Non-simple viscometer geometries

There are a munber of popular viscometer geometries where the shear rate is not the same everywhere. In order to convert the basic experimental data into unambiguous viscosity/shear-rate data, an intermediate calculation step is needed. This uses an assumption about the liquid, usually that at any particular value of shear rate, the local viscosity/shear-rate data can be described by a power-law-type behaviour, where the slope of the log/log curve is given by n. (For true power-law Uquids, this is the same as n, the power-law index.) The following are the necessary equations for wide-gap concentric cylinders the paraUel-plate geometry and tubes used as viscometers, hi each case the viscosity data is related to a certain shear rate calculated at some fixed point in the geometry, and n is related to the basic measured parameters. 

The software provided by some viscometer manufacturers for calculating viscosities in concentric-cylinder geometries only makes use of the narrow-gap approximation (you should check this in your manual). However, this only applies to gaps of at most a few percent of the outer-cylinder radius, and assumes that the shear rate and shear stress are approximately constant throughout the gap. This is not the case in many practical cases, and if for instance the inner cylinder is being rotated, the value of the shear stress decreases as the inverse square of distance from the centre of rotation as one moves away from the inner cylinder. 

If non-Newtonian liquids are being measured and the narrow-gap approximation is used, the data from different-sized gaps does not coincide. However, the data can be corrected by the use of a number of lengthy analytical methods. However, a simple correction of the data can be made as follows, using an empirical correction factor worked out by the author, for the viscosity at the inner-cylinder, uncorrected shear rate  

---