In rotational methods the test fluid is continuously sheared between two surfaces, one or both of which are rotating. These devices have the advantage of being able to shear the sample for an unlimited period of time, permitting transient behavior to be monitored or an equilibrium state to be achieved, under controlled rheometric conditions. Rotational methods can also incorporate oscillatory and normal stress tests for characterizing the viscoelastic properties of samples. In general, rotational methods are better suited for the measurement of concentrated suspensions, gels, and pastes, but are generally less precise as compared to capillary methods.
Rotational measurements fall into one of two categories: stress-controlled or rate-controlled. In stress-controlled measurements, a constant torque is applied to the measuring tool in order to generate rotation, and the resulting rotation speed is then determined. If a well-defined tool geometry is used, the rotation speed can be converted into a corresponding shear rate. In rate-controlled measurements, a constant rotation speed is maintained and the resulting torque generated by the sample is determined using a suitable stress-sensing device, such as a torsion spring or strain gauge. Some commercial instruments have the capability of operating in either stress-controlled or rate-controlled modes.
The least expensive commercial variant of the controlled-rate rotational viscometer is commonly referred to as a "Brookfield type" viscometer*. This device measures fluid viscosity at fixed rotation speeds by driving a measurement tool ("spindle"), immersed in the test fluid, through a calibrated torsion spring (see Figure 7). Viscous drag of the fluid against the spindle causes the spring to deflect, and this deflection is correlated with torque. The calculated shear rate depends on the rotation speed, the tool geometry, and i the size and shape of the sample container. Conversion factors are needed to calculate viscosity from the measured torque, and are typically pre-calibrated for specific tool and container geometries. For Newtonian fluids the torque is proportional to the product of viscosity and rotational speed, but this proportionality is lost in the case of a non-Newtonian fluid. Because these instruments are robust and fairly simple to use, they have found wide application in industry, but they offer limited capabilities and precision for research-oriented applications.
|Figure 7. Schematic diagram of a Brookfield-type viscometer.|
High-precision, continuously-variable- shear instruments in which the test fluid is sheared between rotating cylinders, cones, or plates, under controlled-stress or controlled-rate conditions, are termed rotational rheometers. Instruments producing oscillatory strains are available, and a few commercial systems permit measurement of the normal stress. The basic rotational system consists of four parts: (i) a measurement tool with a well-defined geometry, (ii) a device to apply a constant torque or rotation speed to the tool over a wide range of shear stress or shear rate values, (iii) a device to determine the stress or shear rate response, and (iv) some means of temperature control for the test fluid and tool. Depending on the design specifications, rheometers may also include built-in corrections or compensations for inertia, drift, and temperature fluctuations during measurement.
Most rheometers depend on the relative rotation about a common axis of one of three tool geometries: concentric cylinder, cone and plate, or parallel plates (See Figure 8).
Figure 8. Schematic diagram of basic tool geometries for the rotational rheometer: (a) concentric cylinder, (b) cone and plate, (c) parallel plate.
In the concentric cylinder (also called Couette or Coaxial geometry, either the inner, outer, or both cylinders may rotate, depending on instrument design. The test fluid is maintained in the annulus between the cylinder surfaces. This tool geometry comes in several configurations, of which the three most commonly encountered are illustrated in Figure 9. The double-gap configuration is useful for low viscosity fluids, as it increases the total area, and therefore the viscous drag, on the rotating inner cylinder, and generally increases the accuracy of the measurement. The cone and hollow cavity configurations are specifically designed to reduce or account for end effects. In addition, to prevent slippage (see no-slip), the inner cylinder surface is sometimes serrated or otherwise roughened. The concentric cylinder geometry is typically used for the analysis of fluid suspensions.
Figure 9. Schematic diagram showing three alternative
cylindrical tool designs in cut-away view:
(a) double gap, (b) cone and plate at the bottom, (c) hollow cavity at the bottom to trap air.
The cone and plate geometry consists of an inverted cone in near contact with a lower plate. The cone is usually designed with an angle of less than 4º. Either the upper or lower surface may rotate depending on instrument design. The parallel plate geometry can be considered a simplified version of the cone and plate, having an angle of 0º. The test fluid is constrained in the narrow gap between the two surfaces. Cone and plate and parallel plate measurement tools are most often used for highly viscous pastes, gels, and concentrated suspensions.
* Certain trade names and company products are mentioned in the text or identified in illustrations in order to specify adequately the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products are necessarily the best available for the purpose.