248 HYDROGEN ION CONCENTRATION 



72. Helmholtz's theory of electroendosmosis-^ 



Let us imagine that a solid diaphragm with capillary pores is 

 inserted into a tube filled vv'ith aqueous fluid. Now, on sending an 

 electric current through this tube, we observe that the water is set 

 into motion, and that after a short time a flow of water with a con- 

 stant velocity will ensue, provided care is taken to prevent hydro- 

 static difference of pressure due to the migration of the water. Let 

 us now consider this stationary condition of our system. To begin 

 with, it is characterized by the fact that the motion produced by the 

 electric current is rendered uniform by the friction. Now the electric 

 force is proportional to the electric density of the double layer a, 

 and to the electric field intensity, H, to which the double layer is 

 exposed. In terms of absolute units the electric force is simply equal 

 to cH. This value remains constant throughout the entire process. 

 If no friction were present it would produce a uniforml}^ accelerated 

 motion of the water. But the friction, checking the motion, changes 

 its rate from a uniformly accelerated to a uniform one. The force 

 of friction is proportional to the specific friction coefficient of water, 

 7? to the velocity v, and inversely proportional to the distance between 



21 The theory is not expounded here in Helmholtz's original terms and scope, 

 for that would require of the reader an extensive knowledge of theoretical 

 physics. It is presented in its simplified form, as given by Perrin. Helm- 

 holtz's own presentation has the advantage of greater strength, especially 

 in regard to the absolute value of the proportionality factors, which is not so 

 convincing in Perrin's interpretation. But since the assumption on which 

 Helmholtz's calculations are based have perhaps not been strictly justified 

 (of. section 78), and since the experimental data available thus far is still 

 insufficient to confirm the theory unqualifiedly, the mode of interpretation 

 given here will have to suffice, in a preliminary way, for physiologists. 



The difficulty in the way of experimental quantitative confirmation of the 

 theory is the following : Adsorption potentials cannot yet be recognized in any 

 other way except through electrokinetic phenomena (electrophoresis, electro- 

 endosmosis, hydrodynamic currents and currents of falling particles). Thus, 

 for example, in Helmholtz's theory the wall potential is calculated from the 

 figures given by electroendosmosis. The theory could only be confirmed by 

 comparing the value of the potential obtained from electrokinetic data with 

 that obtained by using some other method which is entirely independent of 

 electrokinetic technic. Such a method is still unavailable. And thus the 

 quantitative aspect of the theory is still uncertain, while in its qualitative 

 aspect is of great service. 



