Effects of Instrument and Fluid Inertia in Oscillatory Shear in Rotational Rheometers

In a rotational rheometer a sample is measured between a moving member and a fixed member of combined geometries. There are of two types; the combined motor transducer (CMT) and separate motor transducer (SMT). In a combined motor transducer setup torque is measured at the moving surface while in and separate motor transducer a motor drives one member of the geometry and torque is measured as needed to keep the second member fixed. In a combined motor transducer setup total torque is not completely available for stressing of a sample but part of torque is needed to accelerate the moving parts of the instrument when a certain shear is applied.

In a separate motor transducer configuration however the torque is measured separately and instrumental inertial effects are considered negligible due to the fact that torque measured at transducer undergo slight movement as torque rebalance routine is used to move it back after it is deflected by torque transmitted through the sample. However in combined motor transducer rheometer, moving parts of shear fixture must overcome the moment of inertia of rheometer drive. Hence, to know the exact value, certain correction of data must take place.

Drs. Jorg  Laeuger and Heiko Stettin from Anton Paar Germany studied inertia effects of oscillatory shear in a rotational rheometer aroused by the moment of inertia of an instrument and by the sample itself. The new study published in Journal of Rheology described various influences of instrumental and fluid inertia effects in oscillatory shear in different instruments designs and discussed their implications on measurement results.

 Laeuger and Stettin (2016), report measurements and calculations on low viscous materials under combined motor transducer and separate motor transducer as compared to Schrag, (Trans. Soc. Rheol. 1977). Recommendations for further experimental procedures were also noted.

Different mineral oils in a viscosity range of 3mPa s-50mPa s were used as testing samples. MCR302 and MCR502 rheometers, which are single motor instruments and operate solely as combined motor transducer, and MCR702 rheometer, which employ two identical motors and can operate in both combined motor transducer and separate motor transducer mode have been used.

Results from combined motor transducer when using a sample with viscosity of 4 mPa s with cone-and-plate geometry of 60 mm diameter, 0.5⁰ cone angle and angular frequency of 50 rad/s showed that at higher frequencies, a slight and step increase in viscosity occurred. At the smaller frequency measured both total torque (electrical) M_O and sample torque M_S are almost similar indicating that all of applied torque reaches the sample. At an angular frequency of 25 rad/s, the ratio of total torque M_O to sample torque M_S (M_O/M_S =95) i.e. most of electrical torque is used for acceleration. However, still the samples rheological response can be measured.

Results from separate motor transducer mode at three different cone angles and four low viscous samples show that for each geometry used, a baseline in the storage modulus, caused by fluid inertia, exists. As smaller the gap as lower this baseline is. The fluid inertia effect on the Newtonian liquids investigated is purely elastic. Measured and calculated values of phase angles and absolute value of complex viscosity showed good agreement and are in accordance with Schrag, (Trans. Soc. Rheol. 1977).