Electrification at Liquid-Gas Surfaces. 309 



Discussion. 

 Small spheres of gas electrically charged in water move in 

 an electric field with a velocity of the same order as the 

 velocity of colloidal particles. The motion of these particles 

 is regarded as due to a continuous relative displacement in 

 opposite directions of the two faces of a double layer, one of 

 which is fixed to the solid particle. The velocity of such a 

 particle is given by Lamb's formula (B. A. Report, p. 495, 

 1887) 



R P 8 



u=- , 



where u = vel. of particle, p = surf, density of charge, 

 H = pot. grad., 8 = thickness of layer, 



^ = viscosity of liquid. 



This equation will apply to the motion of spheres of gas 

 in a liquid if a double layer exists at the liquid-gas interface, 

 That surface of the double layer which touches the gas would 

 not be attached to a solid surface as in the case of a colloidal 

 particle, but it might be regarded as forming a sort of 

 flexible shell filled with the gas. 



There is no doubt that a film of some rigidity is formed 

 about the gas, which acts toward the contiguous liquid like 

 a solid surface so far as endosmose effects are concerned. 

 Hardy (Proc. Roy. Soc. B. lxxxiv. 1911) has examined with 

 some care the case of a plane air-water surface. An electric 

 current was observed to drive small particles of graphite 

 immersed just under the film past the surface with the same 

 velocity as particles near the solid walls of the containing 

 vessel. Small particles resting upon the film did not move 

 appreciably. A sphere of gas in liquid is enclosed in a film 

 of this sort which forms one surface of the double layer and 

 preserves its identity, more or less, as it moves through the 

 liquid. We may, then, with some reason assume Lamb's 

 formula to be applicable and employ it to find the charge on 

 a bubble of air in water. 



We have in E.s. units : — 



jJLU 



P= R8 



0-01.4.10 



.3 ' xyj 



putting the viscosity at O'Ol and the thickness at 10" 8 cm. 

 or 0-01. 4.10" 4 



coulomb; 



;loo 

 = 4 . 10 ~ 5 nearly 



