By William R. Davis
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3 A sphere rolling down an inclined tube The viscosity η of a liquid can be calculated when a sphere of radius a rolls at a velocity V down a tube of radius R filled with viscous liquid from the expression 4a 2 ∆ρg sin θ R − a η= R 15V 5/ 2 where θ is the angle the tube subtends to the horizontal and ∆ρ is the density difference between the sphere and the liquid. When the sphere is small compared to the size of the tube, the formula simplifies to η = ∆ρga 2 sin θ . V These equations can be used for the rolling ball viscometer , see figure 3.
This pumping/recirculating arrangement is suitable for naturally unstable suspensions such as coal and mineral slurries in water. 6 Chemical attack In some older instruments, chrome-plated brass geometries can be attacked by a number of everyday liquids. Steel and plastic geometries (or even titanium in certain circumstances) are usually recommended, but note the difference between stainless and mild steels, since the latter can produce ions in solution which might alter the viscosity of some aqueous liquids.
Note: (i) in the engineering literature, the viscosity is often represented by the Greek letter mu, µ, and (ii) the word ‘non-Newtonian’ is often spelt incorrectly—the prefix has a lower case ‘n’ and the word is hyphenated. 3 Viscosity of common Newtonian liquids Many liquids display Newtonian behaviour under a wide range of shear rates, and many more show this behaviour within limited ranges. If we limit ourselves to ‘everyday’ shear rates, then the liquids in table 1 show Newtonian behaviour and encompass a large range of viscosities, best shown—like the race distances of chapter 3—on a logarithmic basis.