VISCOMETRY 



In 77/770 



-^ = ^ - hi 



and from the Bingham equation: 



(1 - «/>/0o)/C = A ^ [rj] 



Thus, in the apphcation of the Arrhenius equation, one plots In 77/770 

 against C; and in the apphcation of the Bingham equation, one plots 

 (1 — 4>/(l>o) against C. In both cases, A or [77] is equal to the slope of 

 the straight line fitting the data in the region of low to moderate 

 concentrations. These methods employ a wider range of data than 

 the simpler procedure, and thus allow a more precise evaluation of the 

 intrinsic viscosity. 



When rigid particles of colloidal dimensions are suspended in a 

 solvent, they increase the viscosity of the system. The first successful 

 theoretical treatment of this effect was made by Einstein (7). His 

 approach was from the point of view of hydrodynamics. When a 

 liquid undergoes plane laminar or simple viscous flow, infinitesimal 

 layers of the liquid glide over one another in the direction of flow, and 

 each layer moves slightly faster than the layer on one side of it and 

 slightly slower than the layer on the other side. In this process, energy 

 is dissipated, resulting in the viscosity of tlie fluid. If a rigid solid 

 object, large compared with the infinitesimal layers of liquid, is placed 

 in such a flowing system, some of the layers of liquid in which this 

 particle finds itself will move faster than the particle and some will 

 move more slowly. This will tend to cause the particle to rotate, and 

 it will also make it necessary for fluid to flow around the obstruction. 

 The resultant disturbance in the motion of the fluid results in an added 

 dissipation of energy by the system, in other words, in increased vis- 

 cosity. Einstein derived an equation for the relative viscosity of a 

 suspension of spherical particles as a function of the concentration of 

 the spheres: 77/770 = 1 + 2.5 C, where the concentration is expressed 

 as the volume fraction. On theoretical grounds, this equation should 

 be valid only for an infinitely dilute suspension of spherical particles 

 which are very large compared with the size of the solvent particles 

 and very small compared with the dimensions of the viscometer. More 

 recently, Guth (10) has shown that the viscosity of more concentrated 

 solutions of spheres should be given by the equation: 



r,/rjo = 1 + 2.5 C + 14.1 C- 



