4K Ml!. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHEXtiMI N A 



THK phenomenon of surface tension exhibited at the surface of separation l>etween 

 two homogeneous liquids may be regarded as arising from such a variation in the 

 distribution of the matter composing each of the liquids, in the immediate neighlxnir- 

 hootl of the surface of separation, that the energy of given quantities of the two 

 liquids is greater when these are in the neighbourhood of the surface than when each 

 is in the homogeneous interior of its corresponding liquid. 



On such a view, the tension per unit length in the surface will be equal to dE/dS, 

 where dE is the increase in the potential energy of the system of two liquids, resulting 

 from an increase, dS, of the surface of separation l>etween them. The distribution of 

 energy here referred to may be considered independent of possible electrostatic effects 

 at the surface of separation. 



There is little doubt, however, that there is frequently a potential difference of 

 considerable amount at the surface separating two such liquids as mercury and a 

 solution of a salt in water. There must, therefore, be a corresponding separation of 

 electricities of opposite sign at the surface, and we may regard these as forming a 

 condenser-like " double-layer." This double-layer will give rise to an electrostatic 

 surface energy, whose value we may write as E' = -JcSTr 2 , where c is the capacity of 

 the double-kyer per unit surface and TT is the potential difference across it. S is, as 

 before, the area of the surface separating the two liquids. Now, if a small change of 

 this surface, dS, be supposed to take place while the potential difference across the 

 double-layer is kept constant by an external electromotive force, we get 



This increase in the potential energy of the system, with increase in the surface of 

 separation between the two components, will be an effect that tends to take place 

 under the influence of the external electromotive force, and will be equivalent to a 

 force per unit length tending to increase the surface of separation between the 

 two liquids. 



The observed surface tension will thus be 



y = dE/dS - 



= y a - 



where y is the surface tension arising from the non-electrical distribution of energy 

 first mentioned. The equation will give the relation between the observable surface 

 tension and the potential difference at the mercury surface. 



The above may be regarded as the Helmholtz theory of electro-capillary pheno- 





