On the Use of the Coaxial Cylinders Equivalence for the Measurement of Viscosity in Complex Non-Viscometric, Rotational Geometries

The rheology of macroscopic particle suspensions is relevant in many industrial applications, such as cement-based suspensions, synthetic and natural drilling fluids. Rheological measurements for these complex, heterogeneous systems are complicated by a double effect of particle size. On the one hand, the smallest characteristic length of the measuring geometry must be larger than the particle size. On the other hand, large particles are prone to sediment, thus calling for the use of rotational tools that are able to keep the suspension as homogeneous as possible. As a consequence, standard viscometric rotational rheometry cannot be used and complex flow geometries are to be implemented. In this way, however, the flow becomes non-viscometric, thus requiring the development of approximate methods to translate the torque vs. rotation speed raw data, which constitute the rheometer output, into viscosity vs. shear rate curves. In this work the Couette analogy methodology is used to establish the above equivalence in the case of two complex, commercial geometries, namely, a double helical ribbon tool and a square-shaped stirrer, which are recommended for the study of relatively large size suspensions. The methodology is based on the concept of the reduction of the complex geometry to an equivalent coaxial cylinder geometry, thus determining a quantitative correspondence between the non-standard situation and the well-known Couette-like conditions. The Couette analogy has been used first to determine the calibration constants of the non-standard geometry by using a Newtonian oil of known viscosity. The constants have been subsequently used to determine the viscosity curves of two non-Newtonian, shear thinning fluids, namely a homogeneous polymer solution and two heterogeneous concentrated suspensions. The results show that the procedure yields a good agreement between the viscosity curves obtained by the reduction method and those measured by a standard viscometric Couette geometry. The calibration constants obtained in this work from the coaxial cylinder analogy are also compared with those provided by the manufacturer, indicating that the calibration can improve the accuracy of the rheometer output.