VISCOMETRY 



tential energy barrier. The hyperbolic sine of a variable has the 

 interesting property of being practically equal to the variable for values 

 less than about V2 and practically equal to the exponential of the 

 variable for all values greater than about 2. Therefore, in a liquid 

 in which the potential energy barrier is low, an observable rate of flow 

 can be obtained by the application of a force small enough to be in 

 the linear portion of the hyperbolic sine function. The rate of shear 

 will thus be pi'oportional to the shearing force. In other words, the 

 liquid will exhibit Newtonian flow. If, on the other hand, the force 

 required to cause an observable rate of shear is somewhat greater than 

 that just mentioned, the rate of shear will not be directly proportional 

 to the shearing force, but may be even an exponential function of the 

 force. Such a liquid obviously would not exhibit Newtonian flow, 

 but the diff'erence between it and a liquid which would exhibit New- 

 tonian flow would be a matter of degree and not of quality. 



The application of viscosity to the problems of biology and bio- 

 chemistry usually involves solutions or dispersions in aqueous solvents. 

 In general, when a solute is dissolved in a solvent, the viscosity of the 

 solution, 77, is either greater than or less than that, 770, of the solvent. 

 The ratio of the viscosity of a solution to that of the solvent under the 

 same conditions, 77/770, is called the relative viscosity of that solution. 

 When rigid particles of colloidal or macromolecular dimensions are 

 dispersed or dissolved in an aqueous solvent, the viscosity of the re- 

 sultant solution is greater than that of the solvent; therefore the 

 relative viscosity is always greater than unity for such systems. The 

 relative viscosity of a solution is usually dependent upon the concen- 

 tration of the solute. Experience has shown that an equation of the 

 sort, 77/770 = 1 + AC + 5C" + . . . , usually can be written to describe 

 the relationship between relative viscosity and concentration, C. A 

 and B are arbitrary constants. For low values of concentration, 

 77/770 = 1 + AC or 77/770 — 1 = AC. The expression, 77/770 — 1, is 

 defined as the specific viscosity of the solution. In dilute solutions, 

 this specific viscosity is directly proportional to the concentration. 

 The proportionality constant, A, in the equation written above, was 

 defined by Kraemer (14) as the intrinsic viscosity and is often repre- 

 sented by the symbol, [77]. In strict mathematical language, the 

 intrinsic viscosity is the limit, as the concentration approaches zero, 

 of the ratio of specific viscosity to concentration. It can be repre- 



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