M. A. LAUFFER 



point of view, for it makes possible a study of the variation of apparent 

 viscosity with velocity gradient in non-Newtonian Hquids. 



Certain precautions must be observed when any one of the 

 methods just discussed is used. These are adequately described in 

 readily available publications (12). The investigator who desires to 

 use viscometry must become familiar with them. However, since they 

 are not essential to the understanding of the meaning of viscosity data, 

 they will not be discussed here. 



Usually the purpose of making viscosity measurements in bio- 

 logical and biochemical studies is to evaluate the intrinsic viscosity, 

 [iv/vo — l)/C]c_*o- If either specific viscosity, 17/770 — 1, or relative vis- 

 cosity, v/lo, were a linear function of concentration, this would be a 

 simple matter. As pointed out previously, however, specific viscosity 

 is approximately a linear function of concentration only for very low 

 concentrations. Many equations have been proposed to show the 

 relationship between specific viscosity or relative viscosity and con- 

 centration. Each one seems to work for some specific system or 

 systems. They have been reviewed by Huggins (13). All can be 

 expanded into series of the form t^/ijq — 1 = AC + BC^ + . . . . The only 

 difference between them is in the relative values of the constants B 

 and A. 



The problem of determining intrinsic viscosity reduces itself to 

 the evaluation of the constant A, for it obviously represents the ratio of 

 specific viscosity to concentration as concentration approaches zero. 

 The simplest method of doing this is to plot the observed specific vis- 

 cosity against concentration and then draw a tangent to the curve at 

 the origin. The slope of the tangent will be A. This practice is 

 subject to the limitation that it uses only the data obtained at extreme 

 dilutions, where the experimental error is bound to be great. For that 

 reason, two other methods for evaluating A are sometimes used. The 

 two simplest expressions relating viscosity and concentration are those 

 of Arrhenius (1) and Bingham (2). The Arrhenius equation is 

 In T7/770 = AC, and the Bingham equation is 0/0o = Vo/v = 1 — AC, 

 where <j) is the fluidity or the reciprocal of the viscosity. Both equations 

 can be expanded into series, such as that shown above. Each can be 

 used to evaluate /I, or the intrinsic viscosity. From the Arrhenius 

 equation: 



248 



