M. A. LAUFFER 



rcxohition. Cicncially speaking, during laminar flow, the long axis 

 of a rigid rodlikc or platelike particle will be subjected to a tendency to 

 rotate aboui ilic direction in the (low plane perpendicular to the direc- 

 tion of flow. riiric will be ;i londency for (he particle to rotate most 

 rapidly wlicn I he loui; ;ixis is |)erpcndicular to the flow plane and most 

 slowly when the long axis is in the flow plane. This will result in an 

 average orientation in the direction of flow, the extent of which will 

 depend upon the degree of anisometry. With particles which are 

 small enough, Brownian motion will oppose the orientation and tend 

 to maintain a random state. The contribution that a particle makes 

 to the viscosity of the solution will depend upon its orientation. When 

 the long axis is perpendicular to the direction of flow the disturbance 

 of the motion of the fluid will be greatest, and when it is parallel the 

 disturbance will be a minimum. Thus, a suspension of randomly 

 oriented ellip.soids will have a higher viscosity than a suspension of 

 ellipsoids oriented more or less parallel to the direction of flow. 



Simha (22) has solved the problem for the case of randomly 

 oriented rodlike and platelike ellipsoids of revolution. The intrinsic 

 viscosity depends upon the ratio of the major, b, to the minor, a, axis 

 of the ellipse whose rotation generates the ellipsoid. For elongated 

 ellipsoids, when b/a is considerably greater than 1 : 



(b/ay 14 



15 



1. 



2. 



The factor K is the ratio of the volume occupied by a hydrated particle 

 to its anhydrous volume. For disklike ellipsoids, when b/a is con- 

 siderably greater than 1 : 



W _ 16 b/a 



K 15 arc tan {b/a) 



For the case of elongated ellipsoids oriented parallel to the direction 

 of flow, Eisenschitz (9) has derived the following equation: 



f^ = 1.15 "'^ 



K In (lb/a) 



By comparing this equation with Simha's, it will be obvious that the 

 contribution of a rodlike particle to the viscosity of its solution is much 



252 



