ELECTROKINETICS 365 



capacity of the liquid, is also a factor. Opposing these are 

 mechanical forces, such as friction, which depends on the viscosity 

 of the liquid and the size of the capillary tube. The relation- 

 ship of these factors was mathematically expressed by Helm- 

 holtz. The original formula has been modified several times. 

 Pellat added the dielectric constant of water. The formula as 

 now given is 



where V is the volume of liquid transported per second through a 

 tube of radius r and length /; f, the difference in potential between 

 the stationary charged layer and the outer Helmholtz layer (in 

 electrostatic units); E, the external electromotive force applied 

 to the electrodes at the ends of the capillary tube; D, the dielectric 

 constant of the liquid; and -q, the coefficient of viscosity of the 

 liquid. 



So far, we have centered our attention on the electroendosmotic 

 flow of water and the nature of the charge on the walls of the 

 capillary. We may transfer the same ideas to the migration of 

 individual colloidal particles through water under the influence 

 of an applied electromotive force. 



We may imagine the glass capillary in Fig. 159 broken up into 

 minute bits which are suspended in the water. The same double 

 layer of ions wfll then exist at the surface of the glass as before, 

 with negative ions tightly adhering to the glass and positive ones 

 close by but free in the water. The glass particle, like the glass 

 capillary tube, is negatively charged but being now itself free to 

 move travels to the positive pole. 



A Helmholtz double layer or a modified form of it is usually 

 present at the surface of aU colloidal particles (Fig. 76). The 

 particles of any one colloidal suspension are all of the same sign. 

 Whether the particles are negative, as are those of glass, gold, 

 and living cells, or positive, as are those of copper, lead, and iron 

 hydroxide, depends on whether anion or cation is preferentially 

 adsorbed to the surface of the particle. (Adsorption of ions is 

 generally assumed to be the cause of the charge (see page 109), 

 but in the case of proteins dissociation of ions from the particle 

 may be responsible.) 



