M. A. LAUFFER 



perature is directly proportional to the force applied per unit area on 

 a plane parallel to the direction of flow. A fluid which flows in this 

 manner obeys Newton's law of flow and is said to be Newtonian. The 

 constant which relates the velocity gradient or the rate of shear in the 

 flowing liquid to the applied shearing force is called the viscosity 

 coefficient or, in less exact usage, simply the viscosity. In many liquids, 

 however, the rate of shear is not directly proportional to the shearing 

 force. Therefore, the ratio of the applied force to the resultant rate 

 of displacement is not a constant but a variable whose magnitude 

 depends upon the applied shearing stress or, viewed from a slightly 

 different but more usual position, upon the resultant rate of shear. 

 Thus, there is no such thing as a viscosity coefficient for such a fluid. 

 However, the ratio of the shearing stress to the resultant rate of shear 

 at a particular velocity gradient can be used as a partial description 

 of the flow characteristics of such fluids. This ratio can be called an 

 apparent viscosity coefficient. A complete description of the flow of a 

 liquid of this sort requires that the way in which the apparent viscosity 

 coeflficient varies with the rate of shear be specified. Fluids which 

 flow in this manner are often said to be non-Newtonian. 



Until recently, it was fairly generally believed that Newtonian 

 and non-Newtonian fluids were qualitatively different, but newer 

 developments in the theory of viscous flow permit the interpretation 

 that the difference is only quantitative. Eyring and his associates (24) 

 have attempted to understand the flow characteristics of liquids on the 

 basis of concepts analogous to those employed in chemical kinetics. 

 The basic aspects of the Eyring point of view are that, in order for a 

 liquid to flow: (1) there must be regions or holes in the body of a liquid 

 into which molecules can jump; (2) there are potential energy barriers 

 which tend to prevent any particular molecule from jumping into a 

 vacant region near it; and (3) a shearing stress is a mechanical potential 

 which aids molecules jumping in the direction of the stress and hinders 

 those jumping in the reverse direction, thereby resulting in a net dis- 

 placement in the direction of the stress. Eyring has shown that, 

 based upon these concepts, the resultant rate of shear should be pro- 

 portional to the hyperbolic sine of the ratio of the work contributed 

 by the shearing force in moving a molecule over the energy barrier 

 to the product of the gas constant per molecule and the absolute 

 temperature. The proportionality constant is a function of the po- 



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