UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Microwave resonator investigation of electric field effects on mercury surfaces. Ionides, George Nicos 1969

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1970_A6_7 I65.pdf [ 3.11MB ]
Metadata
JSON: 831-1.0084836.json
JSON-LD: 831-1.0084836-ld.json
RDF/XML (Pretty): 831-1.0084836-rdf.xml
RDF/JSON: 831-1.0084836-rdf.json
Turtle: 831-1.0084836-turtle.txt
N-Triples: 831-1.0084836-rdf-ntriples.txt
Original Record: 831-1.0084836-source.json
Full Text
831-1.0084836-fulltext.txt
Citation
831-1.0084836.ris

Full Text

A MICROWAVE RESONATOR INVESTIGATION OF ELECTRIC FIELD EFFECTS ON MERCURY SURFACES by GEORGE NICOS IONIDES  B.Sc., U n i v e r s i t y of-London, 1  9  &  8  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We a c c e p t t h i s t h e s i s as conforming t o the required  standard  THE UNIVERSITY OP BRITISH COLUMBIA December, I  9  6  9  In p r e s e n t i n g t h i s t h e s i s an a d v a n c e d d e g r e e a t the L i b r a r y I further for  agree  the U n i v e r s i t y  make  tha  it  freely  written  It  The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8 , Canada  Date  / ? g  J<t>.  1910  requirements I agree  r e f e r e n c e and copying of  this  that  not  for  that  study. thesis  by t h e Head o f my D e p a r t m e n t  financial gain shall  of  the  B r i t i s h Columbia,  i s understood  permission.  Department  of  permission for extensive  representatives.  this thesis for  fulfilment of  available for  s c h o l a r l y p u r p o s e s may be g r a n t e d  by h i s of  shall  in p a r t i a l  or  copying or p u b l i c a t i o n  be a l l o w e d w i t h o u t  my  (ii) ABSTRACT The  microwave r e s o n a t o r method f o r s t u d y i n g  amplitude s u r f a c e waves i n l i q u i d s has the time measurement more a c c u r a t e I t was  been improved by making  and much more  used to measure the o s c i l l a t i o n frequency  f a c e as a f u n c t i o n of l i q u i d depth. D i s c r e p a n c i e s the e x p e r i m e n t a l l y d i c t i o n s due  obtained  results  and  small  convenient. of the  sur-  between  theoretical  pre-  to the r i g i d i t y of the mercury meniscus where  c o n t a c t i s made w i t h  the w a l l s of a c y l i n d r i c a l r e s o n a t o r  were found. Prom these  an a c c u r a t e v a l u e f o r the  effective  r e d u c t i o n i n r a d i u s of the r e s o n a t o r because of the meniscus e f f e c t was  o b t a i n e d . A method was  developed f o r a p p l y i n g  s t r o n g e l e c t r o s t a t i c f i e l d s (about s u r f a c e without interesting  i n t e r f e r i n g with  r e s u l t of t h i s was  2 0 kV/cm) onto the  the measuring technique.  itself  square c r o s s - s e c t i o n was  :  T h i s phenomenon mani-  i n a marked r e d u c t i o n i n the damping of  waves j u s t a f t e r a l a r g e f i e l d  An  the o b s e r v a t i o n t h a t the . f i e l d  c l e a n s the s u r f a c e from contamination. fests  fluid  surface  i s a p p l i e d . A resonator  of  used to demonstrate the F o u r i e r ana-  l y z i n g p r o p e r t y of r e c t a n g u l a r  resonators.  ( i l l )  TABLE OF CONTENTS Page ABSTRACT  (ii)  TABLE OF CONTENTS  ( i l l )  LIST OF TABLES  (iv)  LIST OF FIGURES  (v)  ACKNOWLEDGEMENTS  (vi)  CHAPTER 1  INTRODUCTION  ..  1  CHAPTER 2  EQUIPMENT - EXPERIMENTAL PROCEDURE  2.1  Microwave  2.2  Refinement of t i m i n g technique  12  2.3  A p p l i c a t i o n of an e l e c t r o s t a t i c f i e l d on the mercury s u r f a c e  17  CHAPTER 3  arrangement and t e s t c a v i t y  5  RESULTS  3.1  V a r i a t i o n of s u r f a c e mode frequency with f l u i d depth  20  3.2  E f f e c t s of a strong e l e c t r o s t a t i c f i e l d on the mercury s u r f a c e  24  3.3  The r e c t a n g u l a r c a v i t y  30  CHAPTER 4  CONCLUSIONS - FUTURE WORK  4.1  Improvement of measuring t e c h n i q u e  JS  4.2  A p p l i c a t i o n of a s t r o n g e l e c t r i c f i e l d on the f l u i d s u r f a c e  J6  4.3  E f f e c t o f the e l e c t r i c f i e l d mercury s u r f a c e  37  4.4  The square r e s o n a t o r  37  4.5  Seismographic a p p l i c a t i o n s of the microwave r e s o n a t o r  38  on the  REFERENCES APPENDIX  39 THEORY OF THE CLEANING OF THE MERCURY SURFACE BY AN ELECTRIC FIELD  40  (iv) LIST  OP  TABLES  O s c i l l a t i o n frequency measurements  0  Parameters and v a r i a b l e s employed. S u r f a c e wave damping c o e f f i c i e n t  results.  (v) LIST OP FIGURES Page 6  1  The microwave system  '  2  EM mode frequency  3  C a v i t y r e s o n a t o r and a c c e s s o r i e s  4  The l i d of the c y l i n d r i c a l c a v i t y  10  5a,b  Arrangement f o r e x c i t i n g s u r f a c e waves by p e r i o d i c a i r pulses  11  6  M o n i t o r i n g of the amplitude and frequency of a s u r f a c e mode  13  7  Arrangement f o r g e n e r a t i n g  15  8  Trigger pulse a m p l i f i e r  15  9  Time marks r e c o r d e d  16  10  A p p l i c a t i o n of a s t r o n g e l e c t r o s t a t i c f i e l d on the mercury s u r f a c e  19  11  S u r f a c e mode frequency  23  12  Damping of a s u r f a c e wave  26  13  Contamination of the mercury s u r f a c e  28  14  The r e c t a n g u l a r r e s o n a t o r  31  15  Simultaneous d i s p l a y of EM modes on the s c r e e n  32  16  The l i d o f the r e c t a n g u l a r r e s o n a t o r  34  17  S e l e c t i v e response of EM to s u r f a c e modes  35  18  Response of both EM modes t o a s u r f a c e mode  35  19  A c o l l a p s e d monolayer o f o i l on the mercury surface  42  measurement  ? 9  time marks  d i r e c t l y on the f i l m  vs„ f l u i d depth p l o t  20a,b Removal of t h i n o i l f i l m by a s t r o n g e l e c t r i c field  42  21  42  Weight and s t r i n g analogue of the b r e a k i n g of the o i l f i l m  up  (vi) ACKNOWLEDGEMENTS I would s i n c e r e l y l i k e t o thank Dr. F. L. Curzon f o r the s t i m u l a t i n g and encouraging s u p e r v i s i o n t h a t I r e c e i v e d throughout the course of t h i s work. I wish to express my appreciation  to Dr. B. Ahlborn f o r h i s suggestions on the  improvement of the p r e s e n t a t i o n acknowledge numerous v a l u a b l e Mr.  of t h i s t h e s i s . I must a l s o  d i s c u s s i o n s which I had w i t h  J.-P. Huni on both the t h e o r e t i c a l and the e x p e r i m e n t a l ,  a s p e c t s of t h i s work. I am indebted  to Mr. R. Haines f o r h i s guidance du-  r i n g my f a m i l i a r i z a t i o n w i t h the student workshop. S p e c i a l thanks a r e due t o Mr. D. S i e b e r g ,  Mr. J . A. Zanganeh and Mr.  R. Da Costa f o r t h e i r a s s i s t a n c e w i t h the e l e c t r o n i c s and i n the g e n e r a l  maintenance of the equipment.  F i n a l l y , I must express my g r a t i t u d e to the Graduate S c h o o l of the U n i v e r s i t y of B r i t i s h Columbia f o r f i n a n c i a l assistance  through the award of a U n i v e r s i t y o f B r i t i s h  Columbia Graduate  Fellowship.  -1  1  CHAPTER  I N T R O D U C T I O N Experimental  i n v e s t i g a t i o n s o f s u r f a c e waves i n  l i q u i d s h a v e , u n t i l r e c e n t l y , been hampered by t h e l a c k o f a s u i t a b l e d i a g n o s t i c technique. devices developed being  H  o v e r t h e y e a r s had t h e d i s a d v a n t a g e  ( i . e . periodic oscillations  of  the depth  A  surproduct  F  is  t h e w a v e l e n g t h o f t h e s u r f a c e v;aves,  of the l i q u i d ) .  s a t i s f a c t o r y general theory waves  f o r which the  i s v e r y s m a l l compared t o u n i t y , where  the a m p l i t u d e , H  sensing  too I n s e n s i t i v e to permit observations of l i n e a r  f a c e waves FA  Host e l e c t r o m e c h a n i c a l  B u t , a s i s w e l l known,  and  a  ( i . e .non-linear) f o r surface  i n f l u i d s does n o t e x i s t a t p r e s e n t because of the  enormous c o m p l e x i t y o f t h e r e s u l t i n g g e n e r a l e q u a t i o n s . w i t h t h e e x c e p t i o n o f a few v e r y s p e c i a l c a s e s , other simplifying conditions exist ons  "manipulatable",  that render  i n which the equati-  i t i s n o t , i n general, p o s s i b l e to  compare e x p e r i m e n t a l r e s u l t s w i t h e x i s t i n g t h e o r y . t e c h n i q u e s , due t o t h e i r g e n e r a l l y h i g h s p a t i a l  Optical  resolution,  do n o t p r e s e n t us w i t h t h e p r o b l e m o f i n s e n s i t l v l t y  ( i n fact  h o l o g r a p h i c methods a r e e v e n t o o s e n s i t i v e ) b u t a g a i n n o t be c o n s i d e r e d f u l l y asons.  satisfactory  They a r e d i f f i c u l t  comparatively  costly;  can-  f o r the f o l l o w i n g r e -  and c o m p l i c a t e d  t o s e t up and  a l s o , together with the f i r s t  of s e n s i n g devices mentioned, they employed t o observe  So,  class  can i n g e n e r a l o n l y  p e r i o d i c phenomena  ( i . e . no  be  continuous  -2o b s e r v a t i o n of s u r f a c e i n s t a b i l i t i e s  i s p o s s i b l e ) . However,  as was suggested by Curzon and Howard, and developed by Curzon and Pike  (refs. 2,3,4,5),  a microwave r e s o n a t o r  tech-  n i q u e can be employed which does not s u f f e r from the drawbacks of p r e v i o u s  methods. The most important  f e a t u r e s of  t h i s method a r e 1) Waves of s m a l l amplitude l i n e a r i z e d equations 2) U n s t a b l e  ( \0~ cvn) can be s t u d i e d ( I . e . 3  are a p p l i c a b l e ) .  s u r f a c e s can be observed  ( i . e . non-periodic  perturbations). 3) Under s p e c i a l circumstances  the r e s o n a t o r  responds t o  s i n g l e modes of s u r f a c e waves. T h i s e l i m i n a t e s the t e d i o u s F o u r i e r a n a l y s i s which i s normally observations The  with  r e q u i r e d i n comparing  theoretical predictions.  p r i n c i p l e of the technique  i s the f o l l o w i n g . I f  the boundaries of a r e s o n a t i n g microwave c a v i t y a r e perturbed a change i n the resonant  frequency  of a microwave c a v i t y r e s o n a t o r  r e s u l t s . Thus i f one w a l l  i s taken by a  conducting  l i q u i d , any s m a l l s u r f a c e p e r t u r b a t i o n s of the f l u i d can e a s i l y be monitored by m o n i t o r i n g  the resonant  changes of the c a v i t y . C a l c u l a t i o n s of the s h i f t  frequency i n reso-  nance a r e done by u s i n g S l a t e r ' s theorem ( r e f . 6).  I t can  be shown (see r e f . 2, p. 10-13).. t h a t f o r a c y l i n d r i c a l and a r e c t a n g u l a r microwave r e s o n a t o r  the s h i f t  i n frequency  f o r a g i v e n s u r f a c e mode of o s c i l l a t i o n and a g i v e n  electro-  magnetic mode i s p r o p o r t i o n a l t o the amplitude o f the s u r f a c e wave. The method was developed by Pike u s i n g mercury  -3as the conducting d i c t e d values  l i q u i d . He  checked the t h e o r e t i c a l l y  of the o s c i l l a t i o n frequency of a  s t a n d i n g wave, both as a f u n c t i o n of r a d i u s of a microwave r e s o n a t o r He  and  pre-  surface cylindrical  as a f u n c t i o n of depth of the  fluid.  a l s o s t u d i e d the damping of the s u r f a c e waves, w i t h  and  without an a x i a l magnetic f i e l d a c t i n g on the mercury. The  work r e p o r t e d  i n t h i s t h e s i s i s a f o l l o w up  the o r i g i n a l i n v e s t i g a t i o n s . The has  been improved and  electric field  time measuring technique  the f e a s i b i l i t y of a p p l y i n g a  on the mercury s u r f a c e has  our u l t i m a t e f u t u r e g o a l being  of  been demonstrated,  the study of  hydrodynamic i n s t a b i l i t i e s . These are the t h a t a r i s e when a s t r o n g e l e c t r i c f i e l d s u r f a c e of an o s c i l l a t i n g conducting  strong  electrostatlc-  instabilities  i s a p p l i e d on  liquid  (see r e f ,  As a by-product of t h i s i n v e s t i g a t i o n , a technique was f o r removing i m p u r i t i e s (e.g. s m a l l dust  the 7)» found  p a r t i c l e s or  traces  of o i l ) from the s u r f a c e of the mercury by a p p l y i n g a  strong  e l e c t r o s t a t i c f i e l d f o r a s h o r t p e r i o d of time on the  sur-  f a c e . T h i s i s extremely u s e f u l because even minute amounts of i m p u r i t i e s on the s u r f a c e of a l i q u i d have a very d r a s t i c e f f e c t on the p r o p e r t i e s of the s u r f a c e . L a s t l y , the bility  of employing a r e c t a n g u l a r  l y s e the s u r f a c e wave modes was  feasi-  c a v i t y to F o u r i e r a n a -  demonstrated.  In the c a l c u l a t i o n s i n the t h e s i s the r a t i o n a l i s e d MKS  system of u n i t s was  used. To save unnecessary, and i r -  -irritating  r e p e t i t i o n of the same l o n g words the f o l l o w i n g  nomenclature w i l l be c o n s i s t e n t l y used through o u t . "Surf a c e modes" w i l l  be used to r e f e r to any modes o f o s c i l -  l a t i o n o f the mercury s u r f a c e and "EM modes" f o r the r e sonant e l e c t r o m a g n e t i c modes of the microwave r e s o n a t o r .  -5CHAPTER  2  E Q U I P M E N T E X P E R I M E N T A L P R O C E D U R E  . 2.1  A b l o c k diagram of the microwave system  i n f i g . ' 1. A 723 KMc/s  A/B  K l y s t r o n produces  8.6  i s shown  to  9«6  microwaves. These go through an i s o l a t o r whose pur-  pose i s to prevent any s t r a y r e f l e c t i o n s from the r e s t of the system from i n t e r f e r i n g w i t h the k l y s t r o n output. They then go through a c a l i b r a t e d wavemeter which can be used to g i v e the frequency of the microwave resonances. L a s t l y , microwave s i g n a l i s s p l i t a  magic t e e . One  the  i n t o two p a r t s of equal power a t  of these component s i g n a l s goes to the  c a v i t y , w h i l e the o t h e r h a l f i s d i s s i p a t e d i n the t e r m i n a t o r . The r e f l e c t e d s i g n a l from the c a v i t y i s p i c k e d up by a c r y s t a l d e t e c t o r and d i s p l a y e d on one channel of a d u a l beam o s c i l l o s c o p e . The time-base waveform of the o s c i l l o s c o p e i s added to the k l y s t r o n r e p e l l e r v o l t a g e , thereby modulating the output frequency of the k l y s t r o n . In t h i s way,  the time  a x i s of the o s c i l l o g r a m s can be c a l i b r a t e d d i r e c t l y i n terms of the output frequency of the k l y s t r o n . At the resonant f r e q u e n c i e s of the microwave c a v i t y a drop i n the  oscillo-  gram i s seen on the o s c i l l o s c o p e s c r e e n . The resonant f r e q u ency can be a c c u r a t e l y measured by b r i n g i n g the c o r r e s p o n d i n g drop  (or d i p ) i n the s i g n a l due  to the wavemeter i n t o  i n c i d e n c e w i t h the c a v i t y d i p (see f i g . 2).  co-  The microwave  -6-  detector  power terminator magic  klystron power s upply  klystron repeller voltage  dual beam scope  waveguide  sawtooth out  input  FI6  1  B l o c k diagram of microwave s e t up  tee  -7-  FIG  2  Measurement of the resonant frequency o f an EM mode i n the c a v i t y . Dip  1 i s due t o the c a l i b r a t e d wave-meter and can  be moved r i g h t a c r o s s the frequency spectrum o f the k l y s t r o n . D i p 2 i s a t y p i c a l example of a c a v i t y EM mode r e s o n a n c e . F o r our experiments we used a k l y s t r o n frequency range of from 8715 Mc/s to 87^5 Mc/s.  "8 cavity consists  of a n i c k e l p l a t e d  b r a s s c y l i n d e r shown i n  f i g . ; 3. The l a y e r of n i c k e l (0.003 i n . t h i c k )  eliminates  d i s s o l u t i o n of the b r a s s by the mercury. Mercury can be i n t r o d u c e d a t the bottom of the c a v i t y ;  I t s l e v e l can be v e r y  f i n e l y a d j u s t e d by u s i n g a hose c l i p as a t a p c o n t r o l on a s m a l l , l e n g t h of Tygon t u b i n g c o n n e c t i n g the mercury  reser-  v o i r to the c a v i t y . S i n c e the resonant frequency of the EM modes i s a f u n c t i o n  both of the r a d i u s  R and the l e n g t h  of the c a v i t y , resonances a r e seen on the o s c i l l o s c o p e en as the mercury l e v e l i s g r a d u a l l y At a f i x e d c a v i t y l e n g t h  L scre-  r a i s e d . i n the c a v i t y .  the mercury depth can be v a r i e d . b y  means o f a p l u n g e r . The plunger i s a t t a c h e d to. a threaded rod, ses  so i t . c a n . b e moved up and down. The threaded.rod pasthrough a T e f l o n nut which provides, an e f f e c t i v e s e a l ...  f o r the mercury ( f i g . 3)are  A b r a s s p l a t e , d e t a i l s of which  shown i n f i g s . 3 and k i s used as the top of the m i c r o -  wave c a v i t y . The best method of e x c i t i n g s u r f a c e  modes on  the mercury was by p u l s i n g a i r through a . s m a l l hole a t the top by The  o f the c a v i t y . The p e r i o d i c a i r p u l s e s were produced, i n t e r r u p t i n g an a i r j e t w i t h a r o t a t i n g s l o t t e d d i s c . disc i s e l e c t r i c a l l y driven  by a 1/20 hp Bodine e l e c -  t r i c motor. The speed can.be c o n t r o l l e d by v a r y i n g put  the i n -  v o l t a g e w i t h a v a r i a c . A t r a n s i s t o r , p o t e n t i o m e t e r can.  be used f o r f i n e adjustment of the motor speed. This i s necessary since factor  the mercury s u r f a c e  (about 50).  has a f a i r l y h i g h Q  'The whole arrangement i s shown i n f i g . 5»  -9-  WAVEGUIDE AIR INLET  SLOTTED DISC  MERCURY RESERVOIR  PLUNGER FINE TAP  FIG  3  The microwave  t e s t c a v i t y and mercury  reservoir  FIG  4  D e t a i l s of the geometry of the l i d of the c a v i t y . T h i s arrangement g i v e s b e s t r e s u l t s of microwave r e s o n a n c e s . The waveguide i s c a r e f u l l y s o l d e r e d onto the top p l a t e In our case,  R = 3,6k  cm  e  -11-  70  CAVITY  FROM  I  AIR  SUPPLY  FIG  5b  Motor c o n t r o l c i r c u i t . A i r p u l s e arrangement.  V=VARIAC}  BR - BRIDGE  Q-2N373S  HEAT  SUNK  RECTIFIER TRANSISTOR  -12-  Observations  of the o s c i l l a t i o n frequency  and  am-  p l i t u d e of the s u r f a c e modes are made as f o l l o w s . By v i r t u e of the f a c t t h a t our method of e x c i t i n g s u r f a c e modes  ex-  c i t e s o n l y s i n g l e modes, a time r e c o r d of the p e r i o d i c of the E K mode resonance d i p from the l e f t  ing  of the s c r e e n and  the amplitude of the wave i s  p r o p o r t i o n a l to the resonant frequency que  can be o b t a i n e d  which we  right  back g i v e s a l l the i n f o r m a t i o n needed. As  mentioned i n Chapter 1 ,  was  to the  frequency  by a simple  s h i f t . The  oscillation  time measuring t e c h n i -  s h a l l e l a b o r a t e on s h o r t l y . The  time r e c o r d i s  most c o n v e n i e n t l y made by p u t t i n g a very narrow s l i t 0.5 mm)  i n f r o n t of the s c r e e n , as.shown i n f i g . 6.  photographic  f i l m run i n a d i r e c t i o n p e r p e n d i c u l a r  slit  the o s c i l l a t i o n s . A t y p i c a l n e g a t i v e  is  records  sw-  (about Ordinary  to  the  film  record  shown i n the same f i g u r e .  2.2.  The  measuring method and The  p r e v i o u s l y employed method f o r measuring time  on the f i l m was  simply  time-mark g e n e r a t o r .  by t r i g g e r i n g the o s c i l l o s c o p e w i t h  T h i s r e s u l t s i n the f i l m r e c o r d  s i s t i n g of a s e r i e s of dots equal  i t s refinement  (see f i g . 6)  con-  whose s p a c i n g i s  to the r e p e t i t i o n r a t e of the time-mark g e n e r a t o r .  the p e r i o d of the s u r f a c e modes was  a  found by counting  Thus  the  number of dots from peak to peak of the s i n u s o i d a l f i l m t r a c e . T h i s method was  extremely tedious and  time consuming s i n c e  the dots were counted by u s i n g a microscope. T h i s had s e r i o u s disadvantage of c a u s i n g  the  c o n s i d e r a b l e eye s t r a i n ,  not  -13-  OPAQUE SCREEN  >5m/r)  SLIT  SCOPE TRACE  FJ.LM TRACE  MOTION  PERIOD  OF  OSCILLATION  FILM  FIG  OF  6  Method o f m o n i t o r i n g the amplitude and frequency of a s u r f a c e mode by r e c o r d i n g the c o r r e s p o n d i n g EM mode resonance s h i f t o  -14to  mention temporary mental derangment of the  To e l i m i n a t e these d i f f i c u l t i e s we d i r e c t l y on the  now  r e c o r d time marks  film.  A Duraont type 7 8 I A time-mark.generator in  any  experimenter.  f u t u r e r e f e r e n c e as a TKG)  (abbreviated  i s used to g i v e 1, 10  100 msec.marks. These, i n t u r n , are f e d Into three p u l s e a m p l i f i e r s ( a b b r e v i a t e d to TPA) s i g n a l to between 20 and now  and  trigger  which a m p l i f y  the  25 V o l t s . T h i s l e v e l of s i g n a l i s  s u f f i c i e n t to t r i g g e r three T e k t r o n i x type I 6 3 p u l s e  nerators ply.  ( a b b r e v i a t e d to PG)  ge-  powered by a type l 6 0 A power sup-  The r e s u l t i n g pulses, are f e d i n t o the second channel  the d u a l beam o s c i l l o s c o p e . The gered  oscilloscope is itself  e x t e r n a l l y by the 1 msec TMG  of  trig-  marker. The whole a r r a n -  gement, w i t h the e x c e p t i o n of power s u p p l i e s i s shown i n b l o c k diagram form In f i g . and  b u i l t by Mr. All  7 . P i g . 8 shows the TPA,  Jim A. Zanganeh to whom I am  designed  indebted.  three p u l s e s have the same amplitude,  but  the  d u r a t i o n of the 100 msec pulse i s twice as l o n g as the d u r a t i o n of  the 1 and  10 msec  markers. As f i g . :  9 shows, the 1 msec  marks appear at the l e f t of the f i l m . At 10 msec i n t e r v a l s , the 1 and  10 msec markers add,  t a n t marker i s not observed  so t h a t the top of the  i n the s l i t  resul-  a c r o s s the f a c e of  the o s c i l l o s c o p e ; i . e . every t e n t h marker i s m i s s i n g . At msec a l l t h r e e markers c o i n c i d e and  add up except  100  f o r the  r i g h t hand h a l f of the 100 msec marker p u l s e which i s s t i l l visible  i n the s l i t .  The r e s u l t i n g f i l m  i s a l s o shown i n f i g . 9.  -15-  f msec  T  EXTERNAL TRIGGER  PG DUAL BEAM  JO  msec  T  PG  100  msec  T  PG  SCOPE  TMG  FIG TMG  7 -  TPG  Arrangement f o r r e c o r d i n g  TIME  MARK  TRIGGER  GENERATOR  PULSE  = PULSE  AMPLIFIER  GENERATOR  + 7<?~ 2.5"  470 K  AAA^ •/ ?F IN  •  1 h  FIG  8  Trigger  pulse a m p l i f i e r c i r c u i t  V  time marks  -17As i t i s e a s i l y seen, t h i s method of measuring  time  i s v e r y convenient and much f a s t e r t h a n the one employed f o r e . I t i s a l s o h i g h l y adaptable to measuring  of any o r d e r ,  as l o n g as time-marks are o b t a i n a b l e from the TMG. TMG  be-  With the  and the o s c i l l o s c o p e employed, time i n t e r v a l s r a n g i n g  from 1 microsecond up to 1 second can be a c c u r a t e l y measured. An a c c u r a c y of 0.1$  can be a t t a i n e d i n . t h e measurement of t y -  p i c a l p e r i o d i c times of s u r f a c e modes. T h i s i s about ten times as a c c u r a t e as the method used i n the p a s t . 2.3.  A p p l i c a t i o n of a s t r o n g e l e c t r i c f i e l d  mercury  onto the  surface One  of the o b j e c t i v e s of t h i s work was  to develop  a method f o r a p p l y i n g a s t r o n g e l e c t r o s t a t i c f i e l d o s c i l l a t i n g f l u i d . We any,  on the  a l s o sought to f i n d what e f f e c t , i f  the f i e l d would have on the p r o p e r t i e s of the s u r f a c e  itself.  T h i s means t h a t an e l e c t r i c f i e l d must be a p p l i e d  between the top of the c a v i t y and the base. To a v o i d pert u r b i n g the EM modes, any gap between the top .of the c a v i t y and the base must be kept to an a b s o l u t e minimum. We t h e r e f o r e chose to i n s u l a t e the base from the top of the c a v i t y by u s i n g a s u i t a b l e d i e l e c t r i c , hoping t h a t microwave power l o s s e s i n the d i e l e c t r i c would n o t r e d u c e the Q - f a c t o r of :  the  c a v i t y EM modes too much. Mylar sheets proved to be  the  b e s t f o r t h i s purpose. Mylar has a d i e l e c t r i c  of  4kV/0.001 i n c h e s . In our arrangement,  strength  f o u r Mylar sheets  -18-  each 0.005 inches t h i c k , p r o v i d i n g an e f f e c t i v e i n s u l a t i o n .. of  80kV were used. No s e r i o u s r e d u c t i o n . i n the c a v i t y Q-  f a c t o r was observed. A simple l u c i t e clamp was used  t o keep  the top p l a t e i n p o s i t i o n over the c a v i t y . Nylon screws,  to .  a v o i d the p o s s i b i l i t y o f breakdown, were employed t o j o i n the arms of the clamp t o g e t h e r . A n o v e l f e a t u r e o f the a r rangement was the f a c t t h a t s u r f a c e modes c o u l d s t i l l  be ex^-  c i t e d on the mercury., by p u l s i n g the a i r above the Mylar. T h i s demonstrates the f a c t t h a t v e r y l i t t l e to  energy i s r e q u i r e d  e x c i t e s u r f a c e modes and the very h i g h s e n s i t i v i t y of. the  measuring t e c h n i q u e . The l a r g e s t of t h r e e a v a i l a b l e  cavities,  R = 3«64cm, was used f o r the e l e c t r i c f i e l d , runs. The reason for  t h i s was . t h e . f o l l o w i n g . .The*distance between the mercury  and  the c a v i t y l i d was s m a l l e r f o r a. g i v e n EM mode, than the  c o r r e s p o n d i n g d i s t a n c e . i n the other c a v i t i e s . Hence, the app l i e d s t a t i c e l e c t r i c f i e l d was a l s o l a r g e s t i n t h i s  parti-  c u l a r c a v i t y f o r a g i v e n supply v o l t a g e . To a v o i d o p e r a t i n g the microwave equipment a t h i g h p o t e n t i a l s we grounded the lid  o f the c a v i t y and -connected  the base t o a 3OkV power  s u p p l y of n e g a t i v e output. Most of our measurements were . done w i t h t h i s arrangement. However, i n our f i n a l r u n s , a f u r t h e r i n c r e a s e of the e l e c t r o s t a t i c f i e l d s t r e n g t h was e f f e c t e d as f o l l o w s . The method of p u t t i n g Mylar i n t h e path of the microwaves proved little  so e f f e c t i v e and absorbed  so .  power t h a t we extended i t s u c c e s s f u l l y to the micro-  wave waveguides themselves.  The microwave j o i n t between the  -19wavemeter and and  two  the magic tee (see f i g . l ) was  Mylar sheets were i n t r o d u c e d . Again a l u c i t e clamp  w i t h n y l o n screws was  used  to h o l d the j o i n t t o g e t h e r  i n s e r t i o n of the Mylar. Then  B  a second  p o s i t i v e output t h i s time,.'was used to  disconnected  of  50kV  between.the top and  up  i s shown i n f i g .  to r a i s e the c a v i t y l i d power s u p p l i e s i n  effective potential difference  the base of the c a v i t y . The s e t  10.  FIG  after  power supply, of  p o s i t i v e 20kV. T h i s arrangement- of two  s e r i e s enabled us to apply an  ...  10  Method of a p p l i c a t i o n of a s t r o n g e l e c t r i c f i e l d on the mercury sur face.  CHAPTER  3  R E S U L T S 3.1.  V a r i a t i o n of the frequency  of s u r f a c e modes w i t h depth  At f i r s t we compared t h e o r e t i c a l l y of the frequency  predicted  values  of s u r f a c e modes as a f u n c t i o n o f depth  with experimentally  obtained  v a l u e s . T h i s c o u l d be done much  more r e l i a b l y than before with our r e f i n e d measuring  tech-  nique. The  linearised  theory  o f s t a n d i n g s u r f a c e waves on  a f l u i d s u r f a c e g i v e s the d i s p e r s i o n  relation  T K  where  (3.1.1)  T -- s u r f a c e t e n s i o n of the l i q u i d , k = wave number o f o s c i l l a t i o n s , f = frequency  of o s c i l l a t i o n s ,  ^ = d e n s i t y of the l i q u i d , H = depth o f the l i q u i d , , and  g = a c c e l e r a t i o n of g r a v i t y . The  v e r t i c a l displacement  J  £  of the o s c i l l a t i n g  sur-  f a c e from the e q u i l i b r i u m p o s i t i o n i s g i v e n by (see r e f . 8 ) (3.1,2)  where  amplitude o f the o s c i l l a t i o n , B e s s e l f u n c t i o n of order s.  The  boundary c o n d i t i o n t h a t  K  -O  gives (3.1.3)  i s the Uth p o s i t i v e r o o t * of T, (kR) - O . The  where J  self-explanatory notation  T  SU  w i l l be used  t o r e f e r to i n -  d i v i d u a l s u r f a c e modes from now onwards. Formula .(3.1.1) was used  to p l o t f v s . H. The ex-  p e r i m e n t a l l y o b t a i n e d p o i n t s a r e p l o t t e d from t a b l e 1 on the same graph t e r s used  ( f i g . 11). Table 2 g i v e s the v a l u e s of the paramei n the experiment.  The  o s c i l l a t i o n , w i t h k=0»507 cm"'-, was used.  Curzon and P i k e used  the Jol  mode and found d i s c r e p a n c i e s  between e x p e r i m e n t a l v a l u e s of the frequency and v a l u e s d i c t e d by (3«1.1). To e x p l a i n t h i s ,  they reasoned  pre-  t h a t the  mercury meniscus i s v e r y r i g i d a t the edges, where the mercury comes i n t o c o n t a c t w i t h the w a l l s o f the c o n t a i n e r . T h i s b r i n g about an e f f e c t i v e r e d u c t i o n i n R, as f a r as the s u r f a c e modes a r e concerned.  As can. be. seen from  the graph,  i f Ri s  reduced by 0.22 cm, c o r r e s p o n d i n g t o a new k of 0.54 cm ' -  (from e q u a t i o n 3»1»3)« there i s e x c e l l e n t agreement between c o r r e c t e d theory and experiment. T r a n s v e r s e e l e c t r i c EM modes were used periment.  i n the ex-  Modes a r e d e f i n e d i n an e x a c t l y analogous  manner  i n e l e c t r o d y n a m i c s as s u r f a c e modes were d e f i n e d i n (3<>1.2).  * A t t h i s stage, we would l i k e to p o i n t out to the r e a d e r , t h a t a l t h o u g h i n t h e i r theory Curzon and Pike s t a t e t h a t they use the Uth p o s i t i v e non-zero r o o t , i n the a n a l y s i s of t h e i r r e s u l t s they use the same nomenclature as g i v e n here.  -22TABLE 1 F l u i d Depth  H cm  Oscillation  frequency  0.49  1.83  0.62  2.04  0.74  2.22  0.8  2.31  0.99  2.53  1.08  2.6.1  1.19  2.?6  1.53  2.97  1.96  3.20  f c/s  TABLE 2 R = 3 . 6 4 cm k - 0.507  T =490  cia  dynes/cm  p = . 1 3 . 6 gm/cm  3  g = 9 8 O cm/sec* TE,„  mode used .  L ="length, of c a v i t y from mercury = 1 . 6 , 0 cm  s u r f a c e to the top  -23-  *  •  1  :  1 DEPTH  1  2 OF FIG  P l o t of o s c i l l a t i o n  —  —  —  —  "  '  3  Hem  FLUID 11  f r e q u e n c y o f s u r f a c e mode v s . f l u i d  depth.  -243.2.  Results  of the e f f e c t s of a p p l i c a t i o n of a s t r o n g  electric field One  on the mercury  surface  of the most s e n s i t i v e t e s t s t o determine the  p h y s i c a l p r o p e r t i e s of a l i q u i d s u r f a c e , s h o r t of examining i t w i t h an e l e c t r o n microscope, i s to measure the damping c o e f f i c i e n t of s u r f a c e waves. T h i s v i s c o u s damping  coefficient  i s a most, s e n s i t i v e i n d i c a t o r o f the degree of c l e a n l i n e s s of a l i q u i d s u r f a c e ; and most p h y s i c a l p r o p e r t i e s of'the. s u r f a c e depend, almost e n t i r e l y , on how c l e a n the s u r f a c e is has  (see r e f . 9 ) .  Experience i n d e a l i n g w i t h mercury  surfaces  shown us t h a t the minutest amounts of i m p u r i t i e s  to have a most d r a s t i c e f f e c t on the v i s c o u s damping f i c i e n t o Even a monolayer of o r d i n a r y machine o i l , by s p r a y i n g  tend coef-  obtained  the o i l very f i n e l y c l o s e t o the s u r f a c e , so  t h a t contamination occurs  from the o i l vapour,  increases  the v i s c o u s damping c o e f f i c i e n t by a f a c t o r of 2, o r even more. , S u r f a c e waves were e x c i t e d by v a r y i n g the frequency of t h e a i r p u l s e s . When t h i s frequency matched one o f the s u r f a c e mode f r e q u e n c i e s  ( o r sometimes one of the sub-  harmonics) the s u r f a c e o s c i l l a t e d w i t h  that p a r t i c u l a r f r e -  quency. The a i r supply was then shut o f f and the surface, a l lowed t o o s c i l l a t e f r e e l y , the o s c i l l a t i o n g r a d u a l l y damping away. A time r e c o r d of t h i s damped o s c i l l a t i o n was o b t a i n e d on the moving f i l m . A l o g - l i n e a r p l o t of the amplitude of of t h i s damped o s c i l l a t i o n v s  0  time (both obtained  from the  -25f i l m ) r e s u l t e d In a very good s t r a i g h t  line, A typical  i s shown i n f i g . 12. T h i s i m p l i e s an e x p o n e n t i a l decay  e  e x a c t l y as p r e d i c t e d by the l i n e a r i s e d  s l o p e of the s t r a i g h t  plot  amplitude  theory.  The  l i n e i s the damping c o e f f i c i e n t .  The  •period ,of o s c i l l a t i o n c o u l d be o b t a i n e d very a c c u r a t e l y by u s i n g the time markers to measure, the time f o r a number of oscillations/usually  twenty.  , In our experiments, used a t the b e g i n n i n g . The  newly d i s t i l l e d mercury c a v i t y was  cleaned as w e l l as pos-  s i b l e from dust t r a c e s . Then the c l e a n mercury was and  the damping c o e f f i c i e n t measurements performed  found  was  t h a t , even w i t h the above steps to a v o i d  introduced 6  It  was  contamination,  the damping c o e f f i c i e n t v a l u e s were h i g h e r than the v a l u e s theoretically  p r e d i c t e d f o r c l e a n mercury. T h i s r a t h e r an-  n o y i n g e f f e c t has been observed (see r e f . 2 ) . I t a l s o r e s u l t s  by o t h e r workers as w e l l  i n v e r y e r r a t i c and h i g h l y i n -  c o n s i s t e n t v a l u e s f o r the damping c o e f f i c i e n t . A f t e r i n g an e l e c t r o s t a t i c f i e l d  of 18.5  apply-  kV/cm f o r a few,minutes  and then removing i t , the v a l u e s o b t a i n e d f o r the v i s c o u s damping c o e f f i c i e n t  tended  to the c l e a n s u r f a c e v a l u e s .  They a l s o became much more c o n s i s t e n t . The of a p p l i c a t i o n of the f i e l d  time  the more c o n s i s t e n t t h e . r e s u l t s  were. T a b l e 3 shows the r e s u l t s A f t e r we  l o n g e r the  for  comparison.  e s t a b l i s h e d the c l e a n i n g of the s u r f a c e  by the e l e c t r i c f i e l d  the mercury was  allowed to stand i n the  c a v i t y f o r a few days. The damping c o e f f i c i e n t g r a d u a l l y  -  20 10  20  FIG  30  40  50  Time u n i t s  12  E x p o n e n t i a l damping of a s u r f a c e wave i n t i m e .  TT  i n c r e a s e d towards the " d i r t y s u r f a c e " v a l u e s , presumably because the i m p u r i t i e s were s l o w l y r e s e t t l i n g on the s u r f a c e . I t was  very encouraging  c a t i o n of the f i e l d  a g a i n gave us c l e a n i n g e f f e c t .  • A f u r t h e r , t e s t was the c a v i t y was ;  ted  indeed to f i n d t h a t a p p l i -  conducted  as f o l l o w s . The. top of  removed and a p i e c e of cardboard which j u s t  i n t o the c y l i n d r i c a l c a v i t y was  I n s e r t e d i n the  j u s t below the top., A very f i n e spray  cavity  (an atomizer)  was  used  to spray the rim of the c a v i t y w i t h o r d i n a r y machine  oil.  The.cardboard  prevented any o i l d r o p l e t s from  d i r e c t l y on,.the mercury s u r f a c e (see f i g . 13"K removal of the cardboard, c a v i t y , the surface.was  and replacement.of  contaminated  o i l vapour coming t o s e t t l e onto  f  settling  Thus, a f t e r the l i d of the  by minute amounts of  i t . The. v i s c o u s damping  c o e f f i c i e n t v a l u e s became even more i r r e g u l a r than b e f o r e , and d i s p l a y e d a s h a r p . i n c r e a s e , as can be seen from Then the f i e l d was  a p p l i e d as b e f o r e and  table  c l e a n i n g was  3«  again  achieved a f t e r a while. The  same EM and s u r f a c e mode used  measurements of 3*1 of  the cavity-was  frequency  were employed i n t h i s t e s t . The  geometry  i d e n t i c a l and a l l . t h e measurements were  taken w i t h a depth of mercury H = 4.31 It  i n the  cm.  i s seen t h a t . p e r f e c t l y c l e a n v a l u e s are not a t -  t a i n e d . However,-much more c o n s i s t e n t a n d . r e l a t i v e l y c l e a n ;  s u r f a c e r e s u l t s are...obtained... By l o o k i n g a t the .results can s t a t e , w i t h a c e r t a i n amount of c o n f i d e n c e , t h a t the  we.  CARDBOARD  FIG 13 Method o f c o n t a m i n a t i n g w i t h machine o i l vapour.  the mercury s u r f a c e  TABLE 3  cr Before  sec"" f i e l d applied  C o r r e s p o n d i n g o~ After f i e l d applied  0.070  .  0.048  O.O67  0.046  0.079  0.045  0.074  0.044  0.112  0.044  NO OIL  WITH OIL  H = 4.31 cm P e r f e c t l y c l e a n v a l u e p r e d i c t e d by Case and P a r k i n s o n  cr=  0.029 sec"'  Value  p r e d i c t e d by the m o d i f i e d t h e o r y o f Curzon and P i k e  taking a thin, insoluble surface f i l m c o r r e c t e d v a l u e o f k (= 0.54  i n t o account and u s i n g  cnr')» °~= 0.052 sec"'.  -29c l e a n i n g i s a l i t t l e more e f f e c t i v e when o i l i s spread on  the  s u r f a c e i n the manner d e s c r i b e d above. The o i l most p r o b a b l y c a r r i e s dust p a r t i c l e s with i t .  Note t h a t another use of the  Mylar s h e e t s . i s to prevent t r a c e s of o i l from, the a i r supply from e n t e r i n g the c a v i t y . a n d contaminating the mercury. A white gauze„ u s e d . i n an a i r f i l t e r t u r n e d dark brown a f t e r the a i r uras run through f o r about an A good t h e o r e t i c a l approach damping c o e f f i c i e n t was I t was  hour. to c a l c u l a t i n g the v i s c o u s  g i v e n by Case and P a r k i n s o n ( r e f ,  m o d i f i e d by Curzon and Pike ( r e f . . 2)  10).  to take i n t o ac-  count a t h i n i n s o l u b l e f i l m which i n v a r i a b l y forms on a l l exposed  l i q u i d s u r f a c e s . T h i s r e s u l t e d i n an i n c r e a s e i n the  v a l u e of the damping c o e f f i c i e n t s g i v i n g good agreement w i t h experiment.  However, i n view of. the i n c r e a s e d a c c u r a c y of the  t e s t s c a r r i e d out i n t h i s p r o j e c t and  the almost, i n c r e d i b l e .  d i s c o r d a n c e i n observations„ we must conclude, t h a t  a.lot.more  needs, to. be done, b e f o r e a. c l e a r u n d e r s t a n d i n g of.. the p h y s i c a l p r o p e r t i e s of a mercury s u r f a c e i s reached.  -303.4  The  rectangular cavity Our  g o a l i n t h i s p r o j e c t was  F o u r i e r analyzing property  to demonstrate  the  of the r e c t a n g u l a r c a v i t y r e s o -  nator. According and  Pike  to t h e o r e t i c a l work c a r r i e d out "by Curzon  ( r e f s . 2 and  3)  there should  be a s e l e c t i v e  t e c t i o n of s u r f a c e modes i n a r e c t a n g u l a r c a v i t y . By S l a t e r ' s theorem ( r e f . 6), resonant  frequency  b a t i o n s of one  Aw  c  of an EM mode due  ilibrium,  J j  l  J  to s m a l l p e r t u r -  of the s u r f a c e s of the r e s o n a t o r  is  Emboli  C  where u> i s the resonant  using  they showed t h a t the s h i f t i n  S jB MJ*~  w  de-  frequency  with the s u r f a c e i n equ-  i s the p e r t u r b a t i o n , E and  B the e l e c t r i c  and  magnetic f i e l d s a s s o c i a t e d w i t h the EM mode, dA an element of c r o s s - s e c t i o n a l area the r e s o n a t o r  (parallel  i n our case) and  the a x i s of the r e s o n a t o r . I f the c a v i t y has  to the perturbed  dz an element of l e n g t h  the f o l l o w i n g .expression f o r  then Lamb ( r e f . 8 )  f o r the  cylindrical*  geometry of the c a v i t y i s shown  C o n s i d e r i n g TE modes i n the c a v i t y (most u s e f u l  ones and  the ones l i k e l y to be employed), numbered  * See  20  p.  gives  J  where an analogous n o t a t i o n to the one  i n f i g . 14.  along  C denotes the l e n g t h of the c a v i t y .  c r o s s - s e c t i o n axb,  c a v i t y has been used. The  base of  TE  w y i  p  .  FIG  lk  Geometry of the r e c t a n g u l a r c a v i t y  resonator.  -32i n the u s u a l e l e c t r o m a g n e t i c n o t a t i o n , the f o l l o w i n g express i o n s f o r Au/ were o b t a i n e d by Curzon and P i k e I k  /  +2  /P \ I u/C/ r r c  2.1  C  c  where c i s the v e l o c i t y of l i g h t . It i s readily  seen t h a t the g e n e r a l EM mode T E  above w i l l respond  St*,an  >  depicted  M  o n l y to the t h r e e s u r f a c e modes  ?o,*h  a  n  o  '  J a w o  T h i s p r o v i d e s us w i t h a powerful  *  t o o l f o r doing  automatic  F o u r i e r a n a l y s i s o f s u r f a c e modes. A c a v i t y o f square' c r o s s - s e c t i o n was used f o r t h i s experiment. S i n c e the c a v i t y cannot be made e x a c t l y  square,  the degeneracy of the EM modes i s removed s u f f i c i e n t l y f o r two o f them t o appear s e p a r a t e l y w i t h i n the bandwidth of the k l y s t r o n . Hence both modes c o u l d be observed  simultaneously  on the o s c i l l o s c o p e s c r e e n . F i g . I5 shows a photograph o f the k l y s t r o n output EM modes observed  on the o s c i l l o s c o p e s c r e e n w i t h two  on the s c r e e n s i m u l t a n e o u s l y . I f one o f  FIG  15  D i s p l a y o f two EM modes on the s c r e e n  simultaneously.  -33-  them c o u l d be shown to respond t o a s u r f a c e mode w h i l e the o t h e r one d i d n o t , then the F o u r i e r a n a l y z i n g  technique  would have been v e r i f i e d . E x a c t l y the same experimental  arrangement as f o r the  c y l i n d r i c a l c a v i t y was used. The o n l y n o v e l t y w a s t h a t i n the case of the square c a v i t y the microwaves were f e d d i r e c t l y through the c e n t r e of the top p l a t e , w h i l e pulsed  the a i r was  through a h o l e on the d i a g o n a l . The geometry Is shown  In f i g . 1 6 * T h i s m o d i f i c a t i o n was found to i n c r e a s e the Qf a c t o r of the EM modes, r e s u l t i n g In a sharper  separation  between them. P u l s i n g the a i r through an o f f the c e n t r e was no hindrance Various as the frequency  hole  a t a l l to the e x c i t a t i o n of s u r f a c e modes. s u r f a c e modes c o u l d be e x c i t e d and detected, of the a i r pulses, was g r a d u a l l y  increased.  I t was observed, much to our d e l i g h t , t h a t without f i c u l t y we c o u l d e x c i t e resonant  any d i f -  o s c i l l a t i o n s of the s u r f a c e ,  to which o n l y one of the EM modes responded. An example of one  o f our o r i g i n a l f i l m s i s shown i n f i g . 1 7 . The EM mode  d i p s on the s c r e e n b e i n g p r e t t y sharp, the s c r e e n was so arranged The  the s l i t  In f r o n t o f  as to g i v e one t r a c e per d i p .  s i n u s o i d a l curve on the r i g h t hand s i d e i s o b v i o u s l y  a resonant  s u r f a c e mode. A s l i g h t motion o f the l e f t hand  d i p Can a l s o be d e t e c t e d  . I t i s e a s i l y recognised  as the  e f f e c t o f " s t r e t c h i n g " and "compressing" the k l y s t r o n output  curve  on the o s c i l l o s c o p e f a c e by the motion of the  r i g h t hand d i p . I t i s n o t an independent o s c i l l a t i o n .  I f we  -34look c a r e f u l l y  enough we can see t h a t the l e f t hand d i p  o n l y s h i f t s s l i g h t l y to the r i g h t when the r i g h t hand d i p is closest pulls in  t o i t . The r i g h t hand o s c i l l a t i o n e f f e c t i v e l y  the l e f t hand one ( n o t i c e t h a t the l e f t  the o p p o s i t e d i r e c t i o n  shows a s i m i l a r  to the r i g h t hand o n e ) . P i g . 18  experiment i n which both EM modes a r e a f -  f e c t e d by a s u r f a c e mode of d i f f e r e n t case two c l e a r  in  geometry. In t h i s  independent o s c i l l a t i o n s can r e a d i l y  on the f i l m . Both f i l m s sinusoidal  hand moves  are p o s i t i v e  be se  enlargements of the  curve o b t a i n e d on the c o r r e s p o n d i n g n e g a t i v e  the method d e s c r i b e d i n d e t a i l i n c h a p t e r 2 .  0.75 cm  WAVEGUIDE  0.88 cm  FIG  16  Geometry of the top of the r e c t a n g u l a r  cavity.  -35-  PIG  17  Response o f only one EM mode to a c e r t a i n s u r f a c e mode.  -36-  CHAPTER 4 C O N C L U S I O N S 4,1  Improvement of measuring  - F U T U R E  WORK  technique  The method of s t u d y i n g s u r f a c e waves of s m a l l a m p l i t u de by a microwave r e s o n a t o r technique was  improved by making  the time measurement more a c c u r a t e and much more I t was  used to check the o s c i l l a t i o n frequency  convenient.  of a. s u r f ace ..  mode of d i f f e r e n t geometry from the one used before..The Curzon-Pike o b t a i n e d was  meniscus c o r r e c t i o n was  v e r i f i e d . The  .  correction  more r e l i a b l e than p r e v i o u s ones because of the  improvement of the time measuring technique which gave us v e r y a c c u r a t e v a l u e s f o r the o s c i l l a t i o n frequency  •f*•  2  A p p l i c a t i o n of a s t r o n g e l e c t r i c f i e l d The main o b j e c t i v e of t h i s work was  of  applying a strong e l e c t r o s t a t i c f i e l d  surface without  oh the s u r f a c e to f i n d a  way  onto the mercury  i n t e r f e r i n g with the method of  s u r f a c e , p e r t u r b a t i o n s . T h i s was  f ( = 0.1$).  monitoring  done by i n s e r t i n g  Mylar  sheets as i n s u l a t o r s between the l i d of the C a v i t y and base. Then the base of the c a v i t y and to  the  the top were r a i s e d  constant p o t e n t i a l s with a large p o t e n t i a l d i f f e r e n c e  between them. To study the e l e c t r o s t a t i c - h y d r o d y n a m i c instability necessary.  ( r e f . 7, Our  p. 35)  an i n c r e a s e of the f i e l d  is  c a l c u l a t i o n s show t h a t about 70 kV/cm  must be o b t a i n e d  to get any o b s e r v a b l e  e f f e c t s . This  will  -37be done by u s i n g a c a v i t y of l a r g e r diameter than the ones so f a r used. T h i s w i l l enable us between the mercury s u r f a c e and EM mode  thereby  B  to minimize the  distance  the c a v i t y l i d f o r a g i v e n  i n c r e a s i n g the e l e c t r o s t a t i c f i e l d f o r  a g i v e n a p p l i e d p o t e n t i a l d i f f e r e n c e . To a v o i d the poss i b i l i t y of d i e l e c t r i c breakdown i n the c a v i t y s u l p h u r f l u o r i d e gas w i l l be pumped i n t o the r e s o n a t o r a f t e r air  i s expelled.  4.3  E f f e c t of e l e c t r o s t a t i c f i e l d  on the  hexa-  the  surface  In p r e l i m i n a r y experiments d e s c r i b e d i n t h i s t h e s i s the e f f e c t of a s t r o n g e l e c t r i c f i e l d on the p r o p e r t i e s of the mercury s u r f a c e was  demonstrated. A method f o r removing  t r a c e s of .contamination  from, the s u r f a c e was  found. T h i s  can prove v e r y u s e f u l , to p h y s i c i s t s a n d p h y s i c a l Their observations b i l i t y due  have so f a r been plagued by  chemists.  irreproduol-.. .  to the g r e a t s e n s i t i v i t y of l i q u i d s u r f a c e s  to  contamination. 4.4  Square  resonator  The  f e a s i b i l i t y of u s i n g a r e c t a n g u l a r . r e s o n a t o r  an automatic. F o u r i e r , a n a l y z e r was square c a v i t y . T h i s i s a very resonator  technique  demonstrated by u s i n g a  Important p r o p e r t y  f o r studying.surface  of  the  waves, since, d i s -  p e r s i o n r e l a t i o n s can be measured d i r e c t l y , thereby nating Fourier analysis.  as  elimi-  -384.5  P o s s i b i l i t y of a p p l y i n g the method In o t h e r f i e l d s A f i n a l a s p e c t of the method as a whole„  we vrould l i k e  on which  to comment, i s the f o l l o w i n g . T h i s method  of o b s e r v a t i o n of d i s t u r b a n c e s on a f l u i d s u r f a c e can, i n p r i n c i p l e , be employed  as a selsmometrie d e v i c e . An o l d  method of d e t e c t i n g earthquakes was  by o b s e r v i n g the d i s -  turbances on the s u r f a c e of water i n a w e l l r e s u l t i n g from the earthquake. In a s i m i l a r . m a n n e r , the.more s o p h i s t i c a t e d 1  microwave r e s o n a t o r technique can be used as an. earthquake, d e t e c t o r . I t combines graph. F i r s t l y ,  the two b a s i c f e a t u r e s o f . a seismo-  i t i s extremely s e n s i t i v e . T h i s was  clear-  l y demonstrated by our b e i n g a b l e to e x c i t e waves on the s u r f a c e even w i t h the Mylar s h e e t s . i n p o s i t i o n i n the path of the a i r p u l s e s . Secondly, c o n v e n t i o n a l seismographs have a m p l i f i c a t i o n f a c t o r s between  10  and  10  0  depending on  t h e i r purpose (see r e f . 11). Our system a m p l i f i e s waves of 0.001  i n . to motions of about 2 to 3 inches on the o s c i l -  l o s c o p e s c r e e n , i . e . an a m p l i f i c a t i o n of 2 to 3 thousand, right  i n s i d e the range. F i n a l l y , s i n c e the F o u r i e r a n a l y z i n g  p r o p e r t y of r e c t a n g u l a r r e s o n a t o r s has been they can be employed  demonstrated,  to F o u r i e r a n a l y z e an earthquake  signal  a u t o m a t i c a l l y . At p r e s e n t , the F o u r i e r , a n a l y s i s of. seismograms, takes up a l o t of energy of p e r s o n n e l manning seismographs.  -39REPERENCES 1.  Curzon, P. L. and Howard, R. P h y s i c s 39, 1901.  2.  P i k e , R. L. ( I 9 6 7 ) , Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Department of P h y s i c s .  3.  Curzon, P. L. and P i k e , R. L. ( I 9 6 8 ) , P h y s i c s 46, 2 0 0 1 .  Can. J o u r n a l of  Curzon, P. L. and P i k e , R. L. ( 1 9 6 8 ) ,  Can. J o u r n a l of  4.  Physics  5.  46,  (1961), Can. J o u r n a l of  2009.  Curzon, F. L. and P i k e , R. L. ( I 9 6 9 ) , Physics  Can. J o u r n a l of  47,1051.  6.  S l a t e r , J . C. ( I 9 6 3 ) , Laboratories Series.  Microwave  7.  Landau, L. D. and L i f s h i t z , E. M. ( i 9 6 0 ) ' . E l e c t r o dynamics of Continuous Media, Addlson-Wesley.  8.  Lamb, H. ( 1 9 4 5 ) , Hydrodynamics, Inc., New York.  9.  Burdbn,'R. S. ( 1 9 4 9 ) , S u r f a c e Tension and the Spreading of. L i q u i d s , Cambridge. U n i v e r s i t y P r e s s .  10.  Case, K. M. and P a r k i n s o n , Mechanics 2 , 1 7 2 .  11.  R i c h t e r , C. F. ( 1 9 5 8 ) , Elementary Seismology, W . Freeman, San F r a n c i s c o .  12.  R i e s , H. E . J r . , and K i m b a l l , W . A. ( 1 9 5 7 ) . Proceedings of the Second I n t e r n a t i o n a l Congress of S u r f a c e A c t i v i t y , V o l . I , Butterworths S c i e n t i f i c P u b l i c a t i o n s , London,  W.  Electronics, Bell  Dover P u b l i c a t i o n s  C. ( 1 9 5 6 ) , J . of F l u i d H.  -40APPENDIX .THEORY OF  THE  .SURFACE BY  CLEANING OF  THE  THE  A P P L I C A T I O N OF  MERCURY A STRONG  ELECTROSTATIC F I E L D Our tical  purpose i n t h i s appendix i s to propose a  explanation  trostatic field we  would l i k e  of the  has  on  to warn the r e a d e r  the behaviour  t h a t , as any  convey, the  of l i q u i d  experimental  comes t o s t u d y i n g still  surfaces  are  elec-  proceeding,  textbook  still  i s so  techniques  of.  not  be-  fully  i n t r i c a t e and  of  the  any  surfaces  suggest below i s a simple  and  com-  .  so d i f f i c u l t when i t  the a c t u a l s u r f a c e , t h a t a l o t of work  t o be . c a r r i e d o u t b e f o r e  numerous a s p e c t s  strong  physical principles  c l e a r l y understood.. T h e i r behaviour p l i c a t e d , and  t h a t the  the mercury s u r f a c e . Before  P h y s i c a l Chemistry w i l l hind  cleaning effect  theore-  general  c a n be  p i c t u r e of  the  g i v e n . What we  p h y s i c a l model of the  has  shall  cleaning  process. A liquid pure l i q u i d on the  itself.  s u r f a c e , when f o r m e d by  pouring p e r f e c t l y  i n a c o n t a i n e r , soon forms a t h i n , This  i s composed o f  insoluble film  t r a c e s of grease t h a t are  c o n t a i n e r or i n the atmosphere above.the s u r f a c e ,  f i n e dust  particles,  or even o x i d e s  c a l p r o p e r t i e s of the  surface  nated  described  w i t h o i l as was  . The  e f f e c t on  In  very  the  physi-  i s more p r o n o u n c e d when c o n t a m i i n the p r e v i o u s  chapter.  So  we  -41-  s h a l l t r e a t t h i s more g e n e r a l Our  case In our  t h e o r e t i c a l argument.  method of contamination of the mercury  surface  w i t h o i l w i l l r e s u l t i n the f o r m a t i o n of a c o l l a p s e d monol a y e r of o i l on  the s u r f a c e . By a c o l l a p s e d monolayer we  a l a y e r of o i l of m o l e c u l a r t h i c k n e s s  mean  (of the o r d e r of 10  k),  on which c l u s t e r s of o i l molecules forming extremely f i n e droplets  (not v i s i b l e  to the naked eye)  are found at random  p o s i t i o n s on the surface, (see f i g . 1 9 a ) . A mechanism f o r f o r m a t i o n of the p.75 the  to p.84.  c o l l a p s e d monolayer can be found i n r e f .  This f i l m  i s so t h i n t h a t the  surface  12,  charge  conductor (mercury) r e s u l t i n g from...the a p p l i c a t i o n of  field 20  the  can be  kV/cm l i k e  considered  to r e s i d e on  t e s t s there w i l l  of r a d i u s r , we  field  assumed. The  stress trying  the c o n f i g u r a t i o n of f i g . 19c w i l l  weight of the d r o p l e t , c o h e s i v e f o r c e s  by n e i g h b o u r i n g o i l molecules and the mercury w i l l  the be  exerted  adhesive f o r c e s exerted  tend to p u l l i t back i n t o p o s i t i o n . The  a t i o n f o r the balance of f o r c e s  •;&£.%TTY*=  hemispherical  the o i l f i l m a d e f o r m a t i o n w i l l occur when  i s a p p l i e d and  Q_rrr F sinB t  con-  can r e a d i l y v i s u a l i z e the  s i m p l e c l e a n i n g mechanism..Due to the s u r f a c e to p u l l on  be  t h i n o i l f i l m . I f we  s i d e r an o i l d r o p l e t o f , f o r convenience sake, shape ( f i g . 1 9 b )  the  i t . At f i e l d s of about  the ones employed i n the  l a r g e e l e c t r o s t a t i c s t r e s s e s on the  on  can be w r i t t e n  TTr  1  +. p- \  by equ-  as  r r r  3  ^  ( .l) A  -420 1 L DROPLETS  •y  y  MONOLAYER  y—y>—•?—•?——y  y—y—y~  MERCURY  FIG  19  A c o l l a i ^ s e d monolayer  y  y  /  y  y  y  o f o i l on t h e mercury,  y  y  MERCURY FIG-  20a  MERCURY FIG 20b Mechanism o f t h e removal o f contaminants from t h e m e r c u r y s u r f a c e by a s t r o n g e l e c t r i c f i e l d .  FIG Mechanical analogue  21  of the breaking  up o f the t h i n o i l f i l m .  where  :  F = cohesion f o r c e per u n i t  length,  Fp,^ adhesion f o r c e per u n i t  area  P = d e n s i t y of  oil  E = electrostatic and  field  g = a c c e l e r a t i o n of  gravity.  Therefore :  " i F = { f i  l  -  FL  -e^rfjfe  (A.2)  But s i n c e 0 i s a very s m a l l angle F can become a very large f o r c e .  So l a r g e i n f a c t t h a t  w i l l not be a b l e to supply  it  cohesion e f f e c t s  and the o i l f i l m w i l l  break.  Under the upward a c c e l e r a t i o n of the f i e l d the o i l w i l l be a c c e l e r a t e d upwards and w i l l s t i c k top. is  N o t i c e t h a t only micrograms of o i l  q u i t e easy f o r  This  is  are i n v o l v e d  the f i e l d to a c c e l e r a t e the o i l  so  - S-B 5xlO"'^X  1+ xlD  it  oil  ; Nt.  n  -  dynes  (A.3)  A m e c h a n i c a l analogue of the b r e a k i n g up of the o i l f i l m the case of a s m a l l weight ly  horizontal  i s quite for  string  is  a t t a c h e d to the c e n t r e of a n e a r -  as shown i n f i g . 20 . Even i f  the  weight  s m a l l the t e n s i o n i n the s t r i n g w i l l be enormous  very small 9 .  the  upwards.  e a s i l y seen by the f a c t t h a t the s t r e s s on the  s u r f a c e a t f i e l d s o f 20 kV/cm i s .  to the Mylar sheets a t  .  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0084836/manifest

Comment

Related Items