Measurement of the first and second normal stress differences: Correlation of four experiments on a polyisobutylene/decalin solution ?D1?

Abstract

Pressure distribution measurements for a polyisobutylene/decalin solution “D1” in the Truncated Cone-and-Plate (TCP) apparatus are combined with elastic hole pressures obtained for the same solution on the Lodge Stressmeter® in order to provide two independent estimates of the second normal-stress difference (N 2). The values ofN 2 from the TCP apparatus, obtained by numerical differentiation of a function of the center-hole pressure and the pressure gradient, are in good agreement with measurements made on the same sample by Tanner et al. with a direct method, namely the Tilted Trough Experiment, and by Christiansen et al. with a method that requires an extrapolation to the pressure at the free surface of coneand-plate rheogoniometer data obtained with flush-mounted pressure transducers. The viscosities from the modified Stressmeter for low shear rates extend over five decades of shear rate, including a zero-shear-rate region, and agree with the data of Christiansen on a torque-driven flow. The Higashitani-Pritchard-Baird-Lodge (HPBL) equation relatingN 1–N 2 to the hole pressure gives good agreement with the data over a certain range of shear stress. The Newtonian hole pressures for several liquids at 20 and 46 °C compare well with a finite-element calculation for a two-dimensional Poiseuille flow. When the elastic hole pressures from the Stressmeter are combined with the extrapolated rim pressures from the TCP Apparatus in order to extract the value ofN 2, an agreement betweenN 2 from the center-hole pressure andN 2 from the rim pressure can only be obtained up to a shear rate of about 40 s−1, beyond which the value of −N 2 from the rim pressure diverges abruptly to negative values. It is possible that this constitutes the first quantitative estimate of an edge effect in cone-and-plate rheometry. Alternatively, the elastic hole pressure in cone-and-plate flow is not equivalent to the elastic hole pressure in Poiseuille flow, at least at high shear rates. The data of Christiansen et al. with flush-mounted pressure transducers appear to confirm this second possibility. Finally, a single set of shift factors obeying the Williams, Landel and Ferry equation superposes the viscosity, the first and the second normal-stress difference within experimental scatter, which can be less than 1% for a certain combination of normal-stress differences. The data were recorded at 3, 20, 30, and 46 °C in the shear rate range 1–260 s−1.