Characterization of yield stress fluids with concentric cylinder viscometers

The methods normally employed for shear rate calculations from concentric cylinder viscometer data generally are not applicable for fluids with a yield stress. In cylindrical systems with large radius ratios, as usually is the case with suspensions, the yield stress induces two possible flow regimes in the annulus. Unless the yield value is exceeded everywhere in the gap only part of the fluid can be sheared while the remaining region behaves like a solid plug. A correct calculation of the shear rate must take into account the presence of a variable effective gap width determined by the extent of the sheared layer. For time-independent yield stress fluids, a two-step procedure, which does not require any specific flow model, is proposed for analysing the experimental torque-speed data. Under the partially sheared condition, the shear rate can be computed exactly, whereas for the fully sheared flow the Krieger and Elrod approximation is satisfactory. The method is assessed by examining both semi-ideal data generated with a Casson fluid with known properties, and experimental data with an industrial suspension. A more complicated problem associated with characterization of time-dependent yield stress fluids is also identified and discussed. An approximate procedure is used to illustrate the dependence of the shear rate on time of shear in constant-speed experiments.