﻿Long 
  Air-Bubbles 
  in 
  a 
  Vertical 
  Tube. 
  965 
  

  

  5. 
  Limiting 
  length 
  for 
  stability 
  of 
  flow 
  past 
  the 
  bubbles. 
  — 
  

   As 
  indicated 
  on 
  p. 
  963, 
  for 
  great 
  lengths 
  the 
  velocity 
  of 
  

   flow 
  past 
  the 
  bubble, 
  on 
  the 
  assumptions 
  outlined 
  in 
  this 
  

   paper, 
  becomes 
  very 
  great, 
  and 
  from 
  general 
  considerations 
  

   one 
  would 
  expect 
  this, 
  at 
  some 
  definite 
  length, 
  to 
  attain 
  the 
  

   critical 
  velocity 
  of 
  eddy 
  formation 
  in 
  the 
  annulus. 
  Obser- 
  

   vation 
  shows 
  that 
  such 
  is 
  the 
  case, 
  and 
  that 
  in 
  very 
  long 
  

   bubbles 
  stream-line 
  motion 
  breaks 
  down, 
  as 
  is 
  indicated 
  by 
  

   the 
  frosted 
  appearance 
  of 
  the 
  film, 
  at 
  some 
  distance 
  from 
  the 
  

   head 
  of 
  the 
  bubble. 
  Some 
  difficulty 
  was 
  experienced 
  in 
  

   ascertaining 
  the 
  conditions 
  under 
  which 
  this 
  takes 
  place, 
  as 
  

   such 
  bubbles 
  are 
  too 
  long 
  to 
  permit 
  of 
  being 
  photographed 
  

   at 
  short 
  range. 
  In 
  consequence 
  visual 
  observations 
  had 
  to 
  

   be 
  made 
  on 
  the 
  moving 
  bubble, 
  and 
  any 
  estimates 
  of 
  length 
  

   are 
  hence 
  liable 
  to 
  a 
  fairly 
  large 
  percentage 
  error. 
  So 
  far 
  

   as 
  could 
  be 
  observed, 
  the 
  motion 
  is 
  perfectly 
  stable 
  in 
  the 
  

   tube 
  *788 
  cm. 
  diam. 
  for 
  all 
  bubbles 
  of 
  length 
  not 
  exceeding 
  

   15 
  cm. 
  With 
  longer 
  bubbles, 
  however, 
  eddies 
  are 
  formed 
  

   at 
  a 
  point 
  about 
  10 
  cm. 
  from 
  the 
  head, 
  and 
  this 
  appears 
  to 
  

   be 
  approximately 
  true 
  whatever 
  the 
  length 
  of 
  the 
  bubble. 
  

   In 
  the 
  1*68 
  cm. 
  tube 
  the 
  limiting 
  length 
  for 
  stability 
  of 
  flow 
  

   appears 
  to 
  be 
  about 
  25 
  cm., 
  and 
  the 
  motion 
  breaks 
  down 
  at 
  

   about 
  15 
  cm. 
  from 
  the 
  head. 
  

  

  In 
  neither 
  case 
  does 
  there 
  appear 
  to 
  be 
  any 
  tendency 
  for 
  

   the 
  bubble 
  to 
  split 
  up 
  into 
  a 
  series 
  of 
  shorter 
  bubbles, 
  as 
  in 
  

   the 
  case 
  of 
  an 
  air-column 
  in 
  open 
  water*. 
  In 
  the 
  latter 
  case 
  

   the 
  length 
  for 
  maximum 
  instability 
  is 
  found 
  to 
  be 
  6'4,8 
  times 
  

   the 
  diameter, 
  equivalent 
  to 
  approximately 
  5 
  cm., 
  in 
  the 
  

   smaller 
  and 
  10*5 
  cm. 
  in 
  the 
  larger 
  tube. 
  It 
  is, 
  indeed, 
  pro- 
  

   bable 
  that 
  the 
  comparative 
  thinness 
  of 
  the 
  boundary 
  film, 
  

   and 
  the 
  fact 
  of 
  its 
  contact 
  with 
  the 
  walls 
  of 
  the 
  tube, 
  have 
  

   the 
  same 
  effect 
  as 
  regards 
  the 
  tendency 
  to 
  lateral 
  motions 
  of 
  

   large 
  extent 
  as 
  an 
  increase 
  in 
  its 
  viscosity, 
  and 
  so 
  tend 
  to 
  

   minimise 
  the 
  tendency 
  to 
  regular 
  subdivision. 
  

  

  Owing 
  to 
  the 
  difficulty 
  experienced 
  in 
  forming 
  and 
  ob- 
  

   serving 
  the 
  motion 
  of 
  very 
  long 
  bubbles 
  in 
  the 
  tubes 
  of 
  

   greater 
  diameter 
  than 
  5*09 
  cm., 
  no 
  such 
  observations 
  were 
  

   made. 
  It 
  is 
  evident, 
  however, 
  from 
  the 
  data 
  in 
  the 
  table 
  

   on 
  p. 
  964, 
  that 
  the 
  larger 
  the 
  tube 
  the 
  thicker 
  is 
  the 
  film 
  

   between 
  bubble 
  and 
  tube 
  for 
  bubbles 
  having 
  similar 
  ratios 
  of 
  

   length 
  to 
  diameter, 
  so 
  that 
  the 
  tendency 
  to 
  instability 
  must 
  

   be 
  greater 
  in 
  a 
  large 
  than 
  in 
  a 
  small 
  tube. 
  

  

  University 
  College, 
  Dundee. 
  

  

  * 
  Kayleigh, 
  ante 
  cit. 
  p. 
  596. 
  

  

  