VISCOMETRY 



be used, depending upon the nature of the sokitc under study. There 

 are numerous methods of measuring viscosity or apparent viscosity. 

 Perhaps the simplest from a practical point of view is that involving 

 the rate of sedimentation of a sphere in the viscous liquid. According 

 to Stoke's law, the retarding force resisting the translational movement 

 of a large sphere in a viscous liquid is equal to dirr-qv, where r is the 

 radius and v the velocity of the sphere. When the sphere is falling 

 under the influence of gravity, the accelerating force, /a, acting upon 

 it is the mass of the sphere, Ws, minus the mass of the fluid it displaces, 

 Wl, all multiplied by the gravitational constant, G; fa = G{Ws — Wj). 

 Since the mass of the sphere is its volume, Va 7^r^ times its density, 

 fl'„ and the mass of the displaced liquid is equal to the volume of the 

 sphere times the density of the liquid, (11, this equation can be written 

 as /a = G Vs T^r^ids — dj). The sphere settles at a uniform rate when 

 the accelerating force and the retarding force are equal: 



eirr-nv = Vs ^r^Gids - d^), or t? = [Vg r-G(^. - d:}]/v 



Since it is possible to determine the radius and the density of a large 

 sphere, and the gravitational constant is known, the viscosity of a 

 liquid can be obtained by measuring its density and the velocity of 

 settling of the sphere. It is particularly easy to measure relative 

 viscosity* by this method, for: 



r]/r]o = [{ds - dL)/(ds - dLo)](vQ/v). 



The subscript, 0, indicates a quantity describing the solvent. To 

 obtain the relative viscosity of a solution, it is necessary to know only 

 the density of the sphere and to measure the densities of and the 

 velocities of fall of the sphere in both solvent and solution. The 

 velocity of the sphere can be obtained by observing the time required 

 for it to fall a fixed distance. The falling ball method has been used 

 quite satisfactorily, giving results which are in good agreement with 

 those obtained by other methods. This method is not particularly 

 satisfactory for the study of non-Newtonian solutions because the 

 velocity gradient in the liquid surrounding the falling sphere varies 



* Practically all viscosity measurements are relative — even those of pure 

 liquids. Much effort has been expended to determine precisely the absolute vis- 

 cosity of water at 20° C. All other viscosity data are relative to the value assigned 

 to water and are subject to the same error as the absolute viscosity of water. 



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