196 THEORY OF COLLOIDAL BEHAVIOR 



the same temperature will be referred to as the relative viscosity 

 or as the viscosity ratio of the protein solution. This method of 

 measuring the relative viscosity will require improvement but it 

 suffices for an approximate test of the validity of the theory. 



Einstein 1 has developed a theory of the viscosity of solutions 

 which makes the viscosity a linear function of the relative volume 

 occupied by the solute in the solution 



7? = Wl + 2.5<rf (1) 



where rjo is the viscosity of the water at the temperature of the 

 experiment, rj the viscosity of the solution, and <p the fraction of 

 the volume occupied by the solute in the volume of the solution. 

 As Einstein points out, this formula can only be used when <p is 

 very small and when the particles of the solute are spherical and 

 large in comparison with the molecules of the solvent. This 

 condition is no longer fulfilled in protein solutions when the 

 relative volume occupied by the protein in the solution becomes 

 too large. 



Several authors have tried to modify Einstein's formula in 

 order to make it applicable to higher concentrations of protein 

 solutions. Hatschek 2 proposed to replace the constant 2.5 of 

 Einstein's formula by the constant 4.5, but his deductions have 

 been criticised both by Smoluchowski 3 and by Arrhenius. 4 

 Arrhenius has shown that a logarithmic formula, which he derives 

 very ingeniously from Einstein's formula, fits the actual observa- 

 tions in a satisfactory way, this formula being 



log ri - log TJO = <V (2) 



where <p is again the fraction of volume occupied by the protein 

 in solution, $ a constant, while rj and 170 have the same significance 

 as in Einstein's equation. We shall make use of Arrhenius's 

 equation (2) when we are dealing with higher viscosities. 



Both the formulae of Einstein and of Arrhenius make the 

 viscosity a function of the relative volume occupied by the solute 



1 EINSTEIN, A., Ann. Physik, vol. 19, p. 289, 1906; vol. 34, p. 591, 1911. 



2 HATSCHEK, E., Kolloid-Z., vol. 11, p. 280, 1912. 



3 SMOLUCHOWSKI, M., Kolloid-Z., vol. 18, p. 190, 1916. 



4 ARRHENIUS, S., Meddelanden K. Vetenskapsakademiens Nobelinstitut, 

 vol. 3, No. 21, 1917. 



