[ ^ ] 



IV. On Surface Concentration, and the Formation of Liquid 

 Films. By S. K. Milker, F).Sc. (Lond.)\ 



HPHE nature of the mechanism by which solutions of soap 

 A and a few other substances are able to form durable- 

 films has long been a problem of great interest. It is easy 

 to understand why in pure liquids, where the surface tension 

 is rigorously uniform, lasting films should not exist ; for the 

 slightest local disturbance of equilibrium, such as that due to 

 the weight of the films themselves, would make them collapse. 

 A capability of local variation in the tension of its surface 

 is thus seen to be esseutial for the stability of a film. 

 Marangonit in 1871 suggested that this capabilitv is due 

 to the presence on the surface of the film of a pellicle, com- 

 posed of matter having a smaller capillary tension than that 

 of water. By variations in the thickness of this pellicle which 

 immediately ensue as it is pulled over the surface, the tensions 

 will everywhere automatically take up the values necessary 

 to balance all the other forces, and a stable equilibrium will 

 result throughout the film. In 1890 Lord Rayleigh % con- 

 sidered the question, and gave a strong support to the theory 

 by showing that the tension of a soap solution, measured less 

 than T -J - second after the formation of the surface, approxi- 

 mates to that of pure water — for the formation of a pellicle 

 may be reasonably expected to be a matter of time. The 

 existence of a pellicle (or something equivalent to it) may be 

 looked on as substantiated by this work, but little or nothing- 

 is known as regards its nature or method of formation. In 

 the following paper some observations are recorded which, 

 I think, throw a further light on these points and on the 

 mechanism by which the stability of the film is maintained. 



Valuable information on the conditions of the surface of 

 solutions may be gained by studying their surface-tension 

 curves in the light of the thermodynamic relations which 

 exist between the surface tension and the concentration of the 

 dissolved substance in the surface. Consider a solution of 

 which the surface and the volume are capable of independent 

 reversible alterations, the latter by means of a semi-permeable 

 partition which separates the solution from pure water. Let 

 s be the area of the surface, v the volume, r the surface 

 tension, p the osmotic pressure of the solute. The work 

 done on the system by increasing the area by ds at constant 

 volume is rds, that on increasing the volume by dv the 



* Communicated by the Author. 



t Vide Rayleigh, Proc. Royal Soc. xlvii. p. 281 (1890). 



\ Loc. cit. 



