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

Mataz Alcoutlabi, S. G. Baek, J. J. Magda, Xiangfu Shi, S. A. Hutcheson, G. B. McKenna

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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 N1 and N2 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 (Π22)] 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 N1 and N2 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 N1 and N2 values obtained from the PDCP and PDPP methods. However, the measured N1 values were 10-15% below the certified values for the standard poly(isobutylene) solution at higher shear rates. The TFCPPP method yielded N1 values that were in better agreement with the certified values but gave positive N2 values at most shear rates, in striking disagreement with published results for the standard poly(isobutylene) solution.

Original languageEnglish
Pages (from-to)191-200
Number of pages10
JournalRheologica Acta
Issue number2
StatePublished - 2009


  • Normal stresses
  • Rheology
  • Viscoelasticity


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