191S] on Studies on Liquid Films 893 



W/ = E^ ; for the second case, W /' - E' e', or AV / = 4 E' e'. 

 . • . -^E'e = Ee. Now in the Table I. E' = -817, E = -Ss;}, or ap- 

 proximately E' = 2 E, hence the last equation becomes S e' = e, or 

 in terms of x, S x ^ I -=- x I, whence 4:x' = x. 



Gas Transference through Fil]vl Co3iplexes. 



Columns and clusters of bubbles generally reach the " black " 

 stage with great rapidity by the action of the channels (Gibbs rings) 

 of liquid where the segments join together. The black development 

 of an ordinary hanging bubble is different from that of a similar 

 bubble resting on a ring, because in the latter case the action of the 

 Gibbs ring is to assist gravity in withdrawing liquid from the film 

 and thus to accelerate the thinning process, w^hile in the former case 

 the action of the Gibbs ring is against gravity, and thus retards the 

 withdrawal of liquid from the film. The two curves in Fig. 29 show 

 this difference very clearly : the black boundary on the poised 

 bubble descending at an ever-increasing rate, as it approaches the 

 Gibbs canal present on the support ring ; while in the hanging 

 bubble the rate of fall continually decreases. (This is more notice- 

 able when liquid is allowed to accumulate below while the thin black 

 area extends downwards. In the al)sence of suitable drainage, the 

 coloured zone then becomes continually thicker.) When however a 

 bubble was provided with two Gibbs rings, one above and one below, 

 the rate of fall of the black boundary was almost linear for the 

 greater part of the time. 



This was arranged by attaching a small bubble under a large one, 

 supported as usual from a nozzle above. The small bubble was kept 

 steady by a smaller glass ring underneath. The nozzle was 8*3 cm. 

 in diameter, and the size of the small attached bubble was adjusted 

 so that the diameter of the Gibbs ring of contact between the two 

 bubbles was about the same. The greater bubble was 40 cm. high 

 between the equal Gibbs rings top and bottom, viz. where contact w^as 

 made with the nozzle above, and the small bubble film below. The 

 graph of " black fall " plotted with time was very nearly straight for 

 2^ days, by which time the black area had extended over three-fourths 

 of the surface. After this it spread more slowly, and took another 

 day and half to reach the lowest point. The form was therefore 

 intermediate between curves {a) and {b) of Fig. 29. 



Xow, in the more complex clusters there are many channels all 

 connected at various inclinations, therefore not only is any excess 

 liquid quickly discharged, but the films themselves are quickly drained 

 to the " black " state. 



This is the most favourable condition for the study of gas trans- 

 ference, as the film is then at its minimum thickness. The resulting 

 contraction has been measured in the case of straight columns and 

 other complexes by photographs taken periodically. These afford 



2 E 2 



