the q u a n t i t y of molecules s t reaming in a given direct ion per seeond

1 per cm ~ is ~ nc by kinet ic theory ; where n is the number of molecules per cm 3,

c is the mean-speed. In the case of perfect v acu u m there is s t reaming only towards the perfect vaeuum, so the speed of the perfect v a c u u m at 20 ~ is

~oo

2o0

lOO 80

"~ 60

~ 2 0 a b

10-4 iO-O 10-2 lO -~ Pre~~ure-mmhg

Fig. 6. a) The width of the gap of the nozzle is small, the heat input is small; b) The width of the gap of the nozzle is small, the heat input is high; c) The width of the gap of the nozzle is high, the heat input is small; d) The width of the gap of the nozzle is high, the heat input

is h igh [1]

11,7 lit per sec per cm 2 for air and 44 lit per sec cm 2 for hydrogen. This quan t i t y is called the conduetance of the pump orifiee per cm 2 for the given gas.

The Ho-coeff ic ient of a well-designed pump is about 0,5. MXLI~EROr~ [13] found t ha t the a t ta inable Ho-eoeff icient for gases of low molecular weight might not be as high as for air.

3. Theories treating pump performance

Earl ier theories [71, [81, [11], [121, [15], [16], [20], [241 accept the diffusion as working principle of the pump. In GAEDE'S p u m p (Fig. 7) the diffusion occurs in tube AB. In modern pumps, according to [11], [12], [20], [24], the gas diffuses into the vapour beam at plane D (Fig. 8). This supposi t ion made it possible to unde r s t and why the pump speed is cons tant in a wide pressure range and why the p u m p speeds ate different for different gases.

This assumpt ion on diffusion, however , means a gas t r anspor t l imited on ly by the opening of the pump, which does not depend on the vapour jet .

Acta Phys. Hung. Toro. X X . 1966

] 04 G. T‰

To attain reasonably acceptable numerical results secondary effects are assumed (for example baek diffusion).

To understand the tole of the jet, more accurate investigation is needed. JAECKEL [11], [12] assumes backstreaming vapour molecules in the jet (Fig. 9), so he gets more exaet speed results than before. NOELLER [15], [16] examines

I I I I A - B

] ~ Cooling

Fi~. 7. Vacuum pumping by diffusion principle according to GAEDE

J

1 A

. . . . _D__ x-O

-xffiL

"lJ Fig. 8. Single-stage diffusion pump

the jet by the theory of gasdynamics, establishes the formation of shock waves owing to supersonic vapour flow. By this he can interpret the speed curve of diffusion pumps and the difference between diffusion and jet pumps as well.

The above theories assume tha t the diffusion occurs at the mouth of the pump. This assumption, however, may be argued against on the basis that the diffusion phenomena are created by the constant motion of the molecules; thus considering the motion of a single gas molecule ir may not be decided whether it takes place among vapour molecules possessing also a beam speed

Acta Phys. Hung. Toro. XX. 1966

T H E PUMPING T H E O R Y OF DIFFUSION PUMPS 105

in addit ion to t he rma l agitat ion, or it is inf luenced only b y moleeules of the rmal agi tat ion; and so "d i f fus ion" oeeurs all over the pump ehamber .

Thus it seems, it would be be t t e r to t r ea t this problem on the ground of the mot ion and eollision of gas and vap o u r moleeules by kinetie theory . This was attempted reeent ly [1], [3], [4], [17], but on the basis of not ve ry well-founded assumptions. Therefore the results of these theories cont radie t in some respeets the exper imenta l da ta (for example the u l t imate v a e u u m is,

A

Fig. 9. Single-stage diffusion pump

be t t e r for gases of low molecular weight aeeording to [4]), of t h ey ate empirical r a the r t ha n theoret ieal results.

4. The working mechanism by kinetic theory

I t is an obvious assumption t ha t the suetion effect of the diffusion pump is due to eollisions between gas and vapour moleeules. Moleeules possess an irregular molecular mot ion and eollide with eaeh other . Their speeds after eollision ate de te rmined by the speed before the eollision, the mass of the moleeules and the sort of the collision. Thus diffusion in this case means the pene t ra t ion of gas moleeules due to their t he rma l agi ta t ion into a spaee filled with other gas. Ir is evident t ha t the in tens i ty of the pene t ra t ion is influeneed b y the impaets with the moleeules of the o ther gas.

I f the veloei ty-dis t r ibut ion of the gas moleeules in the eonta iner to be evaeua ted is a Maxwell one, the mean molecular veloei ty is zero and no gas s t ream exists.

At the mou th of the pump the gas moleeules having the rmal agi tat ion enter the vapour of the pumping fluid possessing a s t ream veloei ty besides the rmal agi ta t ion and eollide with them. The mixture of gas and vapour moleeules is in eons tan t mot ion all over the pump chamber. Different velo-


106 Go T‰

cities and collisions of molecules exist. Thus it may be stated that the gas enters the vapour jet at every place x, not only at x = 0 (Fig. 8), as in the previous theories. This interaction of gas and vapour molecules causes the gas to flow to the forepressure side, well known from experiment. I t may be supposed tha t the interaetion influenees the velocity distribution of the gas and aceordingly gas flow is obtained in a given direction.

The working mechanism of the suction may be described as follows: the Maxwell velocity distribution of the gas ahers due to collisions between gas and vapour molecules, therefore a gas flow toward the forepressure side will exist.

In the following the gas flow in the pump chamber per unit cross section arca and time will be determined by means of kŸ theory [21], [25].

The investigations will be done on the ground of a pump model shown in Fig. 1.

Aceross the nozzle (c) a vapour beam of high speed streams into the pump chamber. The veloeity and density of the vapour depend upon x and y. Gas molecules enter the pump chamber aeross the pump mouth (e), interact with the vapour moleeules and accordingly they ate driven to the forepressure side (f).

The interaction will not be treated for single molecules, but the encoun- ters of gas and vapour molecules per unit volume and time at x will be invest- igated. The veloeity component of the vapour may be supposed not to cause any gas transport in the direction y, it only influences the density distribution of the gas.

Suppose that the gas has a velocity distribution function l i = f~(vl, x). I f it were known, the gas flow across unir cross-section and in unit time at x could be determined as

i ~- ] V l x f x d v 1 . (1)

Certainly fl is not a Maxwell velocity distribution function beeause the interaction with the vapour ahers the Maxwell distribution, and exactly this process resuhs in the pumping effect.

Ahhough f l is not known, expression [1] may be determtned from the Bohzmann equation:

~247 :o +~~(~:.)=I~ Ot v u , f ' L St Jcol,

(2)

Equation (2) will be more simple in our case because the force action is negligible, and the problem is one-dimensional and independent of time. Therefore:

Vlx ~'-'~- [ ~t Jcoll (3)

Acta Phys. Hung. Toro. XX . 1966


Let us expand fl into infinite series [21], [251:

Define

80

where

fx =f~0)q_ f~l) + . . . .

.l'fi dvi = Y fŸ176 =- ni ,

; I)2 A aV 1 = y v2f~ ~ dvi,

f (0) A l gr I e x p ( _ ~ 2 122)

zt3/2 2RT (4)

R is the universal gas constant, M i is the molecular weight, n a = ni(x ) the number density of the gas; T is the temperature.

The problem will be solved in second approximation taking only f~l) into consideration, f~l) may be expressed as [21]

f [ i ) = cvix [ exp (--fl~ v~),

where c = c(x) is independent of the velocity.

The veloeity distribution of the vapour is eonsidered in first approximation and we assume that every vapour molecule has a mean speed of beato speed v 0 = Vo(X ) besides thermal agitation. Owing to this:

s = A: . : exp [-/~~ (v2 - v0)21,

where ti2 and A z have the same meaning as in [4]: n 2 ---~ nz(x ) is the number density of the vapour.

On the left-hand side of (3) the term f~) can be dropped in comparison with f~o). Equation (3) muhiplied b y Vlx and integrated over all velocity space yields

1 dnl f [~t ] [ a i ] -2-fl 2 d~x- vlx fl dv~= (5) coll ~ t c011

The collision term is considered by examining how the impacts affect the gas flow. In the evaluation of the right-hand side of (5) the influence of collisions only with vapour molecules must be taken into consideration because collisions of the gas molecules with each other can have no effect upon the momentum of the whole gas.


108 G. T‰

Let the mass of a gas molecule be mi, its ve loci ty vi, m a and v 2 the re- spective values f o r a vapour moleeule, w the i r re la t ive veloci ty and u the veloei ty of thei r eommon center of mass. Then

u = , � 9 1 # 2 v ~ , w = v 1 - v 2 ,

//'�91 m2 /'�91 - - ' ~�91 - -

mi + m2 mi + m2

The mean value of the change in gas f low in a single collision is [25]:

A l = - -~2wx (1 - - cos 0 ) ,

where O is the angle with which the relat ive veloci ty deviates due to collision. The to t a l change in gas f low due to all collisions in a second is

q-~ zt

[Oi]=--2~;ffw~t2Wx(1--cosO) Gflf2sinOdOdvldV2, (6) " - ~ t coll

where G is the scat ter ing coefficient. Assuming a h a rd elastic sphere interaction, G is given by

where a 1 and a,, are the diameters of the molecules. To evaluate integral (6) the vaHables are ehanged f rom vi, v 2 to u and w,

and i t i s assumed t ha t the gas and vapour has the same tempera ture . This last assumpt ion has no influence on i, because the equal izat ion of t empera tu res of gas and vapour affects only the thermal agi tat ion of molecules and a t rans- por t is not affected.

After comput ing integral (6) the funct ion c (x ) in f(~~) m a y be determined f rom (5), a nd thus the gas f low m a y be de termined in second approx imat ion from (1).

i _ d n 1 v o qD~ (z ) + Vo ~v., ( z ) n ~ , (7) dx G n 2

~ l ( z ) =

92 (Z) =

z exp(z 2)

[4z 3 -- 2z -~ V ~ qS(z)exp(z 2) (1 + 4z4)]4 V~ '

4z 3 q- 2z + V ~ ~bCz ) exp(z 2) (4z 4 + 4z 2 - 1)

214z 3 -- 2z -~ V ~ q5(z)exp(z 2) (1 q- 4z4)]

Z---- ~2~U0 V ~ I ' (~(Z) = ~ e x p ( - - X 2) d x .

0

Acta Phys. Hung. Toro. XX. 19~6


The numerical values of ~0:(z) and ~2(z) at different beato speeds of vapour for hydrogen and air are shown in Table I. The necessary numerical da ta were taken from [1], [22], [24].

From (7) the in tens i ty of the gas flow i m a y be determined, i f the velocity and density distributions of the vapour are known. Computing i is difficult because ~v: and T2 depend upon x.

5. Calculation for an ideal pump

Qualitative s ta tements may be made if (7) is solved for the simple case when the velocity and densi ty of the vapour is constant , independent of x.

The ul t imate pressure of the pump is obtained by integrat ing (7) in the case of i = 0 :

n = e x p / G n 2 ~2 L ] = e x p [ a ] , (8) no ,~l

where n o i s the number densi ty of the gas at x = 0 (assuming tha t the x component of the beato velocity of vapour is zero at this point), n is the number densi ty at the forepressure side.

The gas at the forepressure side m a y be assumed to have a Maxwell distr ibution because at this place the effect of collisions wi th vapour molecules is neglected, thus the pressure P there is proport ional to the number densi ty: P = kn.

The number densi ty n o of the gas at x ~- 0 m a y be considered to be the same as the number density in the container to be evacuated, because the change in number density from the container to the pump mouth is negligible when compared with the change from x = 0 to the forepressure side. (Obviously the number densi ty of the gas decreases toward the pump inlet because of the vapour molecules being there in thermal agitat ion, and so the gas must diffuse through ir into the pump.) Assume tha t the pressure in the container is proport ional to the number densi ty n 0 : P 0 = kno, so

n P - - ~ - - ( 9 )

/tO P 0

We use da ta from [1] and assume tha t the speed of the vapour is con- s tan t and equal to t h a t at the mouth of the nozzle, fur thermore t h a t a mean vapour densi ty exists and tha t the speed of the vapour beato is exact ly the speed of sound. Taking L ----- 1 cm, we obtain 2 and 27 for the numerical value of (9) in case of hydrogen and air, respectively.

Consider the specific pumping speed obtained with the previous assumption.


110 G. T‰

I n t e g r a t i n g equ. (7), since i is cons tan t ( independen t of x) and according to (21) the speeific speed is

i v0~2[ n 1 s = - , - - e x p ( a ) - - , , (10) n o exp(a) - - 1 n o

where n ' a n d n£ are the gas n u m b e r densities a t the forepressure side and in the con ta iner (in this case n£ is also a p p r o x i m a t e l y the same as the dens i ty

a t x = 0 because n ' �87 n£ We ob ta in f rom (21) t h a t

exp (a) - -

8 0

n p - - �87 1 , ( 1 1 )

nO PO

( n' ~0/ s = v 0 ~2 1 - - , n . n o

(12)

The Tab le shows t h a t ~2 ~ 1. In the working range of diffusion p u m p s the t a t e of fore and fine pressures , n a m e l y the pressure ra t io in a wide pressure range is negligible to t h a t ob t a ined f rom (9) for the case of the u l t ima te

pressure:

?ff n - - 4 - - .

n ‰ n O

Thus

8 ~ 1 ) 0 �9

Therefore in this a p p r o x i m a t i o n the specific p u m p i n g speed is app rox - ima te ly equa l to the beato speed of v a p o u r a t the m o u t h of the nozzle. Aceording to da ta ob ta ined f rom [1], [22] this speed is abou t 2 - 1 0 4 to 6,8.10 4 cm/see, so the speeific speed is abou t 20 - -68 l i t /cm 2 sec. Ev iden t ly the p u m p m o u t h is not considered in this speed, therefore the t rue speed is

1 s ' - - (13)

1 1 '

$ $0

where s o is the specific conduc tance of the p u m p orifice. The p u m p orifice means the t u b e f rom x --~ 0 to the conta iner to be evacua ted . The value of s o f o r a shor t tube is 11,6 lit/see for air and 43 lit/sec for hydrogen a t 20 C o. The conduc tance m a y be smal ler due to v a p o u r mo]ecules above the j e t hav ing only t h e r m a l ag i ta t ion and the gas molecules m u s t diffuse t h rough t h e m f rom the conta iner to the p u m p .


T H E P U M P I N G T H E O R Y OF D I F F U S I O N PUMPS I 1 !

These numerical results show that the former solution of equ. (7) is of optimal value. Apart from this, useful qualitative results ate obtained from the ideal case.

Expression (8) gives a smaller compression capacity for gases of low molecular weight than for high ones.

lncreasing the density of the vapour increases essentially the compression capacity; increasing the beam speed has a role in increasing q02/~1, which also increases the compression capacity.

These resuhs allow us to interpret the experimental data. The Ho-coefficient for this ideal pump is smaller for hydrogen than for

air unless the speed of the vapour is twiee as great as the speed of sound. The number of air molecules pumped by such ah ideal pump is determined

by the diffusion of air molecules across the pump orifice (see equ. (13) and the value ofs 0 and s for air). Therefore such ah ideal pump may be called "diffusion pump" only for air. In the case of hydrogen the ideal pump having less then sonic vapour speeds is a "vapour pump", since now the role of the jet is essential due to the rate of s o and s in (13).

6. Results for real diffusion pumps

It is possible to obtain qualitative results for the performance of real diffusion pumps from the theory and calculations previously performed.

Since a sufficiently low forepressure is needed for forming a suitable jet, diffusion pumps work below a eertain forepressure. The decrease of the fine pressure also makes a change in the jet [15], [2]. To obtain an optimum jet a low fine pressure is necessary. (Further decreasing the fine pressure probably does not aher the jet essentially.) Reaching this condition the pump aehieves a maximum specific speed. Thus the growing parts of the speed funetions obtained by experiments may be interpreted with the change of the velocity and density distribution of the jet. With full knowledge of the distribution function of the vapour jet at any fine and forepressure values it should be possible to determine the speed by equ. (7). Once having this optimum jet the speed will be constant in a pressure range for whieh the bracket expression in (12) is about one. This circumstance exists for a wide pressure range if the uhimate pressure of the given pump is very small. Modern pumps can reach a very low uhimate pressure and, accordingly, their speeds ate eonstant in a wide pressure range (Fig. 5). This pressure range is narrower for H 2 than for air. Near the uhimate pressure the speed deereases. (In the term "uhimate pressure" the effect of the vapour pressure of the pumping fluid is not ineluded.)

Therefore to attain a comparatively high speeifie speed multi-stage pumps are required, especially in the case of light gases. In multi-stage pumps


112 G. T‰

the existing pressure drop in one stage is small compared to the compression capacity of the stage.

I t is evident that a high compression capacity does not assure a high specific speed, only makes it constant f o r a wide pressure range. In the case of gases of low molecular weight the compression ratio necessary for obtain- ing an opt imum jet and the compression capacity of the jet may be of the same order, thus increasing the compression capacity is needed.

Equ. (8) shows that this is attainable by increasing the jet density. B u t a n indefinite inerease of the jet density is impossible beeause the number of the vapour molecules coming into the pump mouth inereases and they hinder the motion of the gas moleeules into the pump so the speed of the pump decreases. This reasoning fits in with the experimental facts (Fig. 6).

There certainly exists ah optimum jet density. A higher density already hinders the motion of the gas molecules but a lower one does not exert a suitable eompression capacity.

Values of specific speeds published in the literature are very different. The reasons for this, beside the difference in pump constructions and testing procedures, ate the experimental eircumstances. Using cooled baffles and refrigeration traps the speed for gases of low molecular weight is higher than for air, because the speed is determined by the conductance of the pump mouth in this case [see equ. (13)], and it is higher for gases of low molecular weight. Ir the conductance of the pump mouth is much smaller than the suetion capacity of the pump, the rate of speeds for hydrogen and air is 3,8, according to the tate of conductances of the pump mouth for the gases in question. Ir the conductance of the pump mouth and the suction capacity of the pump ate of the same order but the latter is higher, different values for the tate of speeds for hydrogen and air should be attained but the speed for air would be higher. If there are no cooled baffles or refrigeration traps and the jet is not convenient the speed for hydrogen would be lower than for air since, as it was shown, ir the compression capacity of the pump is not satisfactory it is much lower for gases of low molecular weight and the speed decreases.

Using cooled baffles and refrigeration traps the speed of a pump will be constant f o r a wider pressure range beeause the diffusion stream across these obstacles is independent of pressure. Their conductances are much smaller than the suction capacity of the pump, thus according to (13) these smaller conductances determine the speed of the pump.

7. Conelusions

From the above theoretical reasoning it is easy to understand why some research workers believe that diffusion is dominant in the operation of pumps. In the original pump of GAS.DE the conductance of the pump mouth was

Acta Phys. Hun~. Toro. XX. 1966

THE PUMPING THEORY OF DIFFUSION PUMPS

Table I

113

Hydrogen -- Mercury .A_ir -- Mercury g1=0,01 ~�91

0,91 1,00

1,2 1,4 1,5 1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0 3,4

0,0091 0,010 0,012 0,014 0,015 0,016 0,018 0,020 0,022 0,024 0,026 0,028 0,030 0,034

0,33 0,26 0,23 0,19 0,18 0,16 0,14 0,13 0,12 0,11 0,10 0,091 0,085 0,072

1,23 1,00 1,01 1,01 1,02 1,02 1,00 0,99 0,99 0,98 0,98 0,98 0,97 0,96

3,73 3,85 4,39 5,33 5,67 6,38 7,14 7,62 8,25 8,91 9,80

10,90 12,14 13,25

0,12 0,13 0,15 0,18 0,19 0,20 0,23 0,25 0,28 0,30 0,33 0,36 0,38 0,43

~l(z) ~2(z)

0,081 1,03 0,070 o,96 0,057 0,95 0,047 0,92 0,043 0,91 0,039 o,9o 0,035 0,88 0,029 0,86 0,025 0,83 0,022 0,81 0,019 0,79 0,017 0,78 0,015 0,76 0,013 0,72

12,7 13,8 16,8 19,8 21,3 22,9 25,3 29,7 33,0 36,7 40,5 45,1 49,0 57,6

v e r y small, being capil lary; in the per formance of modern pumps cooled baffles and t raps are employed to p reven t backs t reaming and the conductance of the pump mou th decreases by this faet ; the conductance is always higher for gases of low molecular weight.

F rom our previous discussions it is clear t h a t there is no real fundamen ta l principle to d e s i g n a pump having a Ho-coefficient of the same value for hydrogen as for air.

I t is apparen t f rom the idealized model t ha t while the compression capac i ty is ve ry high, the specific speed is compara t ive ly small. Thus it m ay be expec ted for the deve lopment of pumps the favour ing of types having high compression rat io stages. I towever , an essential increase in specifie pump speed of I to-coeff icient is impossible; otherwise it has no impor tance due to cooled baffles and t raps .

Besides qual i ta t ive results quan t i t a t ive ones m a y be obta ined if some more detailed knowledge existed abou t the densi ty and veloci ty distr ibution of the je t and its a l terat ion.

The vapour s t ream from the boiler to the nozzle m ay be s tudied by the rmodynamics and this was a l ready a t t e m p t e d [19]. The vapour je t af ter leaving the nozzle m a y be de termined with the aid of gasdynamics or kinetic t h e o r y and then numerica l results m a y be obta ined with the help of equ. (7).

8 Acta Phys. Hung. Tom. XX. 1966

114 ~. T‰

P e r h a p s i t is possible to r e p e a t t he p rev ious p r o c e d u r e for the m i x t u r e o f

a gas a n d a v a p o u r b u t i t seems to be too c o m p l i c a t e d as yet .

The comple t e so lu t ion of the p r o b l e m shou ld m a k e ir possible to d e t e r m i n e

the o p t i m u m j e t for a p ressure r ange , the cross sec t ions of nozzle a n d p u m p

c h a m b e r a n d the neces sa ry bo i le r i n p u t . T h u s the des ign of p u m p s s h o u l d

be ba sed on theo re t i ca l g r o u n d s i n s t e a d of p u r e l y e x p e r i m e n t a l ones.

REFERENCES

1. P. ALEXANDER, J. Sei. Instr., 23, 11, 1946. 2. B. B. DAYTON, Rey. Sei. Instr., 19, 793, 1948. 3. N. FLORESCU, Vacuum, 4, 30, 1954. 4. N. FLORESCU, Vacuum, 10, 250, 1960. 5. D. FLtlKE, Rey. Sci. Instr., 19, 665, 1948. 6. A. FUJtNAGA, T. HANA$AKA and H. TOrTORt, Vac. Symp., 390, 1962. 7. W. GAEDE, Ann. Phys., 46, 357, 1915. 8. W. GAEDE, T. teehn. Phys., 4, 337, 1923. 9. R. J. GIBSON, Rey. Sci. Instr., 19, 276, 1948.

10. W. G. HENDESSON, J. T. MAaK and C. S. GEIGEa, Vac. Symp., 170, 1959. 11. R. JAECKEL, Z. Naturforsch., 2A, 666, 1947. 12. M. MATItlCON, J. Phys. Rad., 3, 127, 1932. 13. N. MILLERON, Vacuum, 13, 255, 1963. 14. H. G. NOELLEa, G. REIC~ and W. BXC]tLE~, Vac. Symp., 72, 1959. 15. H. G. NOELLEa, Z. Angew. Phys., 7, 218, 1955. 16. H. G. NOELLEn, Vaeuum, ~, 59, 1955. 17. L. RtvDtFOnD and R. F. Co]~, J. Sci. Instr,, 31, 33, 1954. 18. R. B. SETLOW, J. Sci. Instr., 19, 533, 1948. 19. H. R. SMtrH, Vac. Symp., 140, 1959. 20. L. WERTENSTEII~, Proe. Cainbr. phil. Soc., 23, 578, 1927. 21. S. C]~AeMAN and T. G. COWI~tNG, The Mathematical Theory of Nonuniform Gases, Cana-

bridge University Press, London. 22. S. DUSHMAN: Scientific Foundations of Vacuumtechnique, Budapest, 1959 (in Hungarian). 23. A. GUTHnIE and R. K. WAKEI~LING, Vacuum Equipment and Technique, MeGraw-Hill,

New York, 1949. 24. R. JAECKEL, Kleinste Drueke, Springer Verlag, Berlin, 1950. 25. E. Ff. KENNAnI), Kinetic Theory of Gases, MeGraw-Hill, New York, 1938.

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Acta Phys. ttung. Toro. XX. 1966

The pumping theory of diffusion pumps - Pennsylvania State...

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