Pressure hole errors in the annular flow measurement of the second normal stress difference

Summary For viscometric, axial, annular flow, the second normal stress differenceN ₂ is related to the difference in normal thrust across the annular space,T _rr . Past attempts using this method have yielded values ofN ₂ for polymer solutions which are different in magnitudeand opposite in sign from those obtained in other experiments. This inconsistency is attributed to errors resulting from the use of pressure holes in the measurement ofT _rr , and is supported by a second-order fluid analysis.The present work focuses on the measurement of the effect of pressure hole errors on the determination ofN ₂ with aqueous polymer solutions. In the measurement ofT _rr , simultaneous use is made of both pressure holes and miniature pressure transducers to measure and account for pressure hole errors. Results indicate that hole errors are sufficiently large to reverse the sign of the computedN ₂. This technique is therefore suggested as a preferred method for determiningN ₂, especially at high shear rates.With 6 figures