Measurement of the Second Normal Stress Difference

The second normal stress difference is the most difficult to measure of the three viscometric functions. Several techniques have been proposed for the determination of the second normal stress difference. The most common method involves the use of a cone-plate rheometer, where 

The stress component shown is simply the normal stress acting on the plate, and this method requires the measurement of the radial distribution of this stress. Miller and Christiansen [120] mounted very small pressure transducers in the plate to determine this distribution, but the development of a plate incorporating micro miniature sensors (MEMS) now makes this measurement much easier and more reliable [121,122]. 

Another method, which makes use of a cone and a partitioned plate, is also based on Eq. 10.76, but instead of making a direct measurement of the radial normal stress gradient, the usual monolithic plate is replaced by one partitioned into two concentric parts, an inner disk with a radius Rj, and an outer ring whose outer diameter is Rq, the same as the cone [123]. The normal force transducer responds only to the thrust R on the inner disk. Data are collected for several samples having radii R, between R , and Rg and the measured thrust f j is related to Nj and Nj as shown by Eq. 10.77 

When Rj = R, Nj can be calculated from F using Eq. 10.77, which reduces to Eq. 10.74. Schweizer [116] reported that a cone angle of 0.148 rad minimized instrument compliance 

The combination of data using cone-plate and parallel disk fixtures was pioneered by Ginn and Metzner [124] and used recently by Brown etal. [40] The cone-plate data are used to determine Nj, using Eq. 10.74. Then data are obtained using step strain tests with parallel disk fixtures having several radii. The shear strain y r) is not uniform in this geometry, but the values of Nj and Nj at the maximum strain y R) are related to each other as follows  

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Magda, J.J. Back, S.G. DeVries, K.L. Larson, R.G. Shear flows of liquid crystal polymers measurements of the second normal stress difference and the Doi molecular theory. Macromolecules 1991, 24, 4460-4468. 

C.-S. Lee, J. J. Magda, K. L. DeVries, and J. W. Mays. Measurements of the second normal stress difference for star polymers with highly entangled branches. Macromolecules, 25 (1992), 4744 750. 

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