274 DAVID R. BRIGGS 



will occur with respect to the fixed wall of the capillary and will be 

 observable as a flow of the liquid through the capillary. This phe- 

 nomenon is called electrosmosis. If, however, the double layer is one 

 existing in the region of the surface of a particle suspended in a fluid 

 contained in a vessel in which no net displacement of the fluid can 

 occur, all the relative movement observable between the two layers 

 of the double layer will be imparted to the particle and it will migrate 

 with respect to the liquid or any fixed point on the vessel containing 

 the system. This phenomenon is called electrophoresis. 



B. ELEMENTARY THEORY 



The force that acts to cause displacement of a particle in electro- 

 phoresis is determined by the magnitude of the charge carried by the 

 particle, and by the strength of the applied electrical field. If the 

 field strength is taken in terms of the voltage drop per centimeter (E) 

 and the net charge on the particle is taken in coulombs (Q), the force 

 of acceleration (/) acting on the particle will be equal to the product 

 of these quantities, i.e., f = EQ. As the particle is accelerated by 

 the action of this force, it will meet a resistance to its motion through 

 the liquid that is a function of the hydrodynamic flow characteristics 

 of the region within the liquid in which viscous flow occurs as the 

 liquid moves around the particle. Two limiting conditions may be 

 treated in describing the magnitude of this force of viscous resistance 

 that the moving particle will encounter within the liquid and with 

 which the force of acceleration will quickly attain equilibrium to de- 

 fine the steady state velocity of the particle. 



If the particle is described as a small sphere of radius r such that 

 r is greater than the dimensions of the molecules of the medium of 

 suspension (condition for validity of Stokes law) but small compared 

 to the thickness, d, of the double layer (r <C d), the particle may be 

 treated as a charged sphere suspended in a uniform field and the force 

 of viscous resistance, /', that it will encounter will be given by Stokes 

 law, i.e., f = Girrjru. At the steady state, f = f and EQ — Qir-qru. 

 Thus u — EQ/QiT'nr, where u is the velocity of the particle (cm. /sec), 

 77 is the coefficient of viscosity (poise) of the fluid through which the 

 particle moves, and r is the radius of the particle. The mobility 

 (w) of the particle (cm./sec./v./cm.) is equal to u/E orm = Q/6irrjr. 

 From this relationship it is apparent that for sufficiently small par- 

 ticles suspended in solutions of constant viscosity and of constant but 

 very low ionic strength (where d ^ r) the mobility of the particle 



