THE COALESCENCE OF LIQUID SPHERES 177 



This law of constant mean curvature is also illustrated by the struc- 

 ture of emulsions. Emulsions are systems of two liquids insoluble in 

 each other, consisting of small globules of one liquid suspended in a 

 second liquid with which it does not mix. The conditions necessary to 

 produce a stable emulsion are such that, when two incompletely miscible 

 liquids are mechanically agitated so as to disperse one in the o ther in the 

 form of globules, a minimum of work must be done upon the system, 

 which is equal to the product of the interfacial surface energy per unit 

 area by the increase in surface due to the globule formation. That this 

 is an appreciable amount of energy, and that the resulting dispersion is 

 unstable, can be shown by the fact that as the coalescence of the globules 

 takes place a measurable amount of energy is liberated. To stabilize an 

 emulsion, it is necessary to add a third substance (the emulsifier) which 

 will form an adsorbed film on the globules. This will prevent their 

 coalescence if the surface energy of each globule is reduced to a mini- 

 mum. In general, the more the emulsifier decreases this surface energy, 

 the more stable is the resulting emulsion. The most effective emulsifiers 

 for fat-water systems are polysaccharide gums, proteins, soaps, lipoids, 

 bile salts, and saponins. 



The Coalescence of Liquid Spheres 



The coalescence of spherical droplets in suspension is primarily attribu- 

 table to the reduction in the potential surface energy. Taylor's [1921] 

 study of this problem convinced him that coalescence of liquid spheres is 

 not due to a molecular attraction, so long as the spheres do not touch. 

 When contact occurs, a " force " comes into play which causes them to 

 coalesce and become one sphere. This occurs with all liquids, independ- 

 ent of the relative size of the spheres, and at all temperatures. 



A fundamental property of the surface energy is to maintain the area 

 of a liquid surface at a minimum. The minimum area that can be 

 attained by any unconstrained mass is spherical. Therefore, if several 

 small spheres, each of surface energy e, were to coalesce, a new sphere, 

 having surface energy E, must be formed. Upon the large sphere a 

 redistribution of surface energy must take place in such a way that the 

 surface energy E is less than the sum of the surface energies of the small 

 spheres. 



Taylor [1921] calculated this redistribution of energy for the coales- 

 cence of three spheres of water whose diameters were 0.3, 0.4, and 0.5 cm. 

 The potential surface energy of these three spheres is 



E= tt{(0.3) 2 + (0.4) 2 + (0.5) 2 }!T 

 or 0.50x7" ergs per square centimeter, where T is the interface tension in 



