1893."] Gravity of Fluid Bubbles through Liquids. 



13 



PART I. 



The physical properties involved in the phenomenon may, perhaps, 

 be best studied by taking a particular case, say that of a bubble of 

 chloroform falling through a column of glycerine contained in a glass 

 tube. The appearance* is very much as shown in section in the 



figure. 



FIG. 1. 



In order that the bubble may descend, the liquid in front has to 

 pass up the sides through the narrow annular space between the 

 bubble and the tube. Were the diameter of the bubble known, the 

 question would reduce itself to a case of viscous flow through an 

 annular space provided we neglected the ends and supposed the walls 

 of the bubble to be rigid. The annular width will be seen to depend 

 on the surface tension between the liquids, for should, the tension 

 become very great, say, the bubble must swell out, blocking up the 

 tube. This tendency is in part counterbalanced by the excess in 

 density of the bubble over that of the liquid column. The case is, so 

 to speak, then that of viscous flow through an adjustable annular 

 orifice. 



The pressure per centimetre, or the pressure gradient driving up 

 the liquid through this annular space, depends simply on the differ- 

 ence in density of the liquids. 



* The length of the bubble was always several times its diameter, so as to get 

 outside the stage where the velocity depends on the length of bubble. 



