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Adiabatic oscillations in liquid helium Machester, Frank Derek 1955

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4DIABATIC OSCILLATIONS IN LIQUID HELIUM II by FRANK DEREK MANCHESTER A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n PHYSICS We accept t h i s thesis as conforming to the standard required from candidates for the degree of DOCTOR OF PHILOSOPHY. Members of the Department of Physics. THE UNIVERSITY OF BRITISH COLUMBIA November, 19f?5. ABSTRACT. This thesis describes experiments designed to t e s t the p r e d i c t i o n made by J . E. Robinson that adiabatic o s c i l -l a t i o n s could be produced i n l i q u i d helium I I . O s c i l l a t i o n s have been observed i n an experimental arrangement consisting of an adiabatic container placed i n a helium I I bath and connected with the bath by means of a "superleak". A "thermal pulse" introduced into the contain-er caused the l i q u i d l e v e l to o s c i l l a t e . Containers of d i f f e r e n t geometries and employing two d i f f e r e n t types of superleak, were successfully used to observe o s c i l l a t i o n s . With one of these the temperature dependence of the f r e -quency was measured between 1 . 3 8 and 2*065 K and found to be of the expected form and magnitude. The damping of the o s c i l l a t i o n s , the rate of f l u i d flow and the thermal rel a x -ation of the container have also been investigated. Both q u a n t i t a t i v e l y and i n th e i r general behaviour, the observed o s c i l l a t i o n s confirm the predictions of Robinson. An analogy i s suggested between the o s c i l l a t i o n s i n an adiabatic container i n l i q u i d helium II and those of a gas i n a Helmholtz resonator. %\\t ISnitorsitg of Pri t is l) (Eohtmhk Faculty of Graduate Studies P R O G R A M M E O F T H E Jffirtctl ($ml Examination for ttye Jtegree of potior of ]$l}Uosoy\))y of FRANK DEREK M A N C H E S T E R M.Sc. (New Zealand) F R I D A Y , N O V E M B E R 25th, 1955, at 3:00 p.m. IN ROOM 300, PHYSICS BUILDING C O M M I T T E E I N C H A R G E DEAN H . F . ANGUS, Chairman J . B. BROWN H . P. MYERS F . A . KAEMPFFER H . M . DAGGETT J , M . DANIELS H . B. HAWTHORNE G. L . PlCKARD G. G. S. DlJTTON External Examiner—K. R. ATKINS University of Pennsylvania ADIABATIC OSCILLATIONS IN LIQUID H E L I U M II ABSTRACT This thesis describes experiments designed to test, the prediction made-by-J~. E . Robinson that adiabatic oscillations could be produced in liquid helium II. Oscillations' have been observed in an experimental' arrangement consist-ing of an adiabatic container placed in a helium II bath and connected with the bath by means of a "superleak". A "thermal pulse" introduced into the container caused" the liquid level' to oscillate* the mechanism being regarded as that of the inertia of the-superfluiduh- the.superleak, together with the re-storing force due to the thermo-mechariical pressure. Containers of different geometries and'employing'two different types of: superleak; were successfully used to observe oscillations.. With one.of these.the temperature dependence of the frequency was measured between 1.38 and 2.065°K and found to be of the expected form and magnitude. The damping; of: the-oscillations, the rate of fluid flow, and the thermal; relaxation, of. the container have also been investi-gated. Both quantitatively and in their general behaviour, the observed oscinations.cpnfirrn.the.' predictions of Robinson. An analogy is; suggested between the oscillations, irr an adiabatic con-tainer in liquid helium II and those of a gas in a Helmholtz resonator. PUBLICATIONS Adiabatic Oscillations in Liquid Helium .11 Canadian Journal of Physics 3.3, 146 ,(1955). Adiabatic Oscillations in Liquid Helium II Communications, Conference de Physique des basses temperatures, Paris (1955) G R A D U A T E STUDIES Field of Study: Physics Electromagnetic Theory W. Opechowski Theory of Measurement - A. M. Crooker Quantum Mechanics - - G . M. Volkoff Nuclear Physics K- C - M a n n Other Studies: Differential Equations .— - T- E. Hull Integral Equations _. -—. T - E - Hull ACKNOYffiEDGEMENTS. I wish to thank Dr. G. M. Shrum.for making i t possible for me to carry out graduate work at the Physics Department of the University of B r i t i s h Columbia. It is a pleasure to express my gratitude to Dr. J . B. Brown, my research supervisor during much of thi s work, for his active help and fo r many informative comments and discussions. I also wish to acknowledge the help I received from Dr. J . M. Daniels and the continued interest shown i n my work by Dr. P. A. Kaempffer. I am grateful to Mr. A. J. Fraser and l a t t e r l y Mr. H. Zerbst, for operating the l i q u e f i e r to produce the l i q u i d helium, often at considerable personal inconvenience to themselves. Mr. J . Lees performed the numerous glass blowing operations required and I am indebted to him for contributing much to the project through his patience and s k i l l . The members of the Physics Department.workshop s t a f f provided a great deal of help f u l advice and assistance with a variety of problems and for t h i s , I wish to thank them. To the members of the Low Temperature Group and p a r t i c u l a r l y Mr. G. Lamarche, I am indebted for the many occasions on which they gave help.with the experiments. I wish to r e c o r d my a p p r e c i a t i o n of the support given by the N a t i o n a l Research C o u n c i l , both by a grant f o r the experimental work and f o r the award of two Studentships. TABLE OP CONTENTS Page A CKN OWLED GEMEN T S. ABSTRACT. INTRODUCTION. 1 I. REVIEW OP ISOTHERMAL AND QUASI-ISOTHERMAL OSCILLATION EXPERIMENTS IN LIQUID HELIUM I I . 9 I I . THEORY OP ISOTHERMAL AND ADIABATIC OSCILLATIONS IN LIQUID HELIUM I I . 18 Theory of Isothermal O s c i l l a t i o n s i n Liquid Helium II H8 General Theory of O s c i l l a t i o n s i n Liquid Helium II and i n P a r t i c u l a r Adiabatic O s c i l l a t i o n s 22 Intermediate Cases of Non Ideal O s c i l l a t i o n s . 26 Helmholtz Resonator Analogue... 31 Curves f o r the Ideal Adiabatic and Isothermal Frequencies. 3k I I I . EXPERIMENTAL APPROACH AND THE APPARATUS. 37 Optical F l a t s Apparatus 38 Second Optical F l a t s Apparatus Lj.1 Glycerine Seal.. 1|2 Stroboscope Heater C i r c u i t ... 7^ Apparatus Used to Detect Temperature Differences ~. 1+9 Wire-Filled-Tube Apparatus 5U IV. EXPERIMENTAL PROCEDURE. 58 Outline of General F a c i l i t i e s for Experiments with Liquid Helium £8 Preparation for an Experiment and General Procedure 59 General Description of Adiabatic O s c i l l a t i o n s i n Liquid Helium II 63 Page Further Remarks on Experimental Procedure.... 6k Method of Taking Observations on Adiabatic O s c i l l a t i o n s 70 Visual' Observations • 72 V. EXPERIMENTAL RESULTS 73 Data Obtained with the Optical F l a t s Apparatus 73 Data Obtained with the Wire-Filled-Tube Apparatus 79 VI. CONCLUSIONS. 9k APPENDIX I. The Characteristics of "Leaded-Brass" Resistance. Thermometers.... •••• 97 APPENDIX I I . The Temperature S t a b i l i s i n g System 101 APPENDIX I I I . The Characteristics and Construction' of the Superleaks 10£ The O p t i c a l l y F l a t Discs 10$ The Wire-Filled-Tube ...... 109 REFERENCES. 116 LIST OP ILLUSTRATIONS. Pacing • Page Pig. 1 . I l l u s t r a t i o n of thermo-mechanical e f f e c t , isothermal and adiabatic oscillations.-.. 3 P i g . 2 . Isothermal o s c i l l a t i o n , A l l e n & Misener 10 Pig. 3 - Container parameters.......•. > ... 18 Pig. I|. Theoretical temperature- dependence of iso--thermal and adiabatic o s c i l l a t i o n frequencies 26 Pig . 5 - Adiabatic and aperiodic regions of solution, approximate 29 Pig. 6 . Adiabatic and aperiodic regions of solution, exact .... 30 Pig. 7* Temperature dependence of "resonator" frequency 32 Pig. 8 . The f i r s t o p t i c a l f l a t s apparatus.... 38 Pig.. 9 . Thermometer and heater arrangement f o r second o p t i c a l f l a t s apparatus Ill Pig. 1 0 . The second o p t i c a l f l a t s apparatus .,... • 1+2 P i g i l l . The stroboscope unit l|7 Pig. 1 2 . The temperature difference detecting system.. 1+7 Pig.13. The wire-f i l l e d - t u b e apparatus 55 Pig.llj.. The glass plug carrying the w i r e - f i l l e d - t u b e . 56 Pig. 1 5 . The s l i d i n g seal 57 I i P i g . l 6 . Experimental i n s t a l l a t i o n 58 Pig. 1 7 . O s c i l l a t i o n recorded with stroboscope 73 P i g . l 8 . General form of adiabatic o s c i l l a t i o n s 78 Pig , 1 9 » Temperature dependence of o s c i l l a t i o n frequency 78 Pacing Page Pig.20. Damping of o s c i l l a t i o n s 82 Pig.2 1 . Aperiodic f a l l of meniscus l e v e l 81+ Pig.2 2 . Relaxation times for aperiodic decrease 8 5 Pig.2 3 . Thermal balance of the container 87 Pig.21+. Plow rates during o s c i l l a t i o n 89 Pig. 2 5 . Steady f i l l i n g r a tes, o p t i c a l f l a t s apparatus 91 Pig.2 6 * Oscillogram of temperature difference produced by "thermal pulse"....,................,. 92 Pig.2 7 . C a l i b r a t i o n curve f o r resistance thermometer. 98 P i g . 2 8 . Current dependence of resistance •• 99 Pig.2 9 . Temperature s t a b i l i s i n g system • 102 Pig.30. Superleak cross-sections... 109 LIST OF TABLES. , Page Table I. Data used for p l o t t i n g t h e o r e t i c a l curves for Isothermal and adiabatic containers ...... 36 Table I I . Dimensions and geometrical factors for adiabatic containers 80 Table I I I . Experimental values of adiabatic o s c i l l a t i o n frequencies ... 78 Table IV. Thermal balance of the adiabatic container 80 INTRODUCTION 1 This thesis describes experiments designed to test the p r e d i c t i o n made by Robinson (1951)> that adiabatic osc-i l l a t i o n s could be produced i n l i q u i d helium I I , These adiabatic o s c i l l a t i o n s and the associated phenomenon of isothermal o s c i l l a t i o n s , together•form a sub-d i v i s i o n of the properties of l i q u i d helium II which may well be discussed as a whole. I t was the experimental work on isothermal o s c i l l a t i o n s which le d Robinson to provide a gen-eral" analysis of l i q u i d o s c i l l a t i o n s i n helium I I and t h i s analysis showed that the o s c i l l a t i o n s could be divided i n t o two types; the previously observed isothermal o s c i l l a t i o n s , A l l e n & Misener (1939)> Atkins ( 1950) , and a new type which he c a l l e d adiabatic o s c i l l a t i o n s . Before proceeding further, i t may help to give a very b r i e f review of those properties and concepts necess-ary for an understanding of the o s c i l l a t i o n s i n l i q u i d helium I I . In the l i q u i d helium II region, that i s at temper-atures below 2.l86°K, (the lambda p o i n t ) , l i q u i d helium may be regarded, at l e a s t from the phenomenological point of view, as being a mixture of two mutually interpenetrating f l u i d s ; the normal f l u i d and the super-fluid. The normal f l u i d i s broadly regarded as having the properties of l i q u i d 2 helium above the lambda point, that i s of a f a i r l y normal l i q u i d , while the superfluid has decidedly abnormal proper-t i e s . The r a t i o of the superfluid to normal f l u i d i s a function of- temperature and the 'superfluid concentration var-ies from zero at the lambda point to 100$ at absolute zero. This two-fluid concept, i n one or other of i t s several forms, has met with a good deal of success i n explaining the pecul-i a r and unique properties of l i q u i d helium I I . See Daunt & Smith ( 1 9 5 U ) . One of these properties i s that the l i q u i d w i l l flow through extremely f i n e channels with almost zero viscos-i t y , A l l e n & Misener (1939), even though the channel dimen-sions have been reduced to the order of 1 0 " ^ cm, or l e s s . On the two-fluid view i t i s the superfluid only which flows i n such channels, the normal f l u i d being immobilised by i t s v i s -c o s i t y . It has further been established, Kapitza (191+1), that the superfluid, when i t undergoes such motion c a r r i e s with i t an experimentally undetectable amount of entropy, so that at the present stage of our knowledge i t can be consid-ered to transport zero entropy. Because of t h e i r role i n superfluid flow, such f i n e channels may be r e f e r r e d to, for the sake of brevity, as "superleaks" or "entropy f i l t e r s " . , There are two important phenomena associated with superfluid flo.w and these are the two aspects of the one r e -v e r s i b l e e f f e c t . They are the thermo-mechanical e f f e c t , A l l e n & Jones (1938), and the mechano-caloric e f f e c t , Daunt & Mendelssohn (1939). These two e f f e c t s may be described by considering the following s i t u a t i o n . A small container i s placed i n a bath of l i q u i d helium II at a temperature T, and so arranged that l i q u i d can only flow between container and bath by way of a superleak. The container i s also designed so that i t i s well thermally i s o l a t e d from the bath. See Pig. 1 (A). I f now a quantity of heat i s supplied to the i n -side of the container, the normal-superfluid r a t i o w i l l change to that corresponding to some temperature T +• A T where i s the increase i n temperature of the container contents. There i s then a flow of superfluid through the superleak from bath to container, and t h i s flow of superfluid towards the region of higher temperature may be regarded as being i n ace cord with the-principle of Le Chatelier, that i s , the. super -f l u i d flows so as to restore the normal to superfluid r a t i o of the o r i g i n a l temperature T. There i s then an accumulation of l i q u i d i n the container and t h i s may b u i l d up a pressure head AP given by A P - A T f S where /0 i s the density of l i q u i d helium II and S i s i t s entropy at the temperature T. This i s H. London's equation f o r the thermo-mechanical e f f e c t , London (1939). The inverse of this e f f e c t may be understood by considering what happens when both the bath and the contents are at some steady temperature and superfluid i s made to flow from the container to the bath, as i t would i f the con-tainer were raised. The outflowing superfluid c a r r i e s away mass but no entropy, so that the s p e c i f i c entropy i n the con-tainer increases, that i s , the temperature of the helium i n the container r i s e s . This i s the mechano-caloric e f f e c t . The R o l l i n f i l m , the r e l a t i v e l y thick f i l m of l i q u i d which appears on surfaces i n contact with l i q u i d helium I I , i s also of interest i n considering o s c i l l a t i o n s . For the pres-ent purposes the f i l m i s i n t e r e s t i n g because i t may be r e -garded as a superleak and one which has a width an order of magnitude smaller (10~^ cm.) than the f i n e s t superleaks pro-duced by experimentalists. In the case of the f i l m the super-flow occurs over the surface of a body, and a container, f o r instance, i s f i l l e d by the flow over the rim of an open end. Both i n a r t i f i c i a l and "natural" ( i . e . the film) superleaks, the l i n e a r v e l o c i t y of superfluid flow i s quite high, e.g. up to 1+0 cm./sec. With the help of the above concepts, the mechanisms of the two types of o s c i l l a t i o n may now be described. Reverting to the previous simple picture of the con-tainer i n the helium bath, i t i s possible to consider two d i s -5 t i n c t s i t u a t i o n s . One when the container i s i n perfect ther-mal contact and one i n which the container i s p e r f e c t l y ther-mally i s o l a t e d from the helium bath. In the former case i t i s not possible to e s t a b l i s h a temperature difference between container and bath, so that any flow which takes place w i l l be without any accompanying thermal e f f e c t s . I f , f o r instance, the container i s raised from the bath, then the l i q u i d flows out through the superleak under the grav i t a t i o n a l pressure head established and the l e v e l of the container eventually reaches that of the bath. As, however, the v e l o c i t y of the superfluid i s quite large even for small pressure heads, the flowing superfluid possesses considerable momentum and the container level"overshoots the bath l e v e l . This s i t u a t i o n thus gives r i s e to o s c i l l a t i o n s i n which there i s a periodic interchange of energy between the k i n e t i c energy of the super-f l u i d i n the superleak and the poten t i a l energy of the d i f -ference i n l i q u i d l e v e l s of container and bath. These are the isothermal o s c i l l a t i o n s , see Pig.r::l (B). They have been observed i n two d i f f e r e n t arrangements. F i r s t by A l l e n & Misener ( 1 9 3 9 ) , using a container connected to the bath by a superleak and l a t e r by Atkins ( 1 9 5 0 ) , using a R o l l i n f i l m as the l i n k between container and bath. ( In the case of perfect thermal i s o l a t i o n of the container from the bath, i t i s now possible to maintain tem-perature differences during flow and the mechanism of the o s c i l l a t i o n s may be viewed as follows. When a displacement 6 of the l i q u i d l e v e l occurs, say upwards r e l a t i v e to the bath, the l e v e l i n the container seeks to return to i t s former po- • s i t i o n . Now i n t h i s case, the outflow of superfluid causes warming of the container contents due to the mechano-caloric e f f e c t and t h i s i n turn produces a temperature gradient . which tends to cause the flow of the superfluid back into the container as a r e s u l t of the thermo-mechanical e f f e c t . As again the moving superfluid posesses i n e r t i a , t h i s s i t u a t i o n produces o s c i l l a t i o n s . These o s c i l l a t i o n s occur immediately following the i n i t i a l displacement of the l i q u i d l e v e l , not upon return to the bath l e v e l as with isothermal o s c i l l a t i o n s . Of course, the g r a v i t a t i o n a l pressure head s t i l l plays a role i n adiabatic o s c i l l a t i o n s but i t i s very small compared with that of the thermal e f f e c t s . The general analysis of o s c i l l a t i o n s , isothermal, adiabatic and the intermediate aperiodic cases corresponding to varying degrees of thermal linkage between container and bath, has been provided by Robinson ( 1 9 5 l ) « The experiments to be described i n t h i s thesis have been aimed at establishing the existence of the adiabatic o s c i l l a t i o n s and examining t h e i r c h a r a c t e r i s t i c s . The o s c i l -l a t i o n s have been observed, Manchester (1955 &»b) i n two d i f -ferent experimental systems involving the use of two types of superleak. The dependence of the frequency of o s c i l l a t i o n on temperature has been investigated and has been found to agree 7 with the predictions of Robinson. Other features of the osc-i l l a t i o n s such as the damping, rate of f l u i d flow and thermal relaxation of the adiabatic container have also been studied. A l l i n a l l , the general picture forecast by Robinson i s very well borne out by experiment. An attempt was also made to detect the temperature o s c i l l a t i o n s associated with the f l u i d motion but t h i s was unsuccessful. In addition to the experimental work confirming the existence of adiabatic o s c i l l a t i o n s , a concept has been i n t r o -duced which brings together two f i e l d s of experiment i n l i q u i d helium II which have hithe r t o been regarded as very l i t t l e r e l a t e d . A formal analogy has been drawn between the o s c i l -l a t i o n s i n and adiabatic container i n l i q u i d helium II and the o s c i l l a t i o n s of a Helmholtz resonator i n a gas, as de-scribed by standard acoustical theory. This analogue brings closer together the phenomena associated with the flow of l i q u i d helium into a container v i a a superleak and those con-cerned with the r e l a t i v e motion of a super and normal f l u i d i n the bulk l i q u i d , as i n second sound. A review of previous experiments dealing with i s o -thermal o s c i l l a t i o n s i s given i n Chapter I, discussing par-t i c u l a r l y those points which are of in t e r e s t i n dealing with adiabatic o s c i l l a t i o n s . This i s followed by a treatment of the general theory of o s c i l l a t i o n s i n l i q u i d helium I I , both isothermal and adiabatic, i n Chapter I I . Chapter III 8 describes the experimental approach and the apparatus used, while Chapter IV deals with experimental procedures. The r e s u l t s are presented i n Chapter V and a general review and discussion of the work i s given i n Chapter VI. 9 CHAPTER I REVIEW OP ISOTHERMAL AND QUASI-ISOTHERMAL OSCILLATION  EXPERIMENTS IN LIQUID HELIUM I I . This review was o r i g i n a l l y undertaken to examine the experimental approach used i n previous o s c i l l a t i o n ex-periments, as a guide to designing an adiabatic o s c i l l a t i o n experiment, and also to see i f there was any evidence of non-isothermal conditions i n the experiments, wiich might pro-vide an i n d i c a t i o n that such conditions could a f f e c t o s c i l -l a t i o n s i i i the expected manner. Some features of the o s c i l -ations are also discussed because they are of intere s t to both isothermal and adiabatic o s c i l l a t i o n s . A l l e n & Misener (1939), were the f i r s t to observe o s c i l l a t i o n s i n l i q u i d helium I I , i n the course of t h e i r pioneering work on superfluid flow. They obtained a r e l a t i o n for the period of o s c i l l a t i o n and through i t used measure-ments of the o s c i l l a t i o n period to determine the cross-sectiohal area of the i r superleak. The cross-sectional area determined i n t h i s manner agreed f o r one case to within 30 perccent of an independent determination by gas flow methods and for another superleak of larger channel diameter i t agreed almost, exactly (see t h i s t h e s i s , Appendix IIlO>. This seemed to indicate that the mechanism of o s c i l l a t i o n had been correct l y represented as being due to the g r a v i t a t i o n a l p o t e n t i a l of the displaced l i q u i d and the i n e r t i a of the superfluid i n the e s o > 09 2 JL X 1 A A M V/\A P 0 J 1 2 3 ^ time (min.) P i g . 2 , Plot of an isothermal o s c i l l a t i o n reproduced from the paper by A l l e n & Misener ( 1 9 3 9 ) . A wire-f i l l e d - t u b e was used as the superleak. The period was 25 seconds at a bath temperature of 1 .20°K. facing page 10 10 superleak. A l l e n &nMlsener used an apparatus, see P i g . I (B), consisting of a narrow glass tube acting as container and a superleak made from a metal tube f i l l e d with a large number of very f i n e wires. Por d e t a i l s of the construction and f-c h a r a c t e r i s t i c s of these w i r e - f i l l e d tubes, see Appendix I I I . A p l o t of an o s c i l l a t i o n observed with A l l e n & Misener&s apparatus is shown i n Pig. 2. The o s c i l l a t i o n s are s l i g h t l y damped and t h i s damping w i l l be discussed further i n con-nection with some l a t e r experiments. Wo r e a l check can be made on whether the actual frequency observed by A l l e n & Misener was affected by lack of isothermal conditions, be-cause of the uncertainty i n the measurements of the cross-sectional area of the i r superleak. It i s conceivable that the required minute temperature differences could be sustain-ed because of the small thermal i s o l a t i o n provided by the j^lass container. The ro l e of the vapour phase as a medium of heat exchange i s such a s i t u a t i o n w i l l be discussed a l i t t l e l a t e r on. A'llen & Misener did intend.to discuss ther-mal e f f e c t s associated with the flow occurring i n t h e i r ex-periments, (see p. lj.82 of t h e i r paper) i n a subsequent pub-l i c a t i o n , but this was apparently never done. Apart from the actual mechanism of the o s c i l l a t i o n s , there are other aspects of t h e i r behaviour which are of i n -t e r e s t , for instance, the v e l o c i t y of f l u i d flow during o s c i l -11 l a t i o n . A l l e n & Misener's experiments were discussed from t h i s point of view by H. London (I9J46), who pointed out that the only two experiments up to that date which had involved superflow"within the rate - o f - f l o w - r e l a t i o n " , were t h e . o s c i l -l a t i o n experiments of Alle n & Misener and the double beaker experiment of Daunt &v:Mendelssohn (I9I46). This point w i l l be discussed more f u l l y i n connection with the present ex-periments i n Chapter V. The next experiments involving o s c i l l a t i o n s were carried out by Atkins. In these experiments Atkins used the R o l l i n f i l m as the superleak connecting the container to the bath and he used the o s c i l l a t i o n s as a means of studying properties of the f i l m . In this way, he investigated the height-thickness v a r i a t i o n and the dependence of the th i c k -ness at a f i x e d height on the temperature. This method pro-vided a dynamical method of studying these properties which was complementary to the o p t i c a l methods used by Jackson and his collaborators ( 1 9 5 1 ) . Apart from the data on the helium II f i l m , Atkins' experiments provide useful data on the o s c i l l a t i o n s them-selves. In the f i r s t place, great care was taken to minimise thermal effects associated with the l i q u i d flow so that the conditions could be regarded as being isothermal to a very 12 high degree. Atkins measured the temperature dependence of the frequency of o s c i l l a t i o n and found i t fc©" have a form sim-i l a r to that expected from the r e l a t i o n P where yOg and jD are the superfluid and bulk f l u i d densit-ies r espectively and COL i s the angular frequency of i s o -thermal o s c i l l a t i o n (see Chapter II f o r d e t a i l s ) . There i s some uncertainty i n t h i s p i c t u r e , however, as the f i l m does not provide a superleak with a cross-section which i s inde-pendent of temperature, so that the f i l m thickness v a r i a t -ion and the (/^/^) dependence are superimposed. Aside from this q u a l i f i c a t i o n however, these measurements are the most complete available of the temperature dependence of the frequency of isothermal o s c i l l a t i o n s . As Atkins points out i n his paper, a determination of the temperature dependence of frequency using a superleak with dimensions which were independent of temperature would e s t a b l i s h f o r certain whether the frequency would have the form (jOsjp} One other feature of the isothermal o s c i l l a t i o n s observed by Atkins i s t h e i r damping, which i s very s l i g h t and apparently less than that shown by the o s c i l l a t i o n s of A l l e n & Misener. Atkins has discussed the damping, and comes to the conclusion that at l e a s t the small damping shows that there i s very l i t t l e f r i c t i o n opposing the motion of the 13 flowing superfluid, and that i t s t i l l leaves open the poss-i b i l i t y that t h i s motion may be completely f r i c t i o n l e s s . Certainly, as Atkins remarks, no experiment can prove that f r i c t i o n a l forces opposing superfluid motion are zero, but an experiment can show that they are d i f f e r e n t i n magnitude from those predicted by a p a r t i c u l a r theory. He quotes as an exam-ple , that the Gorter-Mellink theory applied to the problem of the damping o f the o s c i l l a t i o n s i n his experiments predicts a damping which i s too large by a factor of about 10 . There are not only f r i c t i o n a l forces to be considered i n examining the causes of the damping, but thermal e f f e c t s also. In h i s experiments, Atkins reduced thermal e f f e c t s associated with the l i q u i d flow, by providing the container with a very t h i n copper bottom and also by arranging that the t o t a l amount of l i q u i d i n the container was large with respect to the dimensions of the tube i n which o s c i l l a t i o n s were observed. As an additional test to make sure that the thermal e f f e c t s could be neglected, Atkins measured the temperature depen-dence of the o s c i l l a t i o n frequency using two d i f f e r e n t volumes of the container, so that i f appreciable thermal e f f e c t s had been present, there would have been a noticeable difference i n the frequency. Such a difference was not found. Atkins estimated that the temperature difference between the container and the bath could not be more than 10"^°K at 1.^7°K and that this temperature difference would be mostly a t t r i b -utable to the thermal resistance of the s o l i d - l i q u i d boundary at the copper f o i l - the "Kapitza resistance". Ik Kasuya ( 1 9 5 3 ) , has proposed that t h i s thermal resistance can account for the Slight damping observed by Atkins, but although h i s explanation seems reasonable, there has been no published account given as to whether i t checks q u a n t i t a t i v e l y with ex-periment. Atkins has also observed o s c i l l a t i o n s i n wide cap-i l l a r i e s (e.g. i n t e r n a l diameter 0.6 mm.) as a means of es-timating the v e l o c i t y flow of the superfluid i n such channels and also the v e l o c i t y p r o f i l e across the tube, Atkins ( 1 9 5 l ) . There i s one further set of experiments which r e -ports the observation of o s c i l l a t i o n s i n l i q u i d helium II and these were carr i e d out by Picus ( 1953) ( 1 9 5 U ) . The r e -su l t s of these experiments are somewhat complicated but there are some features of i n t e r e s t for the study of o s c i l -l a t i o n s . In essence, the experiments concerned the empty-ing of a container through the helium II f i l m , under condit-ions where the l i q u i d i n the container was displaced by a loosely f i t t i n g plunger, the annular space between the plun-ger and the walls of the container being one millimetre wide. I f the plunger was set i n motion to displace the l i q u i d i n the container, o s c i l l a t i o n s of the l i q u i d l e v e l i n the an-nular space were produced, the form of these o s c i l l a t i o n s for any given temperature depending on the speed of the plunger. Also, o s c i l l a t i o n s occurred after the motion of the plunger was stopped, and i t i s these o s c i l l a t i o n s which are of i n t e r -15 est i n the present discussion. Picus displays the temperature dependence of the frequency of these o s c i l l a t i o n s i n Pig. 6 of his paper (be-cause of a prin t e r ' s error Figures 6&7 of his paper should be interchanged), the temperature dependence being not nearly so marked as that reported by Atkins and also showing l i t t l e theory for isothermal o s c i l l a t i o n s . In view of t h i s , i t be-comes of even more intere s t to carry, out an experiment on the temperature dependence of the isothermal o s c i l l a t i o n frequen-cy, using a superleak of constant dimensions. The damping of these o s c i l l a t i o n s i s i n t e r e s t i n g because i t i s greater than that reported by A l l e n & Misener and by Atkins, the d i f f e r -ence being p a r t i c u l a r l y noticeable between the experiments of Atkins and Picus as both used the helium II f i l m as the flow path. There were differences i n container geometries between the two experiments and also i n the precautions tak-en to ensure isothermal conditions, so that i t i s d i f f i c u l t to e s t a b l i s h the reasons f o r the difference i n the observat-ions. It i s , however, worth noting that Picus didn't take precautions to ensure isothermal conditions during the flow and that the damping was much greater than Atkins observed. Such damping could be expected from quasi-isothermal condit-ions where thermal effects can play a r o l e . Temperature equalization through the vapour phase plays a very important part i n making the o s c i l l a t i o n s isothermal, but i t seems s i m i l a r i t y to the form expected from the simple 16 possible that i f the above effects are due to quasi-Isother-mal conditions, then there i s something about the evaporat-ion-condensation process that permits some thermal i s o l a t i o n when the temperature differences are very small. The o s c i l -l a t i o n s observed by Allen & Misener are probably also a f f e c t -ed i n thi s way. The damping of o s c i l l a t i o n s w i l l be discus-sed further i n Chapter V. In summary, o s c i l l a t i o n s have been observed i n prev-ious experiments using two types of superleak, the helium II f i l m and the w i r e - f i l l e d tube. A l l these o s c i l l a t i o n s have been of the isothermal kind inasmuch as there has been no non-clear cut evidence of the presence of any f tisothermal e f f e c t s . With a l l the observations, the damping of the o s c i l l a t i o n s has been present and the degree of damping has varied with the p a r t i c u l a r experiment, the main question here being to discriminate between f r i c t i o n a l forces i n the l i q u i d opposing the superfluid flow and thermal e f f e c t s which provide an opposing thermo-mechanical pressure, for instance, i n the case envisaged by Kasuya. The question of whether the f r a c t i o n P&JP i s the same i n superleaks as i n the bulk l i q u i d i s s t i l l not f u l l y answered, but with t h i s proviso, the tem-perature dependence of the isothermal o s c i l l a t i o n s has been measured and th e i r mechanism e s s e n t i a l l y explained. With the exception of the work of Picus, the above experiments had been done at the time Robinson published h i s 1 7 general analysis,of o s c i l l a t i o n s i n l i q u i d helium I I , which included both isothermal and adiabatic o s c i l l a t i o n s as the two extreme cases. Because the adiabatic o s c i l l a t i o n s had hot beenobb< served at a l l , i t was decided to design an experiment to see i f the o s c i l l a t i o n s could be produced and then to attempt to investigate their properties. Certain of the questions r a i s e d i n the review of isothermal o s c i l l a t i o n s can be discussed with regard to the adiabatic o s c i l l a t i o n s and t h i s w i l l be done i n a l a t e r chapter. Pig. 3 . Container parameters for (a) isother-mal, (b) adiabatic containers and (c) Helmholtz resonator. facing page 18 CHAPTER II 18 THE THEORY OF ISOTHERMAL AND ADIABATIC OSCILLATIONS IN LIQUID HELIUM I I . F i r s t of a l l a s i m p l i f i e d treatment of the theory of isothermal o s c i l l a t i o n s w i l l be given, including some com-ment on issues which have arisen i n connection with t h i s treatment. Next the general analysis due to Robinson w i l l be presented, with some minor modifications to take account ©£> the geometrical arrangement used i n the actual experiments. F i n a l l y , the equation for the frequency of i d e a l adiabatic o s c i l l a t i o n s w i l l be shown to be analogous to that f o r the frequency of resonance of a tfelmholtz resonator as given by standard acoustical theory. The Theory of Isothermal O s c i l l a t i o n s i n Liquid Helium I I . "Referring to F i g . 3' (A), consider a container to be immersed i n a bath of l i q u i d helium II and connected to the bath by means of a superleak. For the present discussion i t w i l l be supposed that i n some way the flow of l i q u i d through the R o l l i n f i l m has been prevented and that only flow through the superleak i s being considered. As has been stated previously, o s c i l l a t i o n s may be regarded as being produced by the res t o r i n g force of g r a v i t -ation proportional to the l e v e l difference, and the i n e r t i a of the l i q u i d moving i n the superleak.. Consider the l i q u i d x 9 i n the container as being at some height x. above the equilibrium p o s i t i o n which i s taken to be l e v e l with the bath l i q u i d . The r e s t o r i n g force i s equal to A^px where A i s the area of the l i q u i d surface i n the container, the acceleration due to gravity, f> the bulk density of l i q u i d helium and % the l e v e l d i f f e r e n c e . The p o t e n t i a l energy of the displaced l i q u i d i s then P.E. - k A ^ x 2 . Assuming only the superfluid can move i n the superleak where vs i s the v e l o c i t y of the superfluid, ST the super-leak cross-sectional area. The k i n e t i c energy of the moving superfluid i s then given by where Z> i s the length of the superleak. Prom these two expressions, the frequency of isothermal o s c i l l a t i o n can be obtained as that of a harmonic o s c i l l a t o r with a frequency where i s the angular frequency of isothermal o s c i l l a t i o n at absolute zero and may be regarded as a geometry f a c t o r . A l l e n •& Misener deduced an expression equal to <A> as the normal-superfluid d i v i s i o n had not been introduced at the 20 time of their experiments. Atkins, i n his work with the helium II f i l m as superleak, deduced a r e l a t i o n for OJc i n which he took into account the v a r i a t i o n i n thickness of the f i l m with height and i t i s equivalent to the above expression i f a constant thickness for the f i l m i s assumed. Alternative expressions for U)c based l a r g e l y on Atkins' analysis have been ob-tained by Dash (195H») and by Picus (19£li). cised by Kaganov & Eselson (195>l) who disagreed with Atkins on the application of Euler's equation to the motion of the f l u i d i n the f i l m . As a r e s u l t of a l t e r i n g the equation, they obtained a v a r i a t i o n of the f i l m thickness with temper-ature, at a height of 1 cm., which they claimed i s more i n agreement with the o p t i c a l measurements of Burge & Jackson ( 1 9 5 D . Dingle, (see Daunt & Smith (195U) p.206), i n a p r i -vate communication, has shown that Atkins' derivation i s the correct one for the assumptions which were made. This matter w i l l be dealt with here, because i t i s important i n the de-duction of the equations of the motion of the superfluid i n a superleak. Atkins' analysis i n his o r i g i n a l paper was c r i t i Kaganov & Eselson state that Atkins should have written the Euler equation i n the form 21 whereas Atkins wrote the.equation with p instead of ^ >s on the r i g h t hand side. That Atkins i s correct, provided that the assumptions are made that the composition of the l i q u i d i n the f i l m or superleak i s the same as that of the bulk l i q u i d , and that i t i s the superfluid part only which moves, may be seen from the following. Consider the force acting on an elementary volume of l i q u i d helium II which has the composition Psjf* cor-responding to some p a r t i c u l a r temperature and i s subjected to a pressure gradient acting along the po s i t i v e d i r e c t i o n of the X axis. Then as the force i s e f f e c t i v e on the superfluid f r a c t i o n only. It follows that •D-^s - - > g-nxcL p Dt /> which i s the form used by Atkins. I f an analysis based on the above assumptions does give agreement with experiment, there i s j u s t i f i c a t i o n for accepting them. Atkins' experiments, as mentioned before, do provide some supporting evidence and the r e s u l t s of the work on the temperature dependence of the adiabatic o s c i l l a t i o n s also seem to add further support. 22 The General Theory of O s c i l l a t i o n s i n Liquid Helium II  and i n P a r t i c u l a r the Adiabatic O s c i l l a t i o n s . In the case where the container is thermally i s o -l a t e d from the bath, a temperature difference can occur be-tween container and bath so the thermo-mechanical and mech-ano-caloric effects have to be considered as well as gr a v i -t a t i o n . The following analysis due to Robinson (193>1) i n -cludes these e f f e c t s . The equation of motion f o r the superfluid for the case of small v e l o c i t i e s , Daunt & Smith (1951+) p. 219, i s : i dt P Equation (1) gives the force acting on unit volume, i t being p a r t l y thermal and p a r t l y mechanical. The symbols have t h e i r usual s i g n i f i c a n c e , ft^P a r e t J a e superfluid and bulk f l u i d d e n s i t i e s , "U"s i s the superfluid v e l o c i t y , p i s the pressure, S the entropy of the bulk l i q u i d and T the absolute temperature. In the above, i t has been assumed that the entropy of the superfluid can be put equal to zero. Referring to F i g . 3 (B), i f X, i s the length of the superleak, and T~, the vapour pressure and temperature i n the container and % the l e v e l displace-ment, then equation ( l ) becomes 23 I f the assumption i s made that the normal f l u i d i s completely immobile i n the superleak, then . v u = pay. where 01 i s the cross-sectional area of the c a p i l l a r y i n which the o s c i l l a t i o n takes place and v~~ i s the cross-sectional area of the superleak. Substituting t h i s f>°£± +• «,* + fcife, - S(T-T 0 ) -O (2) Is P the entropy balance for the container may be expressed as / O s v -ST ; v a -\~ yoC(v+"AV^T" +- K ( T - T 0 ) ~ O . (3) where V i s the volume of the container, C the s p e c i f i c heat of helium II and K i s an assumed thermal leakage be-tween container and bath. I f AY i s considered small com-pared with V (3) becomes ^ a x X S +- pCVT +• K(T-TO-) - O which may be written as X +• T +- KX - O and f i n a l l y as X + t +- L.T - O (U) where T =• C T - T 0 ) V C on.dL L - _ K _ a T o S t°vc 21+ geturning to equation (2), the quantity ^-JD0 raay D e e x ~ pressed i n terms of the derivative of the vapour pressure curve., v i z : so that equation (2) becomes where use has been made of the r e l a t i o n for the isothermal o s c i l l a t i o n frequency for the present container P % Equation (2) f i n a l l y reduces to where I1 psUr/^J Equations (1+) and (£) x -r- T +•• LT" — O (^) X -r-U)fx -<*£#r =-0 are l i n e a r , homogenous, simultaneous d i f f e r e n t i a l equations with solutions of the form: A X t r * B e i 2 5 Substitution gives the secular equation^determining the t values of X X3 t U ( l t ^ ) +- X^L +- L u £ - O ( 7 ) Two cases for the solution may now be discussed. F i r s t l y i f L.-5>oo that i s , i f there i s complete heat exchange between . container and bath, then and th i s i s the solution for the isothermal o s c i l l a t i o n s . For the 1 case where L - 0 that i s , complete i s o -l a t i o n , or the i d e a l adiabatic case, then . '4 X - O cLwdl X - i i o A \ -HSC) are solutions. Thus the frequency of the adiabatic o s c i l l a t -ions i s The solution for X-O i s a s t a t i c one and through equation (I4) i t gives the equilibrium condition for the thermo-mechanical pressure X-o^oCl^ The general solutions are o s c i l -l a t i o n s of the l i q u i d l e v e l of frequency OJo. about an equilibrium p o s i t i o n Xa given by the temperature difference and o s c i l l a t i o n s of the temperature difference, also of f r e -quency U)A. about the mean value or s t a t i c temperature . difference given by T£ . 10 12 1-4 < J 6 T K 18 2 0 2 2 P i g . 1+. T h e o r e t i c a l temperature dependence of iso-thermal and a d i a b a t i c o s c i l l a t i o n f r e q u e n c i e s . f a c i n g page 2 6 26 The v a r i a t i o n of CJo. and u)c with temperature i s shown i n Pig. 1|; these curves were calculated from the r e l a t -ions given above, using the dimensions of the apparatus which was used i n the present experiments. The p l o t t i n g of these curves w i l l be described i n more d e t a i l l a t e r i n t h i s chapter. T3ie Intermediate Cases of Non-Ideal O s c i l l a t i o n s ; Returning to consider the secular equation (7) again, the more general class of solutions, (6), i s obtained by considering the values of L other than zero or i n f i n i t e l y l a r g e . The general solution of the secular equation so ob-tained then allows various regions of the solutions, (6), to be established. I f A, i s the discriminant of (7), then the classes of solutions are divided according to the sign of A I f : A less than zero, one root r e a l and two complex -o s c i l l a t o r y region. A greater than zero, three roots a l l r e a l and unequal -aperiodic region. I f X=la-b i s substituted i n (7) and r e a l and imaginary parts are equated to zero, then a* - 3b2 +• 2bL - u)<Z - O (9) 27 and b 3 _ a z ( 3 b - L ) - b * L +U&\> - ( J t L - O ( 1 0 ) where a=0 is also a solution corresponding to the r e a l root. Now i f X=la-b i s a root \--Cd-b i s also a root so that z 2 X . X * =• a +• b and from the theory of equations so that i n the o s c i l l a t o r y region, the r e a l root X 3 corres-ponding to an aperiodic solution i s given by X 3 =• - k ^ L - ( i i ) a b In the ideal adiabatic case, L - 0 ; Xj i s zero and the damp-ing w i l l also be zero, so that again from the theory of equations A - ( x , - x ^ - x 3 ) z ( x 3 - x ) = - 4 - ^ Thus, for the i d e a l adiabatic case, A is" nega-t i v e and the solutions (6) are o s c i l l a t o r y . The solutions w i l l continue to be o s c i l l a t o r y up to some value of L, at which A changes sign and then the roots w i l l be r e a l and give aperiodic solutions. This behaviour w i l l be discussed using the approximations used by Robinson i n his analysis, because they show the form of the solutions i n the simplest 28 possible manner; the more detailed picture can be indicated l a t e r . Equations (9) and (10) may be expressed i n reduced units of (JL-U. for convenience; of - 5b2" +- ZbL - I * O (9)a b*-'3bo& ^ a a L - b a L +-b- » O (10)a where the approximation has been made that the l a s t term i n (10) may be neglected because LL)<X » Eliminating L between (9)a and (lo)a gives o f - r b * - I (12) and using t h i s i n (9)a while (13) gives (13) Hie Thus equations (13) and (li+) give^L dependence of a and b i n reduced u n i t s . Making use of (12), the aperiodic root may now be written as i n the o s c i l l a t o r y region To f i n d the beginning of the aperiodic region, put <X~ O i n equations (9)a and (10)a; o I I I ! " I 1 I T 1 1 / 1 1 " i / m 1 / 1 / i / i # A D I A B A T I C • • i / / A P E R I O D I C R E G I O N I f 1 R E G I O N o// IS ^^ ^^ ^ / 1 • 1 l' 1 • 1 I l i 1 1 1 1 1 10 2 0 3 0 F i g . Adiabatic and aperiodic regions of solut-ion, approximate case. The aperiodic root (equation (11) ) i s not shown. facing page 2 9 2 9 from ( 9)a, b ( 1 5 ) 3 from (10)a, b 2.' (16) Equation (15) i s exact whereas equation (16) incorporates the approximation that UX. Prom (16), i t can be seen that b has r e a l values only for L^Z and that above Z_=2. the roots of (7) are obtained from (16) and a r e l a t i o n s i m i l a r to (11). The values of a l l the roots i n the adiabatic o s c i l l a t -ion and adjacent aperiodic region are shown i n Pig. 5« A complete scheme showing isothermal o s c i l l a t o r y solutions as well i s given i n Robinson's paper. not be made, which i s so for the apparatus used i n the exper-iments, the dependence of a and b on L i s not so simple and requires much more arduous c a l c u l a t i o n . The. value for L at which the t r a n s i t i o n from the adiabatic to aperiodic region occurs i s given by (15>) to be L = 1 . 7 3 2 , and while the L. de-pendence of the b values i n the aperiodic region has the same form, the values themselves are appreciably d i f f e r e n t . In the periodic region, equations (9) and (10) do not permit of much s i m p l i f i c a t i o n , so the dependence of each on L has to be calculated by f i n d i n g the b values from In the case where the approximation Cj a >»CJ <; can o 1 1 1 1 ADIABATIC REGION 1 1 1 1 1 1 1 1 A' / AD*— o j / l / b/ APERIODIC _ REGION 1 1 1 1 1 1 1 1 O 10 2 0 3 0 Pig. 6. Adiabatic and aperiodic regions of solution, exact case. The aperiodic root (equation (11)) i s not shown. facing page 30 which was obtained by eliminating a between (9) and (10). The a values are then found from (9). The appearance of the curves for a and b at a temperature of 1.700C K for the ex-perimental container used i s shown i n P i g . 6. The L values for the t r a n s i t i o n from per i o d i c to aperiodic regions may be obtained from an examination of the discriminant, as was done by Robinson, although i n h i s case, he made use of the approx-imation t O c L » t O c * Thus the solutions of (1+) and (5) can be obtained for a l l values of 'L. The three regions of the solution found f o r equations (I|) and (5) , are p a r t i c u l a r cases of the solution to the general problem of the movement of the super-f l u i d between ahcontainer and a l i q u i d helium bath. The par-t i c u l a r behaviour encountered when such movement i s carried out, w i l l depend on the thermal linkage between the contain-er and the bath and also on the v e l o c i t y which the superfluid a t t a i n s . In the periodic regions, the general solu t i o n of (i|) and (5) f o r the meniscus l e v e l r...>^  may be written as x =- Aebtoa(at-^) 4- B e _ L ^ (18) where A, B and >^ are a r b i t r a r y constants. This represents an aperiodic decrease of temperature and pressure differences between bath and container, with the damped o s c i l l a t i o n s superimposed on t h i s . In general i n the adiabatic region, as the damping term for the o s c i l l a t i o n i s much larger than that 31 f o r the aperiodic decrease, the o s c i l l a t i o n s w i l l die out, before the l i q u i d l e v e l i n the container reaches that i n the bath, whiLeein the isothermal region, the l i q u i d l e v e l i n the container w i l l a t t a i n that of the bath before o s c i l l a t i o n s occur. The case of steady flow between container and bath i s also included i n the solutions. • This then i s the picture of o s c i l l a t i o n s i n l i q u i d helium II which is. given by Robinson's analysis. The Helmholtz Resonator Analogue. Equation (8) which gives the frequency of the i d e a l adiabatic o s c i l l a t i o n s , - A . may be s i m p l i f i e d by making two approximations; that 0< may be written g-vc Then P f^J \!p i\f " c / and making use of the Landau r e l a t i o n f o r second sound v e l -o c i t y , (l?4l) ut - fit TSa 'p~ c 4 F i g . 7 . Temperature dependence of "resonator" frequency. facing page 32 3.2 the expression for ( J * . becomes This gives the frequency for ideal adiabatic o s c i l l a t i o n s , assuming that U)<L »CJC and neglecting the e f f e c t of the vapour pressure over the l i q u i d i n the container. This r e -l a t i o n is pl o t t e d i n Pig. 7 for the container used i n the ex-periments. I f equation ( 1 9 ) is compared with the s i m p l i f i e d r e l a t i o n fgp the frequency of resonance of a Helmholtz reso-nator which holds i n the case of.long wavelengths; Stewart & Lindsay ( 1 9 3 0 ) , a close correspondence i s found. For such a resonator, the frequency of resonance i s given by •4. = c ( | e ) ( 2 » where C is the v e l o c i t y of sound, S the cross-sectional area of the resonator neck, or opening, the e f f e c t i v e length of the neck and V the volume of the resonator, see F i g . 3 (C). There i s good reason, therefore, for regarding the adia-bati c container i n the second sound f i e l d as being analogous to the Helmholtz resonator i n the f i r s t sound f i e l d ; both be-ing considered l o r the long wavelength case only. The reson-ances considered here are of the p i s t o n - l i k e motion of gas i n the one case and superfluid i n the other, not the shape de-pendent cavity resonances, such as are used to produce stand-33 i n g waves i n a c y l i n d r i c a l tube say, as i s commonly done i n v e l o c i t y measurements. I t i s necessary to nave a superleak for the "neck" i n the second sound, case because the pmston-l i k e motion has to be one of r e l a t i v e motion between super-f l u i d and normal f l u i d . Considered from this point o^ view of association with second sound, the adiabatic container may be thought of either as a resonator or an o s c i l l a t o r . As an o s c i l l a t o r emitting r a d i a t i o n , i t could be thought of as a source sim-i l a r to that used by Peshkov (191+8), who placed a superleak i n front of a mechanical transducer emitting f i r s t . s o u n d , so that r e l a t i v e motion of super and normal f l u i d was produced and the device acted as a source of second sound. The sug-gested "adiabatic o s c i l l a t o r " may also' be thought of as the f i r s t example of an o s c i l l a t o r being excited to i t s nasural frequency i n the f i e l d of second sound i n helium I I , and quite d i s t i n c t from a transducer or a resonant cavity. Several authors, Dingle (191+8), Osborne. (1951), Pellam (191+8) (191+9), Peshkov (I9I+8), have commented on or made use of, analogies between second sound propagation and e l e c t r i c a l transmission l i n e s . Pellam and Dingle have used transmission l i n e theory i n analysing R e f l e c t i o n and trans-mission of second sound at boundary surfaces, and Temperley (1951) and Osborne have noted the analogy between shock-waves i n l i q u i d helium I I and shock waves i n ordinary sound 3k theory. The Curves for the Ideal Adiabatic and Isothermal  1 Frequencies. Returning to equation (8), i t may be expressed i n a form which i s convenient f o r c a l c u l a t i o n by making use of the results just obtained: where and kJaH i s the i d e a l adiabatic o s c i l l a t i o n frequency or resonator frequency. To obtain the values of U)c} 6 j a ^Ja//. f o r the experimental apparatus i n which the measurements were made, the following experimental data were used. Values of ^/jo and ^/p i Peshkov (191+6) Second sound v e l o c i t i e s ; smoothed values quoted by Band & Meyer (191+8) and by Maurer & He r l i n (191+9) Entropy of l i q u i d helium I I ; Kramers et a l ( 1 9 j ? 2 ) Vapour pressure of l i q u i d helium I I ; Bleaney & Simon ( 1 9 3 9 ) The method of c a l c u l a t i o n used above has the advantage that i t i s . v e r y i n s e n s i t i v e to the values chosen f e r the entropy 35 and s p e c i f i c heat, which are somewhat uncertain at the pres-ent time, Brewer, Edwards & Mendelssohn ( 1 9 5 5 K The data used i n p l o t t i n g the graph of Fig.lj. are given i n Table I. 36 TABLE I. T k kJc. W a H CL>O. °K radians /sec radians /sec radians /sec 1.0 0.91+6 2.50 0.1+99 2.55 1.1 0.928 2.L+9 0.681+ 2.58 1.2 0.923 2.1+7 0.952 2.63 1.3 0.920 2.1+5 1.27 2.7U i . U 0.919 2.1+1 1.66 2.89 1.5 0.920 2.36 2.11 3.11 1.6 0.921 2.27 2.61+ 3.1+0 1.7 0.923 2.17 3.11 3.69 1.8 0.925 2.05 3.51 3.95 1.9 0.928 1.86 3.81 1+.12 2.0 0.932 1.60 3.91 1+.10 2.1 0.936 1*16 3.30 3.1+0 2.15 • 0.79 2.32 • 2.19 • 0 0 0 CHAPTER I I I . 37 THE EXPERIMENTAL APPROACH AND THE APPARATUS. The design of an experiment to detect adiabatic o s c i l l a t i o n s involved providing a thermally i s o l a t e d contain-er which could be placed i n a l i q u i d helium bath, the only connection between the bath and the container being the super-leak. I f adiabatic o s c i l l a t i o n s existed then they should be observable as o s c i l l a t i o n s of the l i q u i d l e v e l , i n a s u i t -ably designed container of this type. It was decided to attempt to observe adiabatic o s c i l l a t i o n s using an a r t i f i c i a l superleak rather than the helium II f i l m , because.with f i l m flow i t i s d i f f i c u l t to exclude the vapour phase and thus more d i f f i c u l t to thermal-l y i s o l a t e the container. Two types of superleak were used, the annular gap between two glass discs of a moderate degree of o p t i c a l flatness and the p a r a l l e l channels between a large number of fine wires enclosed i n a tube. The construct-ion and c h a r a c t e r i s t i c s of both of these types of superleak are described i n Appendix I I I . The experimental work can be divided broadly into two phases, that using the " o p t i c a l f l a t s " and that using the w i r e - f i l l e d - t u b e . The o p t i c a l f l a t s apparatus w i l l be described f i r s t . J/ liquid h e l i u m i n l e t v a l v e s u p p o r t i n g w i r e t o . w i n c h , g u i d e r o d v a c u u m j a c k e t b e a k e r g l y c e r i n e s e a l . o p t i c a l f l a t s c o p p - e r b o t t o m F i g . 3. The f i r s t o p t i c a l f l a t s apparatus. • . . . f a c i n g page 38 The Optical F l a t s Apparatus. Two versions of the o p t i c a l f l a t s apparatus were used - one with which the f i r s t exploratory experiments were carri e d out and the f i r s t o s c i l l a t i o n s observed and a l a t e r , improved version which was used i n obtaining the f i r s t quan-t i t a t i v e data on the o s c i l l a t i o n s . The general design of the f i r s t apparatus i s shown i n F i g . 8 , the drawing being con-cerned with only that part of the apparatus which i s i n the l i q u i d helium dewar. The modifications made to t h i s appar-atus which resulted i n the second version are shown i n F i g 9» The e a r l i e r apparatus w i l l be described f i r s t . Adiabatic o s c i l l a t i o n s were to be observed i n the c a p i l l a r y (0 . 5 mm. I.D.) of' the glass experimental container, hereafter referred to as the "beaker". The beaker consisted of a main volume A, the c a p i l l a r y B, which was intended to render small volume changes i n A e a s i l y v i s i b l e , and the Volume C, which was designed to minimise any pressure f l u c -tuations above the l i q u i d o s c i l l a t i n g i n the c a p i l l a r y . The beaker was surrounded except at the bottom, by a vacuum jacket which was pumped out and sealed off i n the manner of a dewar. At t h i s bottom end the two glass discs or o p t i c a l f l a t s were placed, providing an annular flow path between the beaker and the external helium bath. To keep these discs i n p o s i t i o n the bottom end of the vacuum jacket was ground 39 f a i r l y f l a t and the discs were pressed against t h i s by a metal framework, the whole being held together by small springs and r e t a i n i n g nuts. When the apparatus was cooled to low temperatures the contraction of the framework was suitably taken up by. these springs, so that no undue stress was put on the optical f l a t s . It was necessary to prevent any l i q u i d helium from flowing between the upper o p t i c a l f l a t and the vacuum jacket i n order to make sure that the l i q u i d that flowed i n or out of the beaker did so only by way of the gap between the op-t i c a l f l a t s . A seal for t h i s purpose was made using g l y c -erine and w i l l be described i n more d e t a i l l a t e r . The metal framework holding f l a t s and vacuum jacket together formed a carriage which was suspended on a wire and could be ra i s e d or lowered by means of a winch placed just above the dewar cap. In descriptions of the apparatus, the metal cap which surmounts the glass dewar and through which the various pumping l i n e s , leads and controls pass into the dewar w i l l be referred to as the dewar "cap" and that end of the dewar, or the room temperature end, as the "head". The whole of t h i s apparatus was enclosed i n a glass envelope (hereafter referred to as the "diving b e l l " ) which was s i m i l a r i n purpose to that used by Atkins ( 1 9 5 0 ) . The use of such an enclosure i s necessary i n the present case also, because of. the glycerine s e a l , a point which w i l l be made more clear when the glycerine seal has been discussed. The lower end of the diving b e l l terminated i n a large copper glass s e a l , the purpose of which was to provide a means of soldering a copper disc to the bottom so that good thermal contact could be made between the contents of the d i v i n g b e l l and the main helium bath. The copper bottom also served as a base support for the rods which served to guide the motion of the earfeftage carrying the experimental beaker. The upper end of the diving b e l l was drawn down to a tube which passed through the dewar cap and was joined to a high vacuum system. A needle valve, operated by a control rod passing through the dewar cap, was used to l e t helium into the div i n g b e l l once the main helium dewar had been f i l l e d . The whoibeaarrangemeiiit when i n p o s i t i o n was similar to that shown i n the photograph of P i g 16. In assembling the apparatus, the o p t i c a l f l a t s , beaker and carriage were put together i n p o s i t i o n on the guide rods and when the carriage unit was completely assem-bled, see Pig. 10, i t was slipped inside the diving b e l l and the copper disc soldered i n place with Wood's metal. The same glass envelope and copper-glass seal were u<§ed i n a l l l i q u i d helium experiments described i n t h i s thes-i s , amounting to a t o t a l of twenty-six, and although the cop-per-glass seal displays many small cracks i t i s s t i l l i n a useable condition. This seal was made i n the laboratory T, AAAA T, p.d. { thef momett-<j-r-cent v-caTfen.  T 2 p- d. {: thermometers, leaded brass wire 2 0 . Q room temp Wv\J H M M araldite seals } heater pd. heater current heater: constantan wire lOO £1 room temp. F i g . 9. Thermometer and heater arrangement f o r second o p t i c a l f l a t s arrangement. f a c i n g page from Pyrex glass and ordinary stock copper tubing and i t s very s a t i s f a c t o r y performance seems to show that i t i s not necessary to adhere to the s t r i c t s p e c i f i c a t i o n s often given for the manufacture of copper-glass seals;(see Martin & H i l l (I9I4.6) f o r instance) even when the seals are to be used at l i q u i d helium temperatures. The Second Optical F l a t s Apparatus. After adiabatic o s c i l l a t i o n s had been observed with the f i r s t apparatus i t was dismantled and a new apparatus was b u i l t , incorporating several improvements and additions. These alt e r a t i o n s only involved the experimental beaker, see F i g . 9, the rest of the apparatus remaining e s s e n t i a l l y un-changed. A photograph of the second o p t i c a l f l a t s apparatus assembled and ready to be placed i n the diving b e l l i s shown i n F i g . 10. The p r i n c i p a l alterations are described below. The upper o p t i c a l f l a t and the volume A were chang-ed so that a heater and a resistance thermometer could be placed i n A and the bottom o p t i c a l f l a t was provided with four small holes to take the necessary e l e c t r i c a l leads. The preparation of these f l a t s i s described i n Appendix I I I . An external resistance thermometer was provided, s i m i l a r to the one i n A, so that temperature differences between beaker and bath could be detected. The arrangement of the thermo-P i g . 10. The Second O p t i c a l F l a t s Apparatus. f a c i n g page \\2 meters and heater can be understood from the drawing of Pi g . 9 and the photograph of P i g . 10. The mirror shown i n the photograph of Pig. 10 was used i n the adjustment of the optical f l a t s . Cotton covered constantan wire of 1|'2 B. & S. gauge was used for the heater and 1+0 B. S. gauge formex covered copper wire was used for the ten e l e c t r i c a l leads connecting the thermometers and heater to the dewar head. The construction and c h a r a c t e r i s t i c s of the resistance ther-mometers are described i n Appendix I. * To make the observ-ation of the meniscus easier, the c a p i l l a r y B was increased i n diameter to 1 mm., the actual diameter being checked by the usual method of weighing a bead of mercury which had occupied a known length of the c a p i l l a r y . By t h i s means, the average diameter over the central region of the c a p i l l -ary was found to be 1.11+ mm.. The Glycerine Seal. The most s a t i s f a c t o r y arrangement for joining the upper o p t i c a l f l a t to the vacuum jacket would be to have them made from the one piece of glass, but thi s was not poss-i b l e i n the present circumstances, so that the f l a t had to be cut from a piece of f i n i s h e d glass and cemented to the vacuum jacket, by a method which involved no appreciable heating of the" glass. Glycerine was chosen for the cement as i t had been used i n low temperature applications before. U3 In use, the glycerine seal seemed good enough to prevent any appreciable frow of l i q u i d helium II i n most cases, but there was one serious source of trouble experienced with i t ; the glycerine would get i n between the o p t i c a l f l a t s when the apparatus was l e f t standing at room temperature. Because of t h i s , several substances were t r i e d to see i f any made better seals than the glycerine but none were found more suitable for this p a r t i c u l a r a p p l i c a t i o n . Some o i l s , Kapitza (191+1), seemed to make good seals at low temp-eratures, but were too f l u i d at room temperature for use i n th i s p a r t i c u l a r apparatus, A recently reported, Hudson & Mc Lane (1951+)» sealing mixture of 2 parts by volume of glyc-erine and 3 parts of 1 - propanol was also t r i e d but i t seem-ed no better than glycerine at low temperatures and i t also, i was too f l u i d at room temperature. In addition, i t had too high a vapour pressure to be used i n an apparatus which would be- l e f t at room temperature for several days i n between ex-periments. The trouble caused by the glycerine getting between the o p t i c a l f l a t s was one of the major reasons for the change i n design of the apparatus which led to the wire - f i l l e d - t u b e version described l a t e r . Other features of the glycerine seal w i l l be discusse.d i n the section dealing with experi-mental method. The Stroboscope. In the preliminary experiments with the f i r s t op-t i c a l f l a t s apparatus the.observed frequency of the adiabatic o s c i l l a t i o n s , which was compatible with theory, was of the order of several cycles a second. Such a frequency meant that i f the movement of the l i q u i d helium meniscus was to be f o l l -owed, the stopwatch and cathetometer normally used for work with l i q u i d helium would not be adequate. To meet t h i s r e -quirement, a scheme was devised which made use of an o s c i l -lograph recording camera and a stroboscopic lamp. The ob-ject was to obtain a succession of shadowgraph images of the meniscus recorded on a f i l m , by focussing the camera on the c a p i l l a r y B, with the l i g h t behind i t , and having the f i l m move smoothly and continuously i n the image plane of the cam-era lens, while the l i g h t flashed repeatedly at a high rat e . In choosing a l i g h t source, two main features had to be con-sidered :-(1) The l i g h t must be capable of being flashed at rates of up to 50 or 100 times a second. (2) It must be photographically u s e f u l , and at the same time not produce any appreciable thermal r a d i a t i o n , which would a f f e c t the temperature equilibrium i n the adiabatic o s c i l l a t i o n experiment. The l i g h t source which was chosen was a gas d i s -charge tube of the type currently used i n photography as an "electronic f l a s h " . This tube, a General E l e c t r i c type no. FT-218, was the best choice of the l i m i t e d number a v a i l -able l o c a l l y and i t f u l f i l l e d the required conditions very w e l l . The lamp shown schematically i n P i g . 11 i s a small Xenon-filled glass tube with two simple electrodes, one at either end, and a " t r i g g e r " electrode which i s wrapped around the outside of the tube at i t s centre. A condenser charged to a high p o t e n t i a l i s placed across the electrodes and the f l a s h i s f i r e d by supplying a voltage pulse of 10 k i l o v o l t s or more to the t r i g g e r i n g electrode. In the normal photographic a p p l i c a t i o n , the tube i s used intermittently as a single f l a s h unit for i l l u m i n a t i n g photographed subjects and i s rated at a discharge energy of a certain number of joules per f l a s h , t h i s r a t i n g being given for a maximum f l a s h rate of one per minute. As a rough guide f o r stroboscopic use, t h i s figure may be thought of as an average d i s s i p a t i o n over the minute, expressed i n watts. Thus the FT-218 tube rated at 120 joules per f l a s h at 100 flashes per second, a rough equivalence of 2 watts average d i s s i p a t i o n . It was found i n practice that t h i s figure was a useful guide and indications were that i t could be exceeded a l i t t l e . $s well as meeting the stroboscope'requirements s a t i s f a c t o r i l y , the lamp produces very l i t t l e thermal d i s -1+6 turban ce, because i t has a high luminous e f f i c i e n c y with a spectral d i s t r i b u t i o n very similar, to that of daylight. In addition, the integrated energy output i s low, when the lamp i s used as a stroboscope, because the duration of each f l a s h i s very short, f o r example, the integrated discharge time i s only a few milliseconds per second when the lamp i s flashed at 50 times a second. Before the stroboscopic lamp was used i n experiments with l i q u i d helium, i t was tested to see i f i t did produce any appreciable thermal r a d i a t i o n . For t h i s pur-pose, the lamp was placed i n front of a sensitive i n f r a - r e d recording spectrometer and compared with another l i g h t source of the same aperture which had a known disturbing e f f e c t on the equilibrium of the helium meniscus i n the experimental beaker. The stroboscopic lamp gave no detectable signal at a l l while the comparison l i g h t source was recorded at quite a high l e v e l . From t h i s i t was concluded that the strobo^ scopic f l a s h lamp would provide extremely l i t t l e thermal perturbation of the helium meniscus and t h i s was l a t e r con-firmed by experience. The method used to provide the tr i g g e r i n g pulse for repeated discharge of the lamp i s shown i n F i g . 1 1 . A thyraton o s c i l l a t o r (frequency up to 100 cycles per second) was used to drive a pulse generator of the "inductive k i c k -er" type, Caffyn & Underwood ( 1 9 5 3 ) , and the pulse produced was fed to the tri g g e r electrode. It was found that the FREQUENCY REFERENCE STROBOSCOPE UNIT OSCILLATOR 10-IOOCRS. TRIGGER PULSE GENERATOR A 10 -15 kv. c F L A S H TUBE IQOOv. H. T. POWER SUPPLY P i g . 1 1 , resistance thermometer HIGH GAIN D.C. AMPLIFIER helical slide wire TEMPERATURE DIFFERENCE DETECTING SYSTEM LOW PASS FILTER OSCILLOSCOPE PEN RECORDER P i g . 12 f a c i n g page 1+7 1+7 f l a s h tube often missed f i r i n g , p a r t i c u l a r l y at the higher frequencies, but t h i s m i s f i r i n g was very much reduced when the t r i g g e r i n g pulse voltage was increased. As a frequency reference for the o s c i l l a t o r , a 1000 cycle per second e l e c t -r i c a l l y maintained tuning fork was used for most of the work, but l a t t e r l y the o s c i l l a t o r was operated at the one frequency synchronised to the 60 cycle mains supply. The camera used i n conjunction with the stroboscope lamp was an oscillograph camera, Cossor Model 11+28, with a continuous f i l m drive provided with a choice of several speeds i n a range from 0 . 0 5 to 25 inches of f i l m per second. This camera was modified f o r use with the stroboscope by replacing i t s lens with an "Elmar" lens of f o c a l length 9 cm. and f = l+.O with adjustable focus, and mounting i t on a suitable stand for work with the dewars. After some i n i t i a l troubles, a f i l m s a t i s f a c t o r y f o r t h i s p a r t i c u l a r application was found. This was Kodak Linagraph Panchromatic 35 mm. f i l m rated at a " r e l a t i v e speed" of 61+0 i n the blue region of the spectrum. Developed for f i f t e e n minutes i n Kodak D - 19 developer, t h i s f i l m gave an image of good contrast and s a t i s f a c t o r y d e f i n i t i o n . The Heater C i r c u i t . The heater i n volume A of the experimental beaker was energised using a simple e l e c t r i c a l c i r c u i t i n which pro-• v i s i o n was made for varying.and measuring the heater current and reading the p o t e n t i a l difference across the heater termin-a l s . The c i r c u i t was arranged so that before i t was intended to use the heater i n the experimental beaker, the current could be switched on and passed through a dummy heater, the resistance of which could be adjusted to that of the actual heater and i t s leads. This arrangement had two advantages. F i r s t l y , the value of the heater current to be used could be read o f f beforehand and f u l l attention subsequently given to watching the meniscus, and secondly, i t was necessary to have such an arrangement with the present experiments, because ad-justing the heater current with the actual heater i n the helium connected, meant a l o t of time wasted waiting f o r equilibrium to be restored. For the " t r i g g e r i n g " of adiabatic o s c i l l a t i o n s , energy was supplied to the heater by discharging a condense* through the current leads. The condenser was compared with a reference capacity (General Radio Type 509-X, 0 . 5 micro-farad) with the aid of a b a l l i s t i c galvanometer. The con-denser was discharged through the galvanometer under the same conditions used i n the helium experiments and with the same voltage ( 1 2 . 6 v o l t s ) ; the voltage on the reference condenser was then adjusted to give the same d e f l e c t i o n of the galvan-k9 ometer when i t was discharged. From t h i s , the capacity of the condenser was found to be 10.9 microfarads (8 microfarad nominal value). It was unfortunate that an e l e c t r o l y t i c con-' denser was f i r s t used for the t r i g g e r i n g condenser and then kept for the rest of the experiments f o r the sake of consis-tency. However, the precautions which were taken as de-scribed above, make i t reasonably cert a i n that i t s capacity i s known with s u f f i c i e n t accuracy f o r the present purposes. The Apparatus Used to Detect Temperature Differences. The equations f o r the adiabatic o s c i l l a t i o n s are solveable f o r the temperature difference as well as the l i q u i d l e v e l difference, (see equations (1+) and (!?)» Chapter II) although from a knowledge of the magnitude of the fountain e f f e c t and the amplitude of the l i q u i d l e v e l o s c i l l a t i o n s , the expected temperature o s c i l l a t i o n s would be of very small amp-l i t u d e , 10 or l e s s . In spite of t h i s small amplitude, i t was decided to t r y to detect the temperature o s c i l l a t i o n s , be-cause i t was thought possible that t h e i r recording might have been easier. No clear evidence of the temperature o s c i l l a t -ions was found but the apparatus used i n these attempts w i l l be described. The thermometers use'd have already been referre d to and are described i n d e t a i l i n Appendix I. These leaded-brass resistance thermometers are not quite as sensitive as - the car-5 0 bon resistance type, but they had an advantage i n the present work because they have very low resistance values, which suited the input c h a r a c t e r i s t i c s of the p a r t i c u l a r amplifier used. i A schematic diagram of the e l e c t r i c a l arrangement used i s given i n Pig. 12. After experimenting with various schemes, a simple Wheatstone bridge was used with a switch-ing arrangement so that either the in t e r n a l thermometer T-^  or the extermal thermometer Tg could be incorporated i n a bridge arm. Another arm was a f i x e d reference resistance and the r e -maining arms were the two parts of a bridge s l i d e wire. The bridge arrangement was designed not to measure the temperature difference but to detect i t and give a signal which would follow the o s c i l l a t i o n frequency. To do t h i s , the bridge was balanced when the l i q u i d helium i n the beaker was i n e q u i l -ibrium with the bath, the o s c i l l a t i o n was"triggered" and the bridge system produced an out of balance signal which f o l l -owed the temperature differences between beaker and bath. This out of balance s i g n a l was amplified and displayed on the oscilloscope. Because of the low l e v e l of the signals involved and the large temperature differences e x i s t i n g between var-ious parts of the c i r c u i t , great care had to be taken to re-duce thermo-electric e f f e c t s as much as possible . There were 51 only two soldered connections at the room temperature end of the c i r c u i t and these were made using a special solder which i s claimed to give a very low thermo-electric e.m.f. with respect to copper. A l l other leads and connections were of copper, the thermometer leads from the thermometers to the switch-box being each one continuous piece of copper wire. Both the switch-box and the shielding can surrounding the bridge slide-wire, were f i l l e d with o i l i n order to help to s t a b i l i s e the temperature. With a l l these precautions, the c i r c u i t was f a i r l y immune to temperature d r i f t s or f l u c t u a t -ions of the kind normally encountered. The bridge slide-wire was approximately 9»5 metres long, with a t o t a l resistance of 8 . 6 5 ohms, and was iSound from 20 B. & S. gauge manganin wire as a h e l i x of 10 turns per inch on a former of l+J" diameter. The 1 .5 v o l t c e l l used fnr supplying the bridge current was kept i n the s l i d e -wire o i l bath to keep i t s e.m.f. more stable. The detector used i n the bridge was a D.C. amplifier of the contact breaker type, Liston et a l (191+6 a), which was available i n the laboratory. This amplifier was designed for amplifying low l e v e l D.C. potentials such as pen recording milliammeters etc. In the present case, the amplifier fed into a Cossor oscilloscope Model IOI49, or an E s t e r l i n e -Angus ( 0 - 1 m.a.) recording milliammeter. The amplifier was 52 a very sensitive detector i n the bridge arrangement but there were some features connected with i t s use which set an upper l i m i t to the s e n s i t i v i t y which could be achieved, a l i m i t which was below that necessary for the detection of the tem-perature o s c i l l a t i o n s * The frequency of the adiabatic o s c i l l a t i o n s was several cycles a second so that i n following the temperature o s c i l l a t i o n s , the amplifier would be acting as a very low frequency A.C. amplifier and the amplifier's speed of response was s u f f i c i e n t l y f a s t to do t h i s . To enable the amplifying system to function with s u f f i c i e n t speed, a low-pass f i l t e r -ing arrangement which was placed between the amplifier and recorder when the amplifier was used i n i t s normal r o l e , had to be modified and immediately this was done, trouble was experienced with "noise". This "noise" was not of a fun-damental nature but was mainly composed of currents induced i n the c i r c u i t by the A.C. mains and then "chopped" by the action of the contact breakers i n the amplifier. The ther-mometer and bridge c i r c u i t was rather susceptible to magnet-i c a l l y induced currents from the mains, because i t was nec-e s s a r i l y spread out, i t had a very low impedance, and at the signal l e v e l s considered here, the influence of the mains supply was d i f f i c u l t to escape. It was not fea s i b l e to carry out any magnetic sheilding but i t was possible to cancel out the induced currents to some extent by inducing an out-of-53 phase 60 cycle current i n the c i r c u i t . In addition to t h i s , the simple R/C f i l t e r used between the amplifier and record-er was replaced with a low-pass, m-derived f i l t e r , which was designed to have a much sharper cut-off and much higher atten uation beyond cut-off. This resulted i n a great improvement but i t s t i l l was not enough to eliminate the background. The attempt to detect the temperature o s c i l l a t i o n s f • was not successful with the arrangement described and the e f f o r t was notpushed further i n t h i s d i r e c t i o n , because the p r i n c i p a l objectives of the experiment could be achieved by the measurements ofi the l i q u i d l e v e l o s c i l l a t i o n s . Many im-provements could be made to the system, such as designing a special amplifier f o r the bridge detector and changing over to the more sensitive resistance thermometers. Carbon re- . sistance thermometers would aiso have the added advantage of beting less dependent on measuring current than the leaded-brass wire thermometers (see Appendix I ) . \ , * One alteraiative approach was started, but not a great deal of e f f o r t was expended on i t , because more a t t -entionfwas given to the l i q u i d l e v e l o s c i l l a t i o n s i n the la t e r experiments. The apparatus for thi s approach was i n -corporated into the wire - f i l l e d - t u b e apparatus to be de-scribed l a t e r , but the temperature detecting part w i l l be described here i n the interests of unity of treatment. .; 51+ The temperature difference detecting c i r c u i t s i n r. the wi r e - f i l l e d - t u b e apparatus were arranged so that either D.C. measurements, of the type previously described, could be carried out, or a simple A.C. bridge could be used. The main feature of the A.C. bridge was a small audio frequency transformer which was placed i n a lead s h i e l d and b u i l t into the carriage assembly carrying the experimental beaker, see P i g . 13. The detector for t h i s A.C. bridge was now an audio frequency amplifier connected to the bridge. by the- trans-former. The purpose of the lead was to provide a magnetic s h i e l d for the transformer when the lead became supercon-ducting at l i q u i d helium temperatures. When thi s occurred, the low impedance part of the c i r c u i t would be well shielded and the secondary side would require only e l e c t r o s t a t i c shielding, because of i t s much higher impedance. The tem-perature o s c i l l a t i o n i n t h i s case would have been displayed as an amplitude modulation of the A.C, signal supplied to the bridge. However, as explained above, this system was not r e a l l y t r i e d i n p r a c t i c e . The results which were obtained with the temper-ature detecting system w i l l be presented i n Chapter V. The Wire-Filled-Tube Apparatus. After a considerable number of experiments had been carried out with the opti c a l f l a t s apparatus, i t was decided 55 for reasons which w i l l be given f u l l y i n Chapter V, to b u i l d a new apparatus of a d i f f e r e n t design. This apparatus, which w i l l be ca l l e d the wire-filled-tube apparatus w i l l now be described. The main features of the improved design were: (1) The superleak was altered to a wi r e - f i l l e d - t u b e . (2) Provision was made f o r pumping the vacuum jacket continuously. (3) The method of attaching the superleak and of s e a l -ing off volume A of the beaker was alt e r e d , the . glycerine seal being retained but improved. (Ij.) The alterations to the thermometer c i r c u i t , which have already been described, were made. A photograph of the wire - f i l l e d - t u b e apparatus i s shown i n F i g . 13. The d e t a i l s of manufacture and the measurement of the ch a r a c t e r i s t i c s of the wire-filled-tubes are given i n Appendix I I I . The experimental beaker was redesigned so as to incorporate the glass plug which formed the bottom of the chamber A, and to provide a maximum of thermal i s o l a t i o n of the beaker by having the plug- evacuated as well as the yacuum jacket. The c a p i l l a r y B and volume C were e s s e n t i a l l y the sam as before, c a p i l l a r y B this time having a diameter of Pig. 11+. The glass plug carrying the wire-filled-tube facing page 56 1.10 mm. average over i t s length, uniform to better than 1% except close to the ends. The volume A was measured d i r e c t -l y and found to be 6.6 cm. . The design of the glass plug, see P i g ll+, incorp-orated several advantages. It carried both resistance thermo-meters, one at each end, as well as the heater, so that a l l the e l e c t r i c a l system could be withdrawn from the beaker i n a convenient manner. The e l e c t r i c a l leads into the beaker were made with 0.0105* tungsten wire sealed d i r e c t l y into the glass at t h e i r ends. Copper wire was silver-soldered to the ends of the tungsten wires to f a c i l i t a t e the joining-of leads and connections. The wire-filled-tube passed down the centre of the plug and was soft soldered to Kovar tubing sealed into the glass of the plug at each end. A small diaphragm was made part of one of these join t s so that the r e l a t i v e con-tractions of the wire-fil l e d - t u b e and glass plug could be allowed f o r . Three springs held the plug i n place as shown i n the photograph. One of the important features of the re-designed apparatus was that i t was much easier to assemble and d i s -mantle than the previous o p t i c a l f l a t s apparatus. Previous experience with the o p t i c a l f l a t s equipment had made i t clear that apparatus of thi s type required to be dismantled quite frequently, so p a r t i c u l a r attention was paid to ease of ass-embly. connection to high vacuum system for jacket wire leads for thermometers etc P i g . 1 5 . The s l i d i n g s e a l . f a c i n g page 5 7 57 As there now had to be a pumping tube to connect the vacuum jacket surrounding the beaker to the high vacuum system at the dewar head, t h i s tube replaced the wire prev-io u s l y used f©B. r a i s i n g or lowering the beaker and the winch was replaced by a s l i d i n g vacuum seal using "0 W r i n g s . D e t a i l s of t h i s s l i d i n g seal and the pumping connections are given i n the drawing of F i g . 1 5 , and they may be seen i n the photo-graph of F i g . 1 6 . A r a d i a t i o n s h i e l d was incorporated into the pumping tube just above the copper-glass seal joining the tube to the vacuum jacket. P i g . 16. Experimental I n s t a l l a t i o n w i t h Dewars Removed. f a c i n g page 5 8 58 CHAPTER IV. EXPERIMENTAL PROCEDURE. Outline of General F a c i l i t i e s f or Experiments with  Li q u i d Helium. A l l experiments on l i q u i d helium described i n t h i s thesis were carried out i n a Pyrex glass dewar set consisting of a l i q u i d helium dewar of inside diameter 6.2 cm. and length 71+ cm., surrounded by an outer l i q u i d a i r dewar of outside diameter 10 cm. and length 75 cm. The dewar set was mounted i n an experimental i n s t a l l a t i o n b u i l t around a bench which could accommodate the necessary f a c i l i t i e s and controls f o r the experiments on l i q u i d helium. These f a c i l i t i e s include two high vacuum systems which could be connected i n various ways to provide the necessary vacua f o r the equipment inside the helium dewar. The photograph of F i g . 16 shows that part of the i n s t a l l a t i o n surrounding the dewar mounting. The l i q u i d helium dewar was connected v i a a pumping l i n e to a large mechanical pump which provided the r e l a t i v e l y high speed, low vacuum, required for pumping the vapour over the l i q u i d helium bath to obtain temperatures below the b o i l -ing point of helium. A butyl pthalate manometer, continuous-l y pumped on the reference side, was used to measure the vapour-pressure of the l i q u i d helium. For t h i s purpose, the pressure i n the s t a t i c atmosphere of the diving b e l l was used, * 9 although i t was imperceptibly d i f f e r e n t from that i n the main bath for a l l but the higher temperatures i n the l i q u i d helium II region. These vapour pressure readings were converted to ab.solute temperature values using the tables of van Dijk and Shoenberg (191+9), "the 191+8 temperature scale". The temper-ature control bridge described i n Appendix II was used to hold the bath temperature steady to within 1 0 4 K or better i n a l l experiments. The l i q u i d helium used i n the experi-ments .was produced by the C o l l i n s l i q u e f i e r i n the Physics Department at the University of B r i t i s h Columbia. The l i q u i d was transferred to the helium dewar of the apparatus by means of a syphon, either from the l i q u e f i e r i t s e l f , or l a t t e r l y , from a l i q u i d helium transport vessel which had previously be.en f i l l e d from the l i q u e f i e r . Preparation for an Experiment and General Procedure. - Because of the nature of the apparatus i n these exper-iments, the pre-cooling necessary before the transfer of l i q u i d helium could take place had to be carr i e d out very slowly. This was done by using a " s o f t " helium dewar, A l l e n (191+6), and the. progress of the pre-cooling was watched with the aid of a thermocouple. Such slow pre-cooling was made necessary to some extent by the many metal-to-glass seals i n the apparatus but the p r i n c i p a l reason was the glycerine s e a l . For the glycerine to be e f f e c t i v e as a seal i n l i q u i d helium I I , i t must cool very slowly so that i t has a chance of form-ing a glass which i s free from cracks at the temperature of of the experiment. In most of the experiments, the glycerine seals performed well but on a few occasions they cracked bad-l y and forced the abandonment of the experiment. Apart from the pre-cooling, the glycerine seal also needed careful treatment at room temperatures, because then the glycerine i s moderately f l u i d and the seal would move out of p o s i t i o n when subjected to quite small pressure differences. When i t was required to evacuate the diving b e l l and the beak-er a f t e r the apparatus had been assembled, the seal had to be hardened by cooling the apparatus well below room temperature. After t h i s had been done, the system was connected to the pumps and only allowed to return to room temperature aft e r a l l the s i g n i f i c a n t pressure differences had been removed. Because the contents of the experimental beaker had to be evacuated through the superleak, t h i s pumping took several hours. Pumping was continued at room temperature u n t i l the apparatus was cleaned of unwanted gases. After an experiment, when the apparatus i n the dewars had returned to room temper-ature, care had to be taken that the pressure i n the diving b e l l did not r i s e , because of leaks, and displace the glycer-ine seal inwards. This d i d happen with the e a r l i e r o p t i c a l f l a t s apparatus, where the glycerine had extremely l i t t l e l a t -itude of movement anyway, and was thus sensitive to a much smaller r i s e i n the diving b e l l pressure than was the case with the wire,-filled tube apparatus. It can be seen from 61 the foregoing that the i s o l a t i o n of the experimental apparat-us i n the diving b e l l was very necessary when dealing with a l i q u i d seal. Thus, preparation for an experiment involved cool-ing the apparatus, pumping i t out, warming i t while s t i l l pumping and then pre-cooling I t ready f o r the transfer of l i q u i d helium. As soon as the l i q u i d helium had been trans-f e r r e d and the dewar f i l l e d , the needle valve connecting the dewar with the diving b e l l was opened, l i q u i d was allowed to flow into the diving b e l l to the desired height, and the valve was then closed. After t h i s , the main helium bath was connected to the pumping system and the temperature lowered to the chosen operating point i n the l i q u i d helium II region.-When t h i s temperature was reached, the temperature s t a b i l i s -ing bridge was brought into operation and the pumping speed and bridge settings adjusted u n t i l the bridge had assumed con-t r o l . The next step was the f i l l i n g of the experimental beaker by drawing superfluid helium through the superleak, eithe r by switching on the heater or lowering the beaker into the bath, so that the l i q u i d could flow i n under a g r a v i t a t -i o n a l pressure head. In the case of the w i r e - f i l l e d - t u b e apparatus, t h i s f i l l i n g - p r o c e s s took about two hours. With such a long time involved, the saving of l i q u i d helium i n the 62 bath, by reducing this time as much as possible was import-ant, so the bath temperature was held at a value of 1 .6°K, where the superfluid flow rate has very nearly reached i t s maximum, but where the evaporation rate from the bath i s the minimum necessary to achieve such a rate. Care had to be taken not to overheat the contents of the beaker by having the heater power at such a value that the superfluid would continue flowing after the heater was turned o f f , (the "over-shoot" of Bowers and Mendelssohn ( 1 9 5 2 ) , and Winkel et a l (1955) ) otherwise, the l i q u i d helium would p a r t i a l l y , or perhaps completely, f i l l the volume C. Once t h i s had hap-pened i t was very d i f f i c u l t to restore the meniscus to an equilibrium p o s i t i o n i n the c a p i l l a r y B, except of course, by r a i s i n g the bath temperature which was usually an undesir-able step. (This point w i l l be c l a r i f i e d further on.) Thus the beaker was f i l l e d as far as possible by gr a v i t a t i o n a l flow, to avoid such troublesome e f f e c t s . With the l i q u i d meniscus i n an equilibrium p o s i t i o n i n the c a p i l l a r y and the bath temperature held steady by the control bridge, the observations on adiabatic o s c i l l a t i o n s could be proceded with. A general description of adiabatic o s c i l l a t i o n s w i l l now be given so that further discussion of experimental procedure and points of int e r e s t will,be made more clear. 63 The eliquibrium p o s i t i o n of the l i q u i d helium men-iscus i n the c a p i l l a r y B was several millimetres above the l e v e l of the bath l i q u i d , i n d i c a t i n g that the temperature of the beaker contents was s l i g h t l y higher than the bath and thus enabling a fountain pressure head to be established. The difference In temperature i s presumably because the bea-ker i s i n a favourable p o s i t i o n to receive r a d i a t i o n . This r i s e i s separate from, and greatly i n excess of, the surface tension r i s e of l i q u i d helium i n the c a p i l l a r y . General Description of Adiabatic O s c i l l a t i o n s i n  Liquid Helium I I . The general pattern of o s c i l l a t i o n behaviour was established i n a series' of experiments and may be summarised as follows. I f the meniscus i s suddenly disturbed from i t s e q u i l -ibrium p o s i t i o n , say by methods (2) or (3) l i s t e d below, i t w i l l move to some new p o s i t i o n and s t a r t to o s c i l l a t e after the p o s i t i o n has been reached. The o s c i l l a t i o n s continue as the mean l e v e l of the meniscus returns toward the i n i t i a l equilibrium p o s i t i o n , but as they are i n general strongly damped, they die out long before that p o s i t i o n i a reached. The general pattern of behaviour of such o s c i l l a t i o n s and i t s v a r i a t i o n with temperature can be seen i n P i g . 18.. 6h The various ways which have been used to " t r i g g e r " o s c i l l a t i o n s are: (1) Quickly r a i s i n g or lowering the beaker - a movement of one millimetre was quite s u f f i c i e n t . (2) Passing a short pulse of current through the heater, or i n quantitative work, discharging a condenser through i t . ( 3 ) Suddenly changing the amount of r a d i a t i o n incident on the beaker, or suddenly a l t e r i n g the bath tem-perature . The o s c i l l a t i o n s were, f i r s t observed with the f i r s t o p t i c a l f l a t s apparatus, using the beam of l i g h t from a pocket f l a s h l i g h t to disturb the meniscus as i n (3) above. The general picture to be obtained from the observ-ations i s that the methods of t r i g g e r i n g described are a l l means of imparting to the l i q u i d i n the superleak a "sudden impetus, so that i t flows with a s u f f i c i e n t v e l o c i t y to over-shoot when the impetus i s removed and then o s c i l l a t e under the influence of the thermo-mechanical and mechano-caloric e f f e c t s . Robinson predicted a l l the essentials of t h i s p i c -ture i n his paper giving the t h e o r e t i c a l treatment. Further Remarks on Experimental Procedure. An i n t e r e s t i n g aspect of the taking of measurements on the adiabatic o s c i l l a t i o n s was the process of changing 6 5 from taking readings at one temperature to the taking of read-ings at a d i f f e r e n t temperature and also the manoeuvering of the meniscus i n the c a p i l l a r y B to obtain a s i t u a t i o n of equilibrium before o s c i l l a t i o n s could be produced fnr meas-urement. I f the beaker and bath were i n thermal equilibrium at some p a r t i c u l a r temperature and i t was desired to change to some other temperature to take a d i f f e r e n t set of readings, i t was found that the only experimentally f e a s i b l e d i r e c t i o n i n which to change the bath temperature, was- to rais e i t . This was so for the following reason. I f the bath temper-ature was raised a certain amount of l i q u i d was drained from the beaker as a r e s u l t of the thermo-mechanical e f f e c t , so that when the bath temperature was s t a b i l i s e d at the newly chosen temperature, the l i q u i d had to be restored to i t s equilibrium p o s i t i o n i n the c a p i l l a r y , : b y using the heater to draw i n more l i q u i d . I f , however, the bath temperature was lowered, the thermo-mechanical e f f e c t forced more l i q u i d into the beaker, with the r e s u l t that when the bath was s t a b i l i s e d a tithe, chosen lower temperature, there was a sur-plus of l i q u i d i n the beaker, which could only be removed by equalising the temperatures of beaker and bath. This could be accomplished either by lowering the temperature of the beaker contents i n some way independent of the bath, or by having some kind of thermal exchange between beaker and '• 66 bath which could be brought into play. Otherwise, the tem-perature of the beaker would have to a t t a i n that of the bath by means of thermal conduction v i a the very small amount of thermal linkage between them, i . e . the "non-adiabacity" of . the container. This process was very slow and used up a l o t of valuable experimental time with the l i q u i d helium. It was not possible to lower the temperature of the beaker contents independently but an attempt was made to use thermal "exchange-gas" to equalise the temperatures of beaker and bath. This did not prove to be e f f e c t i v e , however, so that the only solution for obtaining equilibrium i n thi s s i t -uation was to wait for the slow temperature equalisation to take place, and there were one or two occasions on which t h i s method had to be resorted t o . In general, for any p a r t i c -u l a r run, the lowest temperature at which measurements were to be made was chosen beforehand and t h i s was the f i r s t temperature at which the.bath was s t a b i l i s e d . The remaining temperatures at which measurements were made for that run, were always approached from the low temperature side. In t h i s way, the thermal equilibrium between beaker and bath could most speedily be regained, although care had to be tak-en not to overshoot the equilibrium p o s i t i o n , as was discuss-ed previously. This u n i - d i r e c t i o n a l l i m i t a t i o n also affected the operation of the experiments i n another way, the correction 67 for any overshooting of the equilibrium p o s i t i o n of the men-iscus'. I f t h i s p o s i t i o n was overshot and some l i q u i d accum-ulated i n the? volume C say, then the only f e a s i b l e way of getting i t out at any but the lowest temperatures, was to r a i s e the bath temperature. This was quite often done, as 0 the increase of bath temperature necessary was i n many cases not s i g n i f i c a n t l y d i f f e r e n t from that o r i g i n a l l y chbsen as the operating point, but at the higher temperature end of the l i q u i d helium II region any increase i n bath temperature used for this purpose, was l i k e l y to st a r t a trend of circumstan-°ces which resulted i n a decreasing amount of control over the behaviour of the l i q u i d l e v e l . Such overshoot was much more l i k e l y to occur at the higher temperatures, because, for the reasons given above, they were often reached late i n the run, when the l e v e l of the outer bath helium 1 x*as low and the i n -o fluence of r a d i a t i o n more pronounced. Under these conditions, i f overshoot were counteracted by r a i s i n g the bath temper-ature, the whole system progressed i n the d i r e c t i o n of de-creasing superfluid v e l o c i t i e s , so that the l a g between a counter measure and i t s e f f e c t increased, and also as the thermo-mechanical e f f e c t increases with increasing temperature, 0 the s e n s i t i v i t y to temperature Imbalance increased. To avoid 0 being"beaten back" to the lambda point i n t h i s fashion was not easy and it. made the obtaining of o s c i l l a t i o n data at the higher temperatures very d i f f i c u l t . 68 i * The f a i l u r e to obtain temperature equalisation by using exchange gas, i s i t s e l f an i n t e r e s t i n g point, as the method works so well i n experiments on adiabatic demagnet-i s a t i o n , ( see however, Hull (I9I4.6) p.78 ). The answer seems to be, that the method f a i l e d because of the import-ance of the thermo-mechanical e f f e c t i n t h i s p a r t i c u l a r ex-periment. A gas pressure of 1 0 mm. has been found s u f f i c -ient to provide thermal contact at these temperatures, H u l l ( 1 9 U ° ) , but i n the present case, very much higher pressures produced no noticeable thermal exchange. There was of course., the thermal i n s u l a t i o n provided by the glass walls and about which nothing could be done, but there were some other f a c -tors as well. When the exchange gas was admitted from the warmer parts of the system, i t warmed the central beaker p r e f e r e n t i a l l y and thus enhanced the temperature difference instead of diminishing i t . Also, with the deterioration of the vacuum i n the i n s u l a t i n g jacket, there seemed to be a certain amount of thermal conduction down the pumping tube from the warmer regions above, which had the e f f e c t of keep-ing the beaker just s l i g h t l y warmer than the bath and hence "locking i n " the l i q u i d helium, as long as the exchange gas was present. Such temperature differences as are being con-sidered here are probably very small, but are e f f e c t i v e be-cause of the magnitude of the thermo-mechanical e f f e c t . . 6 9 In almost every case, a run ended at a temperature close to the lambda point, with the beaker f a i r l y f u l l of l i q u i d and the amount of l i q u i d i n the outside bath which was being pumped to maintain the temperature, becoming f a i r l y small. This l i q u i d i n the beaker had been put there by using the superfluid properties of l i q u i d helium II and the problem i n f i n i s h i n g up the run was how to get i t out, i n a s i t u a t i o n where the superfluid properties were not always very much help. With the o p t i c a l f l a t s apparatus, the pro-cedure' -usually used was to raise the beaker clear of the 1' l i q u i d and l e t i t drain by the superfluid flow out through the o p t i c a l f l a t s channel. On the other hand with the wire-filled-rtube apparatus, t h i s was not possible,, as the bottom end of the tube was so f a r down, that by the time i t was clear, the temperature of the beaker l i q u i d would have been far above the lambda point.. In any case, the shape of v o l -ume A i n this apparatus was re-entrant, so that quite a large f r a c t i o n of the l i q u i d could only flow outwards by f i l m flow up the walls of the glass plug and then down the w i r e - f i l l e d -tube. This was a very slow process and there was never suf-f i c i e n t time for i t to occur, so the l i q u i d i n the beaker had to be l e f t to look after i t s e l f . It generally f i l l e d up the beaker completely and then as the temperature continued to r i s e , i t forced i t s way out of the beaker by breaking the glycerine seal at some point. After the helium had a l l been 70 pumped out and the apparatus slowly returned to room temper-ature, a stage was reached where the glycerine seal became f l u i d again and i t gradually re-formed during the next day or two, ready f o r another experiment. Sometimes, an exper-iment had to be postponed for a day or two, while the glyc-erine seal was juggled into a s a t i s f a c t o r y p o s i t i o n by b a l -ancing pressures. It i s worth remarking that on those occasions when the contents of the beaker were at l i q u i d helium I temper-atures, the l i q u i d was responsive to pressure changes only, and very uncontrollable, so that on the question of whether adiabatic o s c i l l a t i o n s could be observed above the lambda point, the conditions for observing them there just did not e x i s t . Method of Taking Observations on Adiabatic O s c i l l a t i o n s . As mentioned previously, i n a l l quantitative work, the o s c i l l a t i o n s were triggered by discharging a condenser • through the heater i n the experimental beaker, the discharge energy i n a l l cases being about 8 , 0 0 0 ergs. A l l v i s u a l observations of the helium meniscus were made with the aid of a two watt neon lamp. Its e f f e c t on the l i q u i d l e v e l i n the c a p i l l a r y could be just detected but i t s use was not considered to be i n any way harmful to the ob-. 71 servations. ' . The photography of the l i q u i d l e v e l movement using the stroboscope, was carried out by having the camera focuss-ed on the c a p i l l a r y with the stroboscopic l i g h t behind, so that a shadow image of the c a p i l l a r y was formed on the focus-sing screen. It was very d i f f i c u l t to consistently obtain an image of the l i q u i d l e v e l which was i n good focus and a con-siderable amount of time had to be spent i n achieving a sat-i s f a c t o r y image. This was one of the reasons why i t was conr sidered worth while to re-design the adiabatic container, so that a longer period of o s c i l l a t i o n and a d i f f e r e n t type of measurement could be used. There was one i n t e r e s t i n g point concerning the l i g h t sources used. The e f f e c t of these l i g h t sources on the l i q u i d l e v e l i n the c a p i l l a r y had to be taken into account when aligning the camera, because the image was of such a s i z e , that the maximum use was made of the f i l m space and a small d i s -placement of the l i q u i d l e v e l could be important, as part of the image might be l o s t . It was found that care had to be ex-ercised i n the interchanging of the l i g h t sources because the perturbing e f f e c t of each was a l i t t l e d i f f e r e n t ; the e f f e c t of the neon.lamp was greater than that of the stroboscope op-erating on i t s lowest r a t i n g , but with increased discharge energy the e f f e c t of the stroboscope would increase to that 72 of the neon lamp. The frequency of the stroboscope f l a s h i n g was frequently checked against the 1,000 cycle per second e l e c t r i c a l l y maintained tuning fork. The films were devel-oped and then examined on a simple viewing arrangement, spec-i a l l y b u i l t for the purpose,, which enabled the p o s i t i o n of the meniscus to be read from the f i l m by means of a t r a v e l l -ing microscope. Zero checks were made during these measure-ments by making use of the appearance i n the photograph of the markings on c a p i l l a r y B. Visual Observations. These were only done with the w i r e - f i l l e d -tube apparatus where the period was s u f f i c i e n t l y long to enable the eye to follow the movement of the meniscus. The proced-ure was simply to record the times of the turning points of the o s c i l l a t i o n s , by watching them through a cathetometer equipped with an eyepiece scale. These readings were r e -peated several times f o r each temperature investigated. Pig. 17. Plot of adiabatic o s c i l l a t i o n at 1.7U3 K taken from a stroboscopic photograph record. Amp-lit u d e approximately 0.2 mm. maximum, and frequen-cy approximately I(..5 cycles per second. facing page 73 73 CHAPTER V EXPERIMENTAL RESULTS. O s c i l l a t i o n s have been observed i n three separate pieces of apparatus employing three d i f f e r e n t geometries and two d i f f e r e n t types of superleak. The o s c i l l a t i o n s were f i r s t observed q u a l i t a t i v e l y i n the f i r s t o p t i c a l f l a t s app-aratus. Some quantitative r e s u l t s were obtained with the second o p t i c a l f l a t s apparatus, but nearly a l l of the data were obtained using the wire-fil l e d - t u b e version. The several methods used to produce.oscillations have already been described i n Chapter IV together with a de-s c r i p t i o n of the general behaviour of the o s c i l l a t i o n s . The measurements made on the o s c i l l a t i o n s as well as on some rela t e d topics w i l l be presented i n t h i s chapter, beginning with the data obtained with o p t i c a l f l a t s apparatus. Data Obtained with the Optical F l a t s Apparatus. Several stroboscopic photographs of the l i q u i d l e v e l o s c i l l a t i o n s were obtained with t h i s apparatus. A graph plotted from one of the better photographs i s shown i n F i g . 17. This photographic record was obtained using the stroboscope operated at £0 flashes per second with a d i s s i p -ation of O.OI4 joules per f l a s h . The trigger discharge energy was 8000 ergs. The graph was plot t e d from measurements made . 71+ . on the f i l m using the "frame number" as a measure of time. Scatter of the points i n P i g . 17 i s thought to be due to the e f f e c t s of bubbles i n the liq_uid nitrogen dewar. The type of record shown i i i Figure 17 served to es-t a b l i s h that the frequency of o s c i l l a t i o n was of the expected order of magnitude and provided the f i r s t quantitative r e s u l t s . As well as t h i s i t gave a representation of o s c i l l a t i o n wave-form which was unobtainable by v i s u a l observation. Because of the l i m i t e d number of periods available for measurement, however, i t was clear that only an ordefc of magnitude value could be expected for the frequency and t h i s meant that the p r e c i s i o n of frequency measurement would have to be improved i f the frequency was to be measured as a function of temper-ature. This l i m i t a t i o n of measurement was mainly imposed by the condition of the experimental beaker, but there were also features of the photographic method which were causing some • . trouble. The disadvantages and d i f f i c u l t i e s of the experiment-i al -approach as i t was at that stage, are best summarised under the two headings given below. The adiabatic container: (1) The damping of the o s c i l l a t i o n s was large and there-fore the number pf periods available for frequency measurement too small. (2) There was no assurance of constant conditions i n the adiabatic container and p a r t i c u l a r l y the super-75 leak. From v i s u a l observations there were quite marked differences i n the behaviour of the o s c i l -l a t i o n s on d i f f e r e n t runs. Other measurements also indicated t h i s state of a f f a i r s , see Pig. 2 5 . The recording with stroboscope and camera: ( 1 ) The chief disadvantage was that i t was not always possible to check that a good record had been ob-tained while there was s t i l l l i q u i d helium i n the dewar, as i t was not generally f e a s i b l e to process a l l films during a run., On occasions, the l i q u i d l e v e l i n the c a p i l l a r y would move out of p o s i t i o n when some thermal disturbance occurred which the temperature control bridge could not completely compensate. With v i s u a l observation t h i s was not serious as the l e v e l would return to the equilibrium p o s i t i o n and the observation could be continued, but with the camera i t often meant that the f i l m record was' wasted. ( 2 ) It was not always easy to get a good image, of the meniscus as was discussed i n Chapter I I I . ( 3 ) The images of the meniscus suffered small d i s -placements on the f i l m , the possible cause of which has already been mentioned. These displacements produced a scattering i n the plotted waveform which upset the frequency determinations see F i g . 1 7 . 76 In spite of the disadvantages discussed above, the stroboscopic l i g h t used with the camera s t i l l remains a very useful m®ifih&& aid i s the only means available so far f o r ob-t a i n i n g a reasonably detailed picture of the o s c i l l a t i o n wave-form. However, the disadvantages of both the adiabatic container and stroboscope method when added to the trouble already experienced with the glycerine se a l , indicated that r e s u l t s might be obtained more e a s i l y and r e l i a b l y i f the con-tainer design and the method of taking observations were a l -tered. Alterations i n design were made and resulted i n the wire - f i l l e d - t u b e apparatus which Is described i n Chapter I I I . The reasons f o r the p r i n c i p a l a l t e r a t i o n s are given below: (1) To-ensure as f a r as possible that conditions of:jfch©p mal i s o l a t i o n were constant for each run, there had to be no doubt about the state, of the vacuum jacket surrounding the beaker, so an arrangement was pro-vided to pump th i s continuously during an experi-ment. (2) I f reproducible conditions could be obtained i n the vacuum jacket i t only remained to provide a super-leak which would stay constant i n cross-section be-tween one run and the next. The wi r e - f i l l e d - t u b e f u l f i l l e d this requirement much better than the 77 optical f l a t s and also possessed a number of other advantages f o r the present design. (3) The r e l a t i o n giving the adiabatic o s c i l l a t i o n f r e -quency, equation (19) Chapter I I , shows that the frequency of o s c i l l a t i o n i s inversely proportional to the length of the superleak. With the wire-f i l l e d - t u b e s i t i s possible to provide a superleak of much greater length than i s the case with the o p t i c a l f l a t s , (see Table II) and t h i s resulted i n a considerable reduction i n frequency. The frequen-cy was low enough for .visual observations to be made on the o s c i l l a t i o n s and there was therefore no need to use the.stroboscope and camera. (1+) The method of incorporating the superleak into the arrangement of beaker .and vacuum jacket was altered with the object of overcoming the troubles prev-io u s l y experienced with the glycerine seal and also to provide better thermal i s o l a t i o n for the beaker contents. The remainder of the i n v e s t i g a t i o n was ca r r i e d out with the wire-filled-tube apparatus and almost a l l the exper-imental r e s u l t s were obtained with i t . TIME, SECONDS P i g . 1 8 . General form of a d i a b a t i c o s c i l l a t i o n s . f a c i n g page 7 8 78 TABLE I I I . T Wa. (exp.) Run Number K 1.39 2.37 k 1.1+32 2.58 5 1.500 2.73 5 1.559 2.68 h •1.61+0 3.02 5 1.700 2.98 k 1.760 3 . 2 5 3 1.835 3.39 5 1.826 3.81+ l 1.906 3 . 6 5 2 1.992 3.93 1 2.065 3 . 2 5 2 . 3 9 Data Obtained with the Wire-Filled-Tube Apparatus, A l l o s c i l l a t i o n s for the observations reported here were produced by discharging a condenser through tlje heater to l i b e r a t e 8.11X10-^ ergs inside the beaker. The general form of the o s c i l l a t i o n s observed at several temperatures i s shown i n F i g . 1 8 . The main features of the o s c i l l a t i o n s are evident from the p l o t s , the frequency increases with temperature for those temperatures shown and so does the damping, while the rate of decrease of the mean l e v e l of the meniscus i s greater at lower temperatures. The Temperature Dependence of the Frequency: The temperature dependence of the o s c i l l a t i o n f r e -quency i s plotted i n F i g . 19, the experimental values used i n th i s p l o t being presented i n Table I I I . The t h e o r e t i c a l curve i s that plotted i n F i g . i| of Chapter I I , the frequency of i d e a l adiabatic o s c i l l a t i o n s for the geometry of the wire-f i l l e d - t u b e apparatus. The agreement of the experimental points with the form of the t h e o r e t i c a l curve i s seen to be good, the difference between a curve f i t t i n g the experiment-a l points and the t h e o r e t i c a l one being due presumably to an uncertainty i n the knowledge of the geometry of the apparatus and some heat leak between beaker and bath. The experimental points were obtained i n a series of runs, those points obtain-ed on a p a r t i c u l a r run being denoted by a common symbol. TABLE I I . 80 Dimensions and Geometrical Factors for Adibatic Containers. Optical F l a t s II Wire-filled-tube Volume A 1+.0 cm.^ 6 . 6 cm.^ C a p i l l a r y diameter 1.11+ mm. 1 . 10 mm. Length of superleak 0 . 6 8 mm. 1 1 . 7 cm. Cross-section of superleak 2 . 1 x. 10"^cm.^ 7 . 1 5 * 10""^cm. TABLE IV. T cm.^x 10"^ ergXlO"- 5 • joules/gm./deg. 1 .992 1 . 9 0 6 1 . 7 6 0 1 . 7 0 0 1 . 5 5 9 1 . 3 8 8 2 . 0 2 . 6 6 3 . 6 1 1+.18 5.1+2 6 . 8 5 8.1+7 8 .50 8 .k3 8.1+1 8.35 8 .20 1.1+5 1.11+ 0 . 9 1 0 . 8 1 0.61+ 0.56 81 It would be desirable to obtain more points i n the region of o the curve above 1 . 9 K i n order to strengthen the evidence f o r the curve having a maximum. However, such points are d i f f i -c u l t to obtain as the amplitude of o s c i l l a t i o n decreases and the damping increases with r i s i n g temperature. As well as t h i s , there i s the experimental s i t u a t i o n of being "backed up to the lambda point", as was discussed i n Chapter IV.' Frequency values obtained on two of the runs were rejected because they were considerably d i f f e r e n t from the values ob-tained at the same temperatures on other runs which were con-sis t e n t with the majority of readings. Departures such as these were'thought to be due to p a r t i a l f a i l u r e of the glyc-erine seal r e s i i l t i n g i n decreased adiabacity and a lower f r e -quency. The measured pe r i o d i c times are considered r e l i a b l e to a l i t t l e better than a tenth of a second i n most cases. The frequency values obtained with the o p t i c a l i f l a t s apparatus are not shown, because no r e l i a b l e figure f o r the separation of the o p t i c a l f l a t s could be obtained to enable - a comparison to be made with theoret i c a l frequency values. In previous calculations a separation of 1.-5 microns was assumed, but to give a reasonable- agreement with theory, th i s figure had to be amended to 3 . 2 5 microns when the geom-etry of the beaker was more c a r e f u l l y measured. The Damping: An in d i c a t i o n of the damping of the o s c i l l a t i o n s O 3 I 2 3 4 PERIOD NUMBER Pig. 20. The* decay of amplitude of the • o s c i l l a t i o n s facing page 82. 82 can be obtained from the data used to p l o t the curves of Pig. 18 by p l o t t i n g the maximum amplitude of o s c i l l a t i o n a-gainst the number of the period after making allowance f o r the aperiodic decrease of the mean meniscus l e v e l . This i s done i n Pig. 2 0 . The accuracy of the points p l o t t e d i n Pig. .-' 20 i s not high because the amplitude values r a p i d l y become of the same order as the uncertainties i n the experimental readings. The curves of Pig. 20 p a r t l y i l l u s t r a t e what was observed during the experiments, that there i s an i n i t i a l damping of the o s c i l l a t i o n s , a f t e r which the o s c i l l a t i o n s continue with a very much slower decrease i n amplitude. This second stage i s reached much more r a p i d l y at higher temperatures. I t should perhaps be remarked that the o s c i l l a t i o n s did not end at the points shown i n F i g . 18 but that readings of the turning points were not taken beyond a certain stage, because at the.lower amplitudes, small f l u c t u a t i o n s , probab-l y due to minute Variations i n bath temperature, became im-portant and often tended to upset the regular pattern of the motion. Even after.the o s c i l l a t i o n s had died down, the men-is c u s , while i t was moving, would execute small fluctuations as though i t were caught up and released swinging again, as i t sought to return to the i n i t i a l l e v e l . An estimate of the damping of the o s c i l l a t i o n s at 1 . 7 0 0 K gives a value of a - 0 - l which corresponds to a 8 3 value for of 0.05 making use of the, graph of Pig. 6. I f the decay constant for the aperiodic decrease of the men-iscus l e v e l i s determined with the help of Pig. 6 and equat-ion (11),. the corresponding value of J-/tOa i s 10 or l e s s . I f the theory i s to be taken as correct when applied to the damping, the two values obtained for L/uJ^ should agree and the fact that they do not, might be taken as evidence for heavier, damping of the o s c i l l a t i o n s , caused by factors other than the purely thermal ones considered i n the theory. The observation that the damping occurs i n two stages may be con-nected with t h i s . Further examination of t h i s question should be postponed u n t i l better experimental data on the damping are available and a proposed experiment for obtain-ing t h i s data i n a much better way i s outlined i n Chapter VI. A closer comparison of theory with experiment could be made i f the geometry of the apparatus were better known as any use of the r a t i o of observed frequency to the i d e a l t h e o r e t i c a l frequency for purposes of obtaining a corresponding l-fu^ value (see Pig. 6 ) , i s of l i t t l e value at the present because of un-certainty about the geometry. The Aperiodic Decrease and Thermal Linkage. The return of the l i q u i d l e v e l to the o r i g i n a l equi-l i b r i u m p o s i t i o n a f t e r the o s c i l l a t i o n s ceased was measured. This i s the f a l l of the mean l i q u i d l e v e l corresponding to the aperiodic root ^ 3 i n the adiabatic o s c i l l a t i o n region, 8 ELAPSED TIME, SECS. Pig. 21. ' The aperiodic f a l l of the meniscus a f t e r o s c i l l a t i o n s have ceased. The curve for 1.992 °K i s f o r a t r i g g e r i n g pulse of 21+000 ergs. facing page 81+ 8h which i s expressed as the second term i n equation (18). Some of the experimental curves are shown i n P i g . 21. A s u r p r i s -ing feature of these curves i s that on a semi-log p l o t they do not appear as straight l i n e s . There i s a straight port-ion corresponding to exponential decay, followed by a region where the rate of f a l l of the meniscus increases, the rate increasing as the meniscus nears the bath l e v e l . This e f f e c t was also found when using the o p t i c a l f l a t s apparatus. One possible explanation of t h i s rate increase i s that there i s a minute temperature r i s e which takes place s t e a d i l y during the period of taking readings of the meniscus l e v e l . Although the temperature of the l i q u i d i n the main helium dewar i s maintained within close l i m i t s by the control bridge, i t i s possible for the contents of the diving b e l l to be at a s l i g h t l y higher temperature because of the f i n i t e , thermal resistance of the copper boundary separating the d i v -ing b e l l l i q u i d from the main dewar l i q u i d . In the case where the l i q u i d l e v e l i n the main helium dewar i s slowly dropping and increasingly exposing the contents of the d i v i n g b e l l to external r a d i a t i o n , a s i t u a t i o n would seem to -exist where the temperature of the l i q u i d i n the diving b e l l .could slowly r i s e . The rate of temperature Increase considered here i s extremely small and well below that detectable with an o i l manometer over the period required f o r takingsread-ings at one p a r t i c u l a r temperature " s t a t i o n " . The above T°K Pig. 22. The temperature dependence of the relaxation time for the f a l l of the meniscus after o s c i l l a t i o n s ceased. The s p e c i f i c heat is normalised to the relax-ation time at 1.5°K« facing page 85 85 explanation i s supported by the observation that the meniscus did not i n general come back to i t s o r i g i n a l s t a r t i n g p o s i t i o n but to a p o s i t i o n just s l i g h t l y below i t , i n d i c a t i n g that the bath was a l i t t l e warmer than before. The straight portions of the graphs showing the l e v e l decay were used to determine the relax a t i o n times for the process; these w i l l be described as "extrapolated relax-ation times". In Pig. 2 2 , the extrapolated relaxation time i s shown plotted against temperature. The smooth curve i n Pi g . 22 i s the s p e c i f i c heat of l i q u i d helium II as determin-ed by Kramers et a l ( 1 9 5 2 ) , normalised to f i t the relax a t i o n time data at 1 .5 K. The agreement between the curve and the , experimental points i s good evidence for regarding the f a l l of the l i q u i d l e v e l as being determined by thermal considerr ations only, at least over that region of the decay which i s exponential. Calculations were made to determine the magnitude of the heat f l u x into the container along various possible paths such as e l e c t r i c a l leads, the metal of the w i r e - f i l l e d -tube and the glass of the glass plug forming the bottom of chamber A. None of these provided a thermal l i n k of the order of magnitude required for agreement with the experi-mental observations, although together they would account for a small part. , 86 A c a l c u l a t i o n was made of the expected heat f l u x through the wire-fil l e d - t u b e superleak using the i n t e r n a l convection r e l a t i o n developed by London & Z i l s e l (I9I4.8), - 2 but the value obtained was too small by a factor of 10 or more. This at least i s i n the same d i r e c t i o n and of about the same magnitude as the discrepancies noted by London & Z i l s e l for channel widths of the size considered here. Thus assuming the possible sources of heat leak have a l l been taken into account, the probable means of thermal linkage is. through the superleak by a mechanism which has as yet r e -mained unexplained by any theory, see Daunt & Smith ( 1 9 5 ^ p. 2 0 0 . The r i s e of the l i q u i d l e v e l i n the c a p i l l a r y from the equilibrium p o s i t i o n to the point where the o s c i l l a t i o n s occur should be a measure of the entropy of l i q u i d helium I I . The energy introduced into the beaker from the t r i g g e r i n g discharge i s known and the change i n meniscus height can be obtained Etoom curves such asathose i n Pig. 2 1 , extrapolating the curves back to zero time to allow for heat leak which occurs during the time of r i s e . I f Q Is the energy supplied and AV i s the change i n l i q u i d volume corresponding to the change i n height, the equation for energy balance should read: GL-r, AVpvL = TSoAV +• (V-H/W)Cf>AT Pig. 23. The thermal balance of the container. Values of (Q. +• AV/cvL")/TpAV compared with the entropy of l i q u i d helium I I . facing page 8 7 87 Where V i s the volume of l i q u i d i n the beaker, and p*r are the d e n s i t i e s of l i q u i d and vapour r e s p e c t i v e l y , T the temperature, S the entropy and G the s p e c i f i c heat, and L the l a t e n t heat of evaporation of l i q u i d helium. I f as a f i r s t approximation the second term on the r i g h t hand side i s n e g l e c t e d , then the expression Tp /W should give values of the entropy. The values obtained from the c a l c u l a t i o n are given i n Table IV and d i s p l a y e d i n P i g . 23. The entropy values of Kramers et a l (19^2), are a l s o p l o t t e d f o r the purposes of comparison. Although the two curves have the same form, the discrepancy i n values i s very great. No reason can be found f o r such a l a r g e d i f f e r e n c e , as a l l the experimental quan-t i t i e s are considered, to be determined to a degree which would discount the occurrence of an e r r o r of t h i s s i z e . The measure-ments on the a p e r i o d i c decrease of the l i q u i d l e v e l , P i g . 21, c e r t a i n l y do not i n d i c a t e a heat leak of s u f f i c i e n t s i z e , and even though the thermal c a p a c i t y of the beaker and thermometer have been neglected t h i s should only i n v o l v e minor c o r r e c t i o n s . A p o i n t worth mentioning, although i t does not pro-vide a d i r e c t answer to the above s i t u a t i o n , i s that the ener-gy of 8000 ergs i s introduced i n t o the beaker i n a time i n t e r -v a l of about 10 J seconds, so the power l e v e l i s q u i t e h i g h , 8 8 ( 0 . 8 watt) for the duration of the pulse. I t may be that some e f f e c t associated with the t r a n s i t o r y high power l e v e l can cause energy loss outside the beaker, Pellam ( 1 9 U 9 ) , i n his paper on measurement of second sound v e l o c i t i e s using pulse techniques, quotes a heat flow density of about 0 . 0 0 2 £ cal/cm^/sec as being the threshold for the production of f i r s t sound i n l i q u i d helium at a temperature of 2°K, The present figure of 0 , 8 watt i s equivalent to about 6 0 times t h i s threshold, so there are some grounds for considering that the condenser discharge pulse used was. s u f f i c i e n t to "overdrive" the l i q u i d helium. Unfortunately, the in t e r e s t connected with this point was not r e a l i s e d u n t i l the oppor-tunity for experimentally checking.it had passed. An e f f e c t was observed i n the experiments which may have had some connection with the rate at which energy was r e -leased i n the condenser discharge. This e f f e c t was only ob-served with the wire-fil l e d - t u b e apparatus, but i t may well have just escaped observation i n the o p t i c a l f l a t s apparatus. The e f f e c t consisted of a very small and rapid o s c i l l a t i o n of the meniscus immediately following the condenser discharge but before the meniscus had begun i t s general movement to the o s c i l l a t i o n point. This o s c i l l a t i o n or "reverberation" as i t was c a l l e d , depended i n both frequency and amplitude on the temperature, the frequency appearing to be lower and the am-pli t u d e greater at higher temperatures. As observations on t h i s e f f e c t were in c i d e n t a l to the main work on o s c i l l a t i o n s , IO 8 'o X u 6 (0 IO . 2 u o U. 4 u. O Ui rr > 1 V = 1 2 6 cm/sec. -O \ o o, o 1-4 1 6 T ° K . 1 8 2 0 2 2 P i g . 2l|. Temperature dependence of flow r a t e s . Upper curve; the 'flow r a t e up t o the o s c i l l a t i o n p o i n t . Lower curve; the flow r a t e d u r i n g the f i r s t backswing of the o s c i l l a t i o n . f a c i n g page 8 9 89 no investigation was made of i t . The observation that the meniscus did vibrate does suggest the p o s s i b i l i t y that a rapid energy exchange might take place through the s l i t but t h i s i s a long way from explaining the discrepancy between the two curves i n Pig. 2 3 . Plow Rates* A further quantity which i s i n t e r e s t i n g when con-sidering o s c i l l a t i o n s i s the flow v e l o c i t y of the l i q u i d . Values of v e l o c i t i e s measured over a range of temperatures are plotted i n P i g . 2 i | , These are average values of v e l o c i t -i e s , no account being taken of accelerations during the mot-ion of the meniscus. An idea of the variations i n v e l o c i t y may be obtained from the more detailed picture of the menis-cus motion given i n Pig. 17* The upper curve of Pig. 2i| shows the v a r i a t i o n with temperature of the v e l o c i t y of the meniscus when t r a v e l l i n g between the i n i t i a l equilibrium po-s i t i o n and the f i r s t turning point at the sta r t of an o s c i l -l a t i o n . The lower curve gives the average v e l o c i t y over the f i r s t backswing of the o s c i l l a t i o n . Both of these curves have a form similar to that of /°»/p usually associated with the temperature v a r i a t i o n of c r i t i c a l v e l o c i t i e s . However, i n the present case, the v e l o c i t i e s are very lowj that for the superfluid v e l o c i t y at 1 .39°K i s indicated on the graph. At the time of writing, no opportunity has occur-red for determining c r i t i c a l v e l o c i t i e s i n steady flow exper-9 0 iments for the wir e - f i l l e d - t u b e Used and therefore the v e l -o c i t i e s shown i n Pig, 21+ cannot be said to be either sub or s u p e r - c r i t i c a l . They are, however, very low, much lower than published values of c r i t i c a l v e l o c i t i e s , see Winkel, Delsing & P o l l (195>5>)» Although there i s some uncertainty i n the knowledge of the superleak geometry, the agreement of thes o s c i l l a t i o n measurements with theory shows that t h i s geometry i s known at lea s t s u f f i c i e n t l y well to e s t a b l i s h the magnitude of the superfluid v e l o c i t y . Therefore, the v e l o c i t i e s prob-ably are below the c r i t i c a l and such curves as the ones i n Pig. 21+ may be likened to the curves of the temperature var-i a t i o n of v e l o c i t y through a superleak under a constant g r a v i t a t i o n a l pressure head, where the pressure head i s very low, Swim & Rorsach (1951+). A v e l o c i t y below the c r i t i c a l i s consistent with previous r e s u l t s obtained with isothermal o s c i l l a t i o n s , see Chapter I, Knowledge that flow i s taking place at les s than a c r i t i c a l rate i s of l i t t l e value i n i t s e l f . I t i s of value, however, i f i t helps to elucidate the mechanism of a c r i t i c a l v e l o c i t y or provide some information about superfluid flow. This question i s involved with that of the damping of the o s c i l l a t i o n s , which has already been discussed to some extent. It was suggested by P. London, (1951) that the study of adiabatic o s c i l l a t i o n s might y i e l d information on conditions under which there was a c r i t i c a l rate of flow v e l o c i t y . No 91 help with these questions can be obtained from discussing the v e l o c i t y measurements obtained i n the present experiments but the same experiment which i s proposed for the damping measure-ments and which i s outlined i n Chapter VI, may well give very useful data on f l u i d flow. A few r e s u l t s on flow rates obtained with the o p t i c a l f l a t s apparatus are shown i n P i g . 2 5 . The chief reason for taking these measurements was to use them as a guide to the con-d i t i o n of the gap between the o p t i c a l f l a t s . The flow rates were lower than those reported i n other experiments, Bowers & Mendelssohn ( 1 9 5 2 ) , Kapitza (19^1) J which could mean that the flow channel was wider ( i . e . that some normal f l u i d flow was involved). The flow rates, however, did give some assurance that the channel was not more than a few microns wide. The coincidence of the curves for 1 .9^2 and 1 . 8 5 7 K which were taken on d i f f e r e n t runs, shows the lack of reproducible con-ditions which was one of the drawbacks of the o p t i c a l f l a t s equipment. Temperature Measurements. The system for detecting temperature" differences was not used successfully i n detecting temperature o s c i l l a t -ions, although, as was discussed i n Chapter IV, the e f f o r t expended on t h i s method i n the l a t t e r part of the programme was secondary to that spent on l i q u i d l e v e l o s c i l l a t i o n s . F i g . 26 . O s c i l l o g r a m of temperature d i f f e r e n c e produced by thermal p u l s e of 8 0 0 0 e r g s . facing page 92 92 One representative r e s u l t obtained with the o p t i c a l f l a t s apparatus i s shown i n Pig. 26. This oscillogram was o obtained at a temperature of l.l|3 K with the usual tr i g g e r discharge of about 8000 ergs. The second trace i n the photo-graph displays a 60 cycle per second reference s i g n a l . There was almost no coupling between the e l e c t r i c a l c i r c u i t s so that the observed d e f l e c t i o n was s o l e l y due to the temper-ature change i n the beaker. No o s c i l l a t i o n s are evident a-bove the background noise, although the main temperature change of approximately 10 ^ K i s shown quite we l l . The rapid decay of the temperature shown i n the photograph d i d not occur on a l l runs with t h i s apparatus to the same extent, conditions on t h i s p a r t i c u l a r run not having been quite as good as on some of the others. It does seem possible that with the im-proved apparatus represented by the w i r e - f i l l e d - t u b e version, and some improvements i n the thermometer c i r c u i t s , there i s s t i l l a hope of pushing the temperature s e n s i t i v i t y an order of magnitude further, where the temperature o s c i l l a t i o n s should be observable. Some measurements were also taken of the temperat-ure difference between beaker and bath when using the o p t i c a l f l a t s apparatus to measure flow rates under steady conditions such as those shown i n Pig.. 2 5 . However, these measurements were sandwiched i n between observations on o s c i l l a t i o n s so '• 93 that r e l a t i v e l y few of them were made. Those that were made showed that there was a temperature difference between beak-er and bath for quite low v e l o c i t i e s of flow; much lower than the "knee" of curves such as those i n Pig. 25>. This i s i n contradiction to the findings of Kapitza (I9I4I), who used the onset of a temperature difference between beaker and bath as an i n d i c a t i o n that the c r i t i c a l v e l o c i t y had been reached. I t i s much more l i k e l y that the appearance of a temperature difference depends on the s e n s i t i v i t y of the thermometer used, the shape of the experimental beaker and i t s thermal i n s u l a t i o n . I f l i q u i d i s drawn into a beaker of the design used i n the present experiments, a change i n height of the l i q u i d l e v e l i s produced very e a s i l y and this difference i n height i s immediately e f f e c t i v e as a temperature difference through the thermo-mechanical e f f e c t . 9k CHAPTER VI  CONCLUSIONS. Os c i l l a t i o n s of l i q u i d helium II i n an adiabatic container have been observed and measured. The general behaviour of the o s c i l l a t i o n s agrees with the th e o r e t i c a l picture presented by Robinson, (1951) O 0 while the measured frequency i n the range 1.38 K to 2.065 K has the same form of temperature dependence and agrees well i n magnitude with the t h e o r e t i c a l l y computed values f o r the apparatus. The observed agreement with the t h e o r e t i c a l l y pre-dicted values of frequency gives support to the assumption made i n the theory, that the f l u i d composition i n the super-leak is that of the bulk l i q u i d and that i t - i s the superfluid f r a c t i o n which moves. The case for the f i l m superleak has been investigated by Atkins, although as discussed i n Chap-ter I, there i s some uncertainty i n interpretation of the res u l t s because the temperature v a r i a t i o n of the f i l m t h i c k -ness i s not f u l l y understood at present. A s a t i s f a c t o r y comparison cannot be made at present between the observed damping and the theory. This i s because of uncertainty i n the heat leak factor, and i n s u f f i c i e n t l y precise measurements of the decrease of o s c i l l a t i o n ampli-tude. The f l u i d flow rates correspond to v e l o c i t i e s which 95 appear to be well below c r i t i c a l values for the channel d i -mensions i n the superleak but with the experiment i n i t s pres-ent form, there does not appear to be any way of studying the conditions governing sub or s u p e r - c r i t i c a l flow as was sug-gested by P. London ( 1 9 5 1 ) . A considerable amount of work remains to be done to provide a more complete description of the adiabatic o s c i l -l a t i o n s . Extension of the frequency measurements to cover a wider range of temperatures and with greater precision would be one task. E s t a b l i s h i n g the geometry factor for the apparatus within much closer limits.would enable the theory to be applied more successfully i n estimating the heat leak of the adiabatic container. Coupled with more accurate measurements on the waveform th i s should give a check on the t h e o r e t i c a l value for the damping. A s l i g h t l y d i f f e r e n t experimental approach i s sug-gested by the Helmholtz resonator analogue discussed i n Chap-ter I I . This involves the use of a source of second sound placed externally to the adiabatic container and designed to operate at frequencies i n the region of resonance of the con-ta i n e r . Second sound generated by t h i s source should produce movement of the meniscus i n the c a p i l l a r y of the adiabatic container and enable the resonance curve of the container to be traced by v i s u a l observation of the amplitude of the men-iscus motion. The resonance curve could then give a value 96 for the resonant frequency and a measure of the damping of the system. Measurements of the damping carried out i n t h i s man-ner should give more r e l i a b l e information than that obtained i n the present experiments. I t should also be possible to investigate flow through the superleak at various rates by a l t e r i n g the amplitude of the second sound i n a controlled manner. In th i s way, London's suggested examination of con-di t i o n s for the occurrence of a c r i t i c a l v e l o c i t y could pos-s i b l y be carried out. 97 APPENDIX I THE CHARACTERISTICS OF "LEADED-BRASS"  RESISTANCE THERMOMETERS. The leaded-brass wire used was manufactured by Messrs. Johnston Mathey Ltd. at the suggestion of Dr. K. Men-delssohn of the Clarendon Laboratory, Oxford, and Dr. Mendel-ssohn very kindly supplied some of the wire for use i n the present investigation. The use of t h i s wire was a develop-ment based on e a r l i e r experimental work, Babbitt & Mendel-ssohn (1935)» i n which the superconducting t r a n s i t i o n for a s i l v e r - r i c h , l e a d - s i l v e r a l l o y was investigated. A p a r t i c -ular percentage concentration of lead was found which altered the resistance-temperature curve at the transition-temperat-ure, so that the same decrease i n resistance took place, but over a much wider temperature i n t e r v a l . In t h i s broadened t r a n s i t i o n region the wire could be used as a resistance ther-mometer, as the temperature i n t e r v a l was wide enough to be useful and the resistance-temperature curve was very steep. The leaded-silver wires were not e a s i l y prepared and presum-ably the leaded-brass wire evolved, because I t was more con-venient. The resistance thermometers were made by winding the leaded-brass wire (diameter 0.06 mm.) on small formers made from "Tufnol"*- and of about 1 cm. diameter. As the •K-"Tufnol" i s a laminated, synthetic, r e s i n bonded material manufactured by Tufnol Ltd., Birmingham, England. 10 1-3 1-5 17 1-9 2-1 T°K Pig. 27. Calibration curve for leaded-brass wire resistance thermometer. facing page 98 98 wire was not insulated, the outside surface of the former was cut with a double screw thread, so that the wire could be doubled back on i t s e l f and wound non-inductively by run-ning i t i n two p a r a l l e l grooves around the former. Special care had to be exercised i n handling the wire when winding the c o i l s , as i t i s very springy and there was a danger of forming kinks and breaking the wire. Kinks were avoided but some trouble was experienced when the wire on one c o i l broke very e a s i l y after i t had been used several times i n l i q u i d helium. The wires wound i n t h i s manner seemed to maintain constant c a l i b r a t i o n . A c a l i b r a t i o n curve for one of the thermometers i s shown i n Pig. 2 ? . The value of d^er obtained from t h i s curve i s 1.53/°K, a value which i s leas than the value for a carbon resistance thermometer, ( - 2 . 6/°K), but of the same magnitude and constant over most of the l i q u i d helium II range. The shapes of the c a l i b r a t i o n curves of these wires are very dependent on the state of s t r a i n i n the wires and can be appreciably altered by annealing, Parkinson & Quarr-ington ( 1 9 5 4 ) . This dependence on annealing seems to be caused by the manner i n which the lead i s present i n the brass. One of the requirements, for a p a r t i a l superconducter of this type, i s that the metals should not form a s o l i d solution-and that i n the present case, for instance, the lead should be i n the form of "islands" i n the brass. In the wire drawing pro-I I I I L: I L O I 2 3 4 5 6 7 MEASURING CURRENT, (m.a.) F i g . 28. The current dependence of the resistance for the leaded-brass wire. fac i n g page 99 99 cess these crystals of lead are. drawn out to form long threads, van Dijk ( 1 9 5 1 ) , and i t has been suggested, Babbitt & Mendel-ssohn (1935)» that the size dependence of the t r a n s i t i o n tem-perature for these threads, causes the wire resistance to de-crease r a p i d l y , as more and more threads are brought into the superconducting chain. Such a mechanism would c e r t a i n l y be •. very sensitive to st r u c t u r a l changes-within the wire. In th i s connection i t i s worth mentioning that a strong depen-dence of the steepness of the resistance-temperature curve on the wire diameter has been found for phosphor-bronze wiftes, ' Peshkov ( 1 9 W ; vanL'BIp: ( 1 9 5 1 ) . The resistance of these wires also depends on the magnitude of the measuring current used and some measurements were made of t h i s resistance v a r i a t i o n . Except for a r e f e r -ence to "the usual dependence on measuring current", Parkin-son & Quarrington (195U)> there seems to be no account of t h i s e f f e c t i n the l i t e r a t u r e . The r e s u l t s are p l o t t e d i n P i g . 28. It can be seen that-ibbst of the resistance change occurs when the power dissipated i n the wire i s 1 0 " ^ watts or l e s s , so t that i t i s u n l i k e l y that the e f f e c t i s connected with a prop-erty of l i q u i d helium I I . The e f f e c t i s presumably connected with the destruction of superconductivity i n the lead f i l a -ments. Whatever the explanation, the magnitude of the v a r i a t -ion i s of p r a c t i c a l i n t e r e s t when using such wires as r e s i s -tance thermometers. For a potentiometer measurement of r e s i s -100 tance, the current dependence presents no d i f f i c u l t i e s , but for bridge measurements, care must be taken to ensure that the measuring current is constant i n the thermometer i f actual temperature readings are wanted. In the present experiments, an out of balance current i n a Wheatstone bridge was used to indicate the r a p i d i t y of temperature change only, so that the current dependence was not a serious l i m i t a t i o n . 101 APPENDIX I I . THE TEMPERATURE STABILISING SYSTEM S t a b i l i s a t i o n of the l i q u i d helium bath temperature was a v i t a l necessity i n the adiabatic o s c i l l a t i o n experi-ments because of the magnitude of the thermo-mechanical e f -fe c t and the important part i t plays i n the mechanism of the o s c i l l a t i o n s . I f measurements of the p o s i t i o n of the meniscus l e v e l i n the c a p i l l a r y of the adiabatic container are to be made.to within a tenth of a millimetre, the bath temperature should be s u f f i c i e n t l y stable so that fluctuations of the men-iscus caused by the thermo-mechanical e f f e c t w i l l be less than t h i s . Making use of the London equation for the thermo-mechanical e f f e c t , a pressure difference of one tenth of a millimetre of l i q u i d helium corresponds to a temperature difference of 0.5xi0~^°K at 1.5°K. Thus at l.£°K the tem-perature must be s u f f i c i e n t l y stable f o r the temperature fluctuations not to exceed this value, at lea s t f o r periods of several minutes, while the s t a b i l i t y must be only an order of magnitude or so less f o r periods of up to an hour or so. The method used for s t a b i l i s i n g the bath temperat- .. ure was one recently described by Boyle & Brown (1951+), and also by Sommers (195U)» Dr. Brown kindly made the method available f o r the present experiments, i n advance of p u b l i -1000 cp.s. F i g . 29. The temperature s t a b i l i s i n g system. facing page 102 102 cation, when he arrived i n thi s Department. The method i s described i n the or i g i n a l papers, but a very b r i e f outline w i l l be given here to f a c i l i t a t e the discussion of one or two points. The diagram of Pig. 29 shows the essentials of the apparatus. A carbon resistance thermometer i s placed i n the l i q u i d helium bath and connected as one arm of a simple r e -o sistance bridge operated at audio frequencies. A high gain audio amplifier i s placed across the bridge, i n the p o s i t i o n of detector, with i t s output connected to a heater also i n the l i q u i d helium bath. The l e v e l of the amplifier output can be watched on an oscilloscope. To s t a b i l i z e the bath at a chosen temperature, the bridge i s set so that a small out of balance condition e x i s t s , i n such a sense, that the bridge would balance i f the temper-ature of the bath were s l i g h t l y lowered. . However, the condit-ion i s maintained because the heater supplies power to the bath, which together with the natural rate of heat i n f l u x balances the rate at which energy i s removed from the l i q u i d by evaporation. Once set, t h i s system w i l l correct the bath o temperature when i t fiiatiiuatas as a r e s u l t of pumping speed v a r i a t i o n s , etc. A bridge system was b u i l t and used for c o n t r o l l i n g the bath temperature i n a l l adiabatic o s c i l l a t i o n experiments 103 The temperature control was s u f f i c i e n t l y good to enable the o s c i l l a t i o n s to be measured, although as discussed i n Chapter VI, the fluctuations did become important when the o s c i l l a t -ion amplitude decreased to about a tenth of a millimetre. Also, there were occasional temperature surges which the con-t r o l bridge did not completely compensate, although i t must have very much reduced them. Some sample data which provide an index of the performance of the bridge are given below. Following the treatment given by Boyle & Brown, the s t a b i l i t y factor for the device i s i n which ^ w dip and n - -2^L<x Ee Q df?^ Where; W = rate of removal of heat by evaporation C5X 10~ 2 watt) V = vapour pressure of bath (1 . 3 8 8 K, 2.01 mm.Wa) 9>£ = gradient of vapour pressure curve d T (ll+ . 8 x lO-Mynes/ cm 2/K) f± = voltage gain of amplifier (9 . 3 X10-*) <X = bridge s e n s i t i v i t y factor (0 . 2 £ ) E =ninput voltage to bridge (0.1+ v o l t ) So = amplifier output voltage (0.71+ v o l t ) RB = resistance of heater (190 ohm) RFL = resistance of thermometer 10k For the resistance thermometer used had the value - 2.16/°K at 1.388°K. Using the above values m~= 0.55 watts/°K and n = -l5«7 watts/°K, which gives a s t a b i l i t y factor of 30. This factor could be increased by running the bridge further of f balance and feeding more power into the bath with the heater but i t represents a compromise reached between suf-f i c i e n t temperature control and the minimum evaporation rate required to achieve i t . 105 APPENDIX III THE CHARACTERISTICS AND CONSTRUCTION OF THE SUPERLEAKS. For experiments involving almost exclusive flow of the superfluid through a channel, at least one of the channel dimensions must be small enough to e f f e c t i v e l y stop the flow of any normal f l u i d . At the same time, s u f f i c i e n t superfluid must be able to flow so that i t s rate of flow can be measured by observing the change i n quantity of l i q u i d i n a container at one or other of the channel ends. Thus a l l superleaks have the common feature that they have channels with one d i -mension quite small and the other large i n comparison. From experience gained i n experiments with such channels i t has been found that the small dimension must be about one micron or l e s s , to provide flow with e s s e n t i a l l y superfluid charac-t e r i s t i c s . See Daunt & Smith, (1951+ b) p* 8 1 . Two types of superleak were used i n the adiabatic o s c i l l a t i o n experiments, a p a i r of o p t i c a l l y f l a t glass discs and a metal tube f i l l e d with a large number of very f i n e wires. The O p t i c a l l y F l a t Discs. These dis c s , henceforth referred to as "the o p t i c a l f l a t s " , were chosen for the superleak i n the f i r s t experi-ments because thay had been used by several workers i n prev-ious experiments, Kapitza (191+1), Bowers and Mendelssohn ( 1 9 5 2 ) , Hung, Hunt & Winkel ( 1 9 5 2 ) , and t h e i r construction seemed 106 straightforward, i f , as i t l a t e r turned out, somewhat tedious. The glass used was a b o r o - s i l i c a t e crown i n the form of " f i l l e r blanks", 3 mm. thic k , kindly supplied by Dr. A. M. Crooker. As i t was not fea s i b l e to o p t i c a l l y f i n i s h the discs after they had been cut, the cutting had to be done with great care to avoid chips being taken out of the edges and scratches being made on the surface. The cutting was done i n the well ,. known manner with a cylinder of copper turned to the approp-r i a t e size rotated i n a pool of carborundum and water by means of a d r i l l press. The glass was given a protective coating of shellac before being subjected to thi s process. In t h i s manner, two pairs of discs were made. The f i r s t p a i r used i n the preliminary experiments, were 3.6 cm. i n diameter with a central hole of 0.5 cm. diameter i n the upper d i s c . The sec-ond p a i r , used i n the second o p t i c a l f l a t s apparatus, were 3.5 cm. i n diameter, with a central hole i n the upper disc of diameter 2.10 cm., see Pig. 30. In addition to the cutting out of the di s c s , four small holes, s u f f i c i e n t to pass 36 B.&S. gauge constantan wire through, were d r i l l e d i n the bottom f l a t of the second p a i r , see Pig. 9» The wires were leads to the thermometer and heater inside the adiabatic chamber. The holes i n the glass were made with a high speed d r i l l press d r i v i n g a d r i l l made from a small copper wire which was fed with carborundum powder and lubricant. This was an extremely tedious process, 107 but one which f i n a l l y produced four neat holes i n the glass without causing any damage to i t s useable surface. After the small holes were cut, the four wires were cemented i n place with "A r a l d i t e " The Ar a l d i t e was polymerised or "cured" by heating the o p t i c a l f l a t to make the seal and then main-ta i n i n g i t at a temperature of 130°C for ten hours. The heat-ing did not seem to a f f e c t the o p t i c a l f l a t to any noticeable degree. The seals produced.in t h i s way were mechanically strong, even after use at l i q u i d helium temperatures, but they did show fine cracks when examined a f t e r they had been used in. several experiments. These cracks were small, almost a l l of,them showed interference fr i n g e s , but i t must be r e -garded as quite possible that several of. them went through from one side of the f l a t to the other. There would then be - a flow path of unknown size i n p a r a l l e l with the gap between the o p t i c a l f l a t s but from the number and size of the cracks, i t i s not considered l i k e l y that they were any appreciable ' f r a c t i o n of the f l a t ' s gap. The measurement of the separation of the f l a t s could only be done to the extent of providing an order of magnitude. Each time the apparatus was assembled and also each time It was cooled down, the separation of the f l a t s would a l t e r , so that f o r a precise measurement, the separation would have to -» " A r a l d i t e " i s the trade name of a group of hardenable resins (ethoxylines) d i s t r i b u t e d i n Canada by Ciba Ltd. of Montreal. 108 be measured when the apparatus was i n p o s i t i o n at a low tem-perature. Gas flow measurement could not be used because the experimental adiabatic chamber was single ended and any meas-urements carried out with another chamber could not be applied with any certainty to the actual s i t u a t i o n when the f l a t s were being used for o s c i l l a t i o n experiments. Measurements with l i q u i d helium I were likewise unsuitable. Optical interferom-e t r y i s applicable to the measurement of the separation, but d i s t o r t i o n introduced by the glass wall of the diving b e l l near the copper glass seal made the observation of the fringes hopeless so that without elaborate provision, o p t i c a l methods could not be used at low temperatures. Under these circumstances, the method adopted was to use an o p t i c a l arrangement to check that the separation was the minimum that could be obtained when the f l a t s were being assembled; i n other words, to make sure that the maximum number of dust p a r t i c l e s had been removed. To do t h i s , a sim-ple arrangement was set up so that Pizeau fringes could be ob-served, using the l i g h t from the mercury green l i n e , see Pi g . 30. When the apparatus was assembled i n the dewars, a rough check was made of the separation of the f l a t s by observing the broad and diffuse coloured fringes produced when white l i g h t was shone on the apparatus. The presence of these fringes served as an i n d i c a t i o n that the o r i g i n a l separation was being more or less maintained and the i r observation was unaffected by d i s t o r t i o n i n the surrounding glass.. It was OPTICAL INTERFERENCE FRINGE PATTERN SHOWING THE CONTOURS OF THE GAP BETWEEN THE "OPTICAL FLATS? F i g . 30 facing page 1 109 found that on almost every occasion when the apparatus was cooled down, the interference colours disappeared before . l i q u i d a i r temperature had been reached and that they reappear-ed when the apparatus warmed up again. It would seem from t h i s that the gap between the f l a t s decreased because they were f o r c -ed closer together when the supporting metal frame work contrac-ted. No trouble was experienced from the e f f e c t of the low temperatures on the o p t i c a l f l a t s , they did not chip nor crack, nor seem to suffer any permanent warping. The Wire-Filled-Tube. For reasons discussed i n Chapter VI of t h i s t h esis, i t was decided to use a w i r e - f i l l e d tube as a superleak. These tubes were introduced by A l l e n & Misener ( 1 9 3 9 ) , and have since been used by others, Brown & Mendelssohn (19l|7)» The technique of.manufacture for the w i r e - f i l l e d -tubes used i n the present work was l a r g e l y based on informat-ion supplied by Dr. J . B. Brown, The wire-filled-tubes used i n experiments were short lengths cut from the one length of tube which was prepared i n the following way. Constantan wire of 0 . 0 0 2 " diameter was wound i n a loop of 600 turns and th i s loop was pulled into a cupro-nickel tube so that there were 1200 wires threading the tube. Then the tube was passed through successively smaller holes i n a s t e e l die plate to "draw i t down". This drawing 110 down process forced the tube and the wires closer and closer together so that -the spaces between the wires were reduced i n a f a i r l y uniform mariner.' After the wire-i'fiiled-t-ube-had'-bee'n drawn through several holes, helium gas was passed through i t to check that i t was not blocked and also to get \a measure-ment of the cross-sectional area of the channels between the wires. As the tube was reduced i n diameter, these measure-ments were made after every drawing. In the present case, the drawing was stopped after the tube had been passed through th i r t e e n holes, a piece was cut o f f , drawn through one further hole and i t s cross section measured. It was intended to use thi s as a superleak for the adiabatic o s c i l l a t i o n measurements but after i t had been soldered i n p o s i t i o n , the tubing s p l i t l o n g i t u d i n a l l y from one end and had to be discarded. I t seems most l i k e l y that such a s p l i t would be caused by work harden-ing of the tubing and that the tube should be annealed once or more during the drawing process. To carry out the measurements of channel cross-sect-ion, the glass cone carrying the tube was sealed into an arran-gement where helium gas could be supplied to one end of the tube and the other end was connected to a vacuum system equip-ped with a McLeod gauge. The rate of r i s e of pressure i n the vacuum system was measured when the pump was shut o f f and the helium gas was flowing i n the tube. This was done fo» the system, alone arid then f o r the' system plus a known volume of I l l comparable s i z e . Prom th i s the volume flow rate was obtained and used i n Poiseulle's r e l a t i o n to f i n d the area of the cross-section. However, before t h i s could be done, some other data had to be obtained. In order to f i n d out something about the channels between the wires, a photomicrograph was taken of a cross-section of the w i r e - f i l l e d - t u b e . A short length of the tube was cut o f f , and was mounted, polished and etched i n the manner used for examining metal specimens with a metallurg-i c a l microscope. Dr. J., G. Parr of the Mining and Metallurgy Department very kindly performed t h i s service. When viewed under the microscope, the edges of the wires were shown up quite c l e a r l y by the etching and the wires were found to be arranged i n a very regular pattern of close packed hexagons, see Pig. 30. The flow channels between the wires could be regard-e d as being rectangular i n cross-section, the broad dimension being that of the sides of the hexagons. The mean length of the sides of the hexagons was measured with the microscope and found to be 21+.6 microns. A l l e n & Misener mention that they examined some of the i n d i v i d u a l wires from t h e i r tubes and found them to be of hexagonal cross-section also. For the completion of the data required to apply Poiseulle's r e l a t i o n , the number of channels i n r e l a t i o n to the number of wires must be known. A l l e n & Misener assumed \ 112 two channels per wire i n th e i r calculations but t h i s only app-l i e s to the case when the wires are s t i l l c i r c u l a r . The case for when the wires are hexagonal i n cross-section and enclosed i n a c i r c u l a r envelope can be treated as follows. Consider the hexagons as arranged i n rings concentric about some centralv,wi?Be, and f i n d out how many channels are r e -moved per r i n g i f the wires are removed a r i n g at a time, start-= ing from the centre. The r e s u l t would be as displayed i n Table A. TABLE A Ring Wires Channels l o s t Channels l o s t number. removed. per r i n g . per wire pe.E.\; r i n g . 0 1 6 6 1 6 6%k k 2 1 2 6 x k + 6 * 3 3 . 5 3 1 8 6 x ^ + 6 * 3 * 2 3 . 3 3 k 2k 6 * k + 6 * 3 x 3 3 . 2 5 5 3 0 ? 6xL++6x3*]+ 3 . 2 6 3 6 6 x h + 6 x 3 x 5 3 . 1 6 Let N = t o t a l number of wires R = t o t a l number of rings C = t o t a l number of channels removed Then, making use of the second column of Table A : N ^ 6 (l +• 2. +• 3 H -t-R) |M ^ R(R+i) ~6 Z 113 and from the t h i r d column The case of the f i r s t wire has been neglected. Prom t h i s , the number of channels per wire can be calculated. For the tube -used i n the experiments, N = 1 2 0 0 , which gives R = 1 9 . 5 , .C = 3717 and C/N = 3 . 1 channels per wire. With these data avai l a b l e , the Poiseulle r e l a t i o n for streamline flow i n a channel of rectangular cross-section with p a r a l l e l sides can be applied to y i e l d the channel width h, v i z : where T J = v i s c o s i t y of gas = 200X10"6 c.g.s. u n i t s . JL = length of channel = 1 1 . 7 cm. V = volume rate of flow = 1 . 5 8 X 1 0 " ^ cm.3 '/sec. Ap = pressure difference = 1.02X10"^ dynes/cm.2 a. = channel breadth = 2 i | . 6 x i 0 " ^ cm. For these values, h = 7 , 8 x i o " - ' cm. and the t o t a l area of -4 a cross-section, v~ =• 7-15 x CO cm. From the value of 21+.6 microns for the average length of the side of the hexagon which forms the wire cross-section, the t o t a l perimeter of gill the wires i s found to be 1 7 . 7 cm.. The perimeter calculated using the o r i g i n a l d i a -meter of the wires ( 0 . 0 0 2 " ) i s 1 9 . 1 cm. nil The data on the tube used i n the experiments are summarised i n Table B. TABLE B. lumber of wires : 1200 Type of wires; : Constantan 0 . 0 0 2 " diam. O.D. of the tube before drawing O.D. of the tube aft e r drawing Number of channels 0 . 1 U 2 " 0 . 0 9 2 " 3717 It would be useful to check these data by carrying out measurements on isothermal o s c i l l a t i o n s with the wire-f i l l e d - t u b e , i n the manner of• A l l e n & Misener,but at the time of writing there has been no opportunity to do t h i s . Such measurements would give the dimensions at the actual temper-ature of the l i q u i d helium experiments. It was found i n the present work with the wire-f i l l ed-tubes, that they could be soft soldered into p o s i t i o n without seeming to af f e c t the flow cross-section of the channels.. Some preliminary work was carried out with one other type of superleak, but t h i s was never used i n l i q u i d helium experiments. Gas flow measurements were made of the width of the gap between the dry cone and sccket of a ground glass j o i n t . A "Quick f i t " B29 joint was used i n i t s o r i g i n a l con-115 d i t i o n without any working of the surfaces. The value found for the width of the gap was 5 microns, i n d i c a t i n g that such a joint would have to be given extra p o l i s h i n g before i t could be used for a pure superfluid flow channel. Similar joints have been used f o r superleaks, Bowers & Mendelssohn ( 1 9 5 2 ) , but they apparently suffer from the disadvantage that there are circumferential grooves i n between the surfaces because grinding can be done only i n a rotary fashion. 116 REFERENCES. A l l e n , J . F. & H. Jones Nature 11+1, 21+3' ( 1 9 3 8 ) . H & A. D. Misener Proc. Roy. Soc. (Lond) A172, 1+67 ( 1 9 3 9 ) . w Rep. Int. Conf. Low Temp. Cambridge (191+6) p.8 7 . Atkins, K. R. Proc. Roy. Soc. (Lond.) A 2 0 3 , 119, 21+0 (1950). tt Proc. Phys. Soc. A 6 J t , 833 ( 1 9 5 1 ) . Babbitt, J . D. & K. Mendelssohn P h i l . Mag. (7) 20, 1025 ( 1 9 3 5 ) . — Band, ¥. & L. Meyer Phys. Rev. 7l+, 389 (191+8). Bowers, R. & K. Mendelssohn Proc. Roy. Soc. (Lond.) A213, 158 (1952.). Bleaney, B. & F. Simon Trans. Faraday "Soc. 3,5, 1205 (1939). Boyle, W. S. & J . B. Brown Rev. S c i . Inst. 2£, 359 (1951+). Brewer, D. F; D. 0. Edwards & K. Mendelssohn Comm. Int. Conf. Low. Temp. Par i s (1955). Brown, J . B. & K. Mendelssohn Nature 160, 670 (191+7). Surge, E. J . & L. C. Jackson Proc. Roy. Soc. XLond.) A20J>, 270 (195D. Caffyn, J . E. & R. M. Underwood J . S c i . Inst. 30, 257 (1953). Dash, J . G. Phys. Rev. 2k, 1091 (1951+). Daunt, J. G. & K. Mendelssohn Nature 11+3, 719 (1939). il tt Nature J57> 839 (191+6). & R. S. Smith Rev. Mod. Phys. 2 6 , 172 (1951+). Dingle, R. B. Proc. Phys. Soc. 61, 9 (191+8). Hudson, R. P. & C. K. McLane Rev. S c i . Inst. 2£, 190 (1951+). H u l l , R. A. Rep. Int. Conf. Low Temp. Cambridge (191+6) p.72. 117 Hung. G. S; B. Hunt & P. Winkel Physica 18, 629 ( 1 9 5 2 ) . Kaganov, M. I. & B. N, Eselson Zu. Eksper. Teor. P i z . 21, 656 ( 1 9 5 D . Kapitza, P. L. J . Phys. U.S.S.R. 59 (191+1). Kasuya, T. Prog. Theor Phys. Japan 9_, 8 9 ( 1 9 5 3 ) . Kramers, H. C.; J . D. Wascher & C. J . Gorter Physica 18, 3 2 9 ( 1 9 5 2 ) . Landau, L. J . Phys. U.S.S.R. £, 71 (19l+l). List o n , M. D. et a l Rev. S c i . Inst. 17., 19k (191+6). London, H. Proc. Roy. Soc. (Lond.) A171, I|8h (1939). " Rep. Int. Conf. Low Temp. Cambridge (191+6) p.1+8. London, P. & Z i l s e l , P. R. Phys. Rev. 7l+» H l + 8 (19i|8). " Proc. Int. Conf. Low. Temp. Oxford ( 1 9 5 l ) p . 5 . Manchester, P. D. Can. J . Phys. 33, lk6 ( 1 9 5 5 ) . " Comm. Int. Conf. Low Temp. Paris ( 1 9 5 5 ) . Martin, L. H. & R, D. H i l l "A Manual of Vacuum P r a c t i c e " , Melbourne Univ e r s i t y Press,' (191*6). Maurer, R. D. & M. A . H e r l i n Phys. Rev. 76_, 950 ( 1 9 l | 9 ) . Osborne, D.. V. Proc. Phys. Soc. A6I4, I l k ( 1 9 5 1 ) . Parkinson, D. H. & J . E. Quarrington Proc. Phys. S 0 C . B 6 7 , 6hk ( 1 9 5 k ) . Pellam, J. R. Phys. Rev. 73, 608 ( 1 9 U 8 ) . " Phys. Rev. 7 5 , 1183 (19k9). Peshkov, V. P. Rep. Int. Conf. Low Temp. Cambridge ( 1 9 k 6 ) p.19. " Zu. Eksper. Teor. P i z . 18, 857 (191+8). " Zu. Eksper. Teor. P i z . 18, 867 ( 1 9 U 8 ) . 118 P i c u s , G. S. Phys. Rev. 90, 719 (1953). " Phys. Rev. l!+59 (195L|). Robinson, J . E. Phys. Rev. 82, 1+1+0 (1951). Stewart, G. W. & R. B. Lindsay " A c o u s t i c s " (Van Nostrand Co. Inc. New York, 1930) p.1+7. Somers, H i S. Rev; S c i . I n s t . 2£, 793 (195U). Swim, R. T. & H . E. Eorsach Phys. Rev. 9_J_, 25 (1955). Temperley, H,1,N. V. Proc. Phys. Soc. A61+, 105 ( 1 9 5 D . van D i j k , H . & D. Shoenberg. Nature 161+, 151 (191+9). n Proc. I n t . Conf. Low'Temp. Oxford (195D p.1+9. Winkel, P.; A. M. G. D e l s i n g & J . D. P o l l P h y s i c a 21, 332 (1955). ~~ 

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