TK.. ELECTROPHORESIS 275 



is a function only of its net charge and of its radius, if spherical. 

 With small particles and low ionic strength of solutions it is to be 

 expected that shape of particle will also be a factor in determining 

 its mobility. 



If the particle is of such dimensions that its radius of curvature is 

 large compared to the thickness of the double layer then, independent 

 of particle shape, the double layer may be considered as parallel 

 plates of zero curvature with respect to the api)lied field (i.e., curva- 

 ture will be parallel to the contour of the applied field in the neigh- 

 borhood of the particle surface) . The net charge carried by the par- 

 ticle, Q, can be resolved into the net charge density per unit of surface, 

 0", by the relationship a = Q/A, where A = the area of the particle 

 surface (cm.^). The force of acceleration (/) experienced per unit of 

 surface by the particle under field strength E will then be / = Ea. 

 All relative movement between the particle and the fluid must then 

 take place in the fluid existing between the planes of the double layer, 

 and a resistance to this movement will exist determined by the vis- 

 cosity of the liquid, the velocity of the particle, and the distance in 

 the liquid between the point of maximum motion {i.e., that of the 

 layer fixed on the particle surface) and the point of no motion {i.e., 

 beyond the outer layer of the double layer). If the viscous flow 

 of the liquid between these regions can be considered linear, as be- 

 tween two parallel plates moving with respect to each other, the 

 frictional resistance, per unit of particle-liquid interface, to relative 

 motion of the particle and the fluid phase will be given by the expres- 

 sion/" — Tju/s, where 77 is the viscosity coefficient (poise) of the liquid 

 in the region of the interface, u is the velocity of displacement (cm./ 

 sec.) of the particle with respect to the liquid, and s is the distance 

 (cm.) between the regions of maximum motion and no motion. At 

 equilibrium, when the steady state is reached, wherein the force of 

 acceleration and force of resistance to motion are equal, Ea = tjw/s 

 or u = Eas/r] and m = as/rj. Since the entire force of resistance is 

 exerted within the volume of liquid existing between the two layers 

 of opposite charge {i.e., within the double layer) it can be assumed 

 that s will be equal to or proportional to the thickness of the double 

 layer and will vary with the ionic strength of the solution in the same 

 manner as will the thickness of the double layer. It is evident from 

 this relationship that the electrophoretic mobility of a particle sus- 

 pended in a solution of a given viscosity and ionic strength is a func- 

 tion only of its net charge density when the particle is large enough 



