# A comparison of three different methods for measuring both normal stress differences of viscoelastic liquids in torsional rheometers

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## Abstract

A novel pressure sensor plate (normal stress sensor (NSS) from RheoSense, Inc.) was adapted to an Advanced Rheometrics Expansion System rheometer in order to measure the radial pressure profile for a standard viscoelastic fluid, a poly(isobutylene) solution, during cone–plate and parallel-plate shearing flows at room temperature. We observed in our previous experimental work that use of the NSS in cone-and-plate shearing flow is suitable for determining the first and second normal stress differences *N* _{1} and *N* _{2} of various complex fluids. This is true, in part, because the uniformity of the shear rate at small cone angles ensures the existence of a simple linear relationship between the pressure [i.e., the vertical diagonal component of the total stress tensor (Π_{22})] and the logarithm of the radial position *r* (Christiansen and coworkers, Magda et al.). However, both normal stress differences can also be calculated from the radial pressure distribution measured in parallel-plate torsional flows. This approach has rarely been attempted, perhaps because of the additional complication that the shear rate value increases linearly with radial position. In this work, three different methods are used to investigate *N* _{1} and *N* _{2} as a function of shear rate in steady shear flow. These methods are: (1) pressure distribution cone–plate (PDCP) method, (2) pressure distribution parallel-plate (PDPP) method, and (3) total force cone–plate parallel-plate (TFCPPP) method. Good agreement was obtained between *N* _{1} and *N* _{2} values obtained from the PDCP and PDPP methods. However, the measured *N* _{1} values were 10–15% below the certified values for the standard poly(isobutylene) solution at higher shear rates. The TFCPPP method yielded *N* _{1} values that were in better agreement with the certified values but gave positive *N* _{2} values at most shear rates, in striking disagreement with published results for the standard poly(isobutylene) solution.

## Keywords

Viscoelasticity Normal stresses Rheology## Notes

### Acknowledgements

Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research, grants 45968-AC9 for M.A. and J.J.M. and 40615-AC7 for the McKenna research group at TTU. The McKenna research group also acknowledges the John R. Bradford Endowment at TTU for partial support of this work. We thank RheoSense, Inc. (San Ramon, CA, USA) for providing the pressure sensor plate adapted to the ARES Rheometer at Texas Tech University.

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