84 E. G. P I C K E L S 



77(0- — P20) /gx 



S20 = S ; {6) 



1720(0- - p) 



2. Frictional Coefficient 



In an infinitely dilute solution, the frictional force acting on each 

 mole of sedimenting material per unit sedimentation rate is called the 

 frictional coefficient, fs. Thus, if the force is proportional to the 

 rate, the resisting force per mole in a centrifugal field is given by: 



F, = /, -^ = /, SC02 X (4) 



at 



But Fs must be equal to the net motivating force, F^, which is simply 

 the difference between their combined centrifugal weight and the 

 buoyancy exerted by the displaced medium. Hence: 



Fc = Mo^^x - ^^^ = Mco^xil - Vp) (5) 



a 



where M is the molecular weight and V is the partial specific volume 

 of the solute, equivalent to l/a. From this it follows that: 



/. = ^^^^^=^ (G) 



s 



In the diffusion process, the frictional coeflricient /d for dilute solu- 

 tions is given by: 



/d = RT/D (7) 



where D is the diffusion constant of the material, T is the absolute 

 temperature, and R is the gas constant (8.313 X 10^). 



For spherical particles, it is known from the Stokes formula (82) 

 that the frictional coefficient is related to particle size as follows : 



/o = STdrjN - QwvN (3MF/47riV)'/' (8) 



where N is the Avogadro constant and d is the particle diameter. 



When spherical particles having a molar frictional coefficient 

 equal to /o become enlarged (solvated) symmetrically by combining 

 with some of the suspending medium, the frictional coefficient is in- 

 creased (83) in proportion to the diameter. Expressed in other terms : 



