The Principles of Film-Formixg Sprays 59 



meters of water in contact with the benzene. The total free surface 

 energy is then represented by twice the surface tension of the ben- 

 zene and twice the interfacial tension, since in each case two square 

 centimeters of surface are exposed. 



Second condition — Total Surface Energy = 2 Sur. Ten. Benzene 

 -|- 2 Inter. Ten. Benzene-Water. 



The question as to whether the benzene will completely cover the 

 water or only one square centimeter of its surface will depend upon 

 which of these equations gives the smallest sum, or in other words 

 which arrangement shows the least free surface energv. In this par- 

 ticular case the values of the surface tensions are known and mav be 

 given as an illustration. Substituting in these equations the values of 

 surface tensions of pure benzene and pure water, the following is 

 obtained. 



First condition — Total Surface Energy = 72.05 + 28.17 -f 34.68 



= 134.9 dynes. 

 Second condition — Total Surface Energy ^ 2( 28.17) -^2(34.68) 



= 126.7 dynes. 



It is thus seen that in this particular case the second equation, 

 that is, where benzene is spread over the total surface of water, gives 

 the smallest value for the free surface energy ; and in actual experi- 

 ment pure benzene will immediately spread over pure water. 



If, however, the water has been in contact with benzene for a 

 short time the values are changed, since the surface tension of the 

 water is reduced by the benzene dissolved in it while the surface 

 tension of the benzene is reduced by the water dissolved in the ben- 

 zene and the interfacial tension is increased. Substituting these new 

 values in the equations the following are obtained : 



First condition — Total Surface Energy -=60.19 -f 27.90 + 44.63 



= 132.77 

 Second condition — Total Surface Energy = 2(27.90) +2(44.68) 

 = 145.16 



The first condition represents the smallest sum and the benzene will 

 collect in the form of a drop on the surface of the water rather than 

 as a film over its whole surface. In an actual experiment, when pure 

 benzene is spread over the surface of pure water, it will be observed 

 that after a period of time suf^cient for the water to dissolve some of 

 the benzene and the benzene to dissolve some of the water, the 



