WILLIAM D. HARKINS 169 



ELECTRICAL CHARACTERISTICS OF EMULSIONS AND SUSPENSIONS 



If an emulsion or a suspension is placed between a positive and a negative elec- 

 trode, it is fcund that the particles move (with respect to the water) toward one of the 

 two electrodes, and that in general all of the particles of the same material in the same 

 medium move at the same speed, whether they are large or small. This phenomenon 

 of the movement of small particles in the electric field is known as "cataphoresis." It 

 may be considered that this is analogous to the conductance of electricity by the ions 

 of a salt in electrolysis. 



If equal parts of hexane and an aqueous solution of a sodium oleate soap are mixed 

 together by shaking or by stirring with an egg-beater, it is commonly found that the 

 droplets vary from less than 0.2 /x to about 10 tx in diameter, with the largest number 

 of drops at a diameter of 1-1.5 m. 



Determinations of the amount of soap absorbed indicate that each droplet of oil in 

 a stable emulsion is surrounded by a monomolecular film of soap. Since soap is part- 

 ly hydrolyzed, the film should consist of molecules of sodium oleate and of oleic acid. 

 The total number of oleate molecules in the film around a droplet of a diameter of i /u 

 is of the order of 10,000,000 or 15,000,000. 



According to the orientation theory, the hydrocarbon groups of the soap are 

 turned toward the oil and the polar groups with their positive sodium ions toward the 

 water. It is to be expected that such a droplet ivill act like a highly polyvalent salt mole- 

 cule, and that sodium ions will diffuse off into the solution, leaving a negative charge 

 on the droplet. The question now arises, To what extent is the droplet ionized? Since, 

 however, the different sodium ions diffuse to different distances, the ionization should 

 be expressed as a relation concerning the distribution. However, it is easy to calculate 

 a mean or effective ionization by the use of the law of Stokes for the motion of a 

 spherical droplet in a viscous medium. 



In this way it is found that the velocity of such a particle (4 /j, per second per volt 

 per centimeter) corresponds to a negative charge of 2,430 electronic charges on a par- 

 ticle I (X in diameter, i.e., if all of the 10,000,000 or 15,000,000 molecules of the soap 

 except the 2,430 were completely un-ionized, and if the 2,430 molecules of sodium 

 oleate were so completely ionized that the 2,430 Na+ ions are at an infinite distance, 

 then the oil droplet should have a negative charge equal to that of 2,430 univalent 



negative ions. The equation is 



j^T_ 6Trrr] v 

 e A 



in which e is the charge on the electron, N is the number of charges, 77 is the viscosity 



V 



of the solution, and ^ is the mobility or the velocity for unit potential gradient. 

 The potential of a charged sphere is 



, Ne , dirri V 



<p = -— ; so (i) = — . 



^ Dr' ^ D X 



The use of this potential instead of the fictitious zeta potential was suggested to 

 the writer by Professor A. C. Lunn. According to this equation, the potential is 84 



