爬杆流变测量法的再探讨
Rod-climbing rheometry revisited
摘要：
爬杆效应（英语：rod climbing effect）或韦森伯格效应（英语：Weissenberg effect）是一种流行且令人信服的实验，证明了聚合物流体中弹性的存在。界面形状取决于旋转速率、流体弹性、表面张力和惯性。通过求解二阶流体在低旋转速率极限下的运动方程，出现界面偏转与流体材料函数（具体地，第一法向应力差和第二法向应力差）之间的数学关系。在过去，这个关系式已经被用来测量爬升常数，它是由低惯性极限下杆爬升的实验观测得到的第一（$Ψ_{1,0}$）和第二（$Ψ_{2,0}$）法向应力差系数的组合。然而，这种观察与现代扭转流变仪的能力的定量和解是缺乏的。为此，我们结合小振幅振荡剪切流测量和稳态剪切测量的第一个正常的应力差从商业流变仪的爬杆实验，以量化的值的两个正常的应力差为一系列的聚合物解决方案。此外，通过保留经常被忽视的惯性项，我们表明，即使当流体，事实上，经历棒下降的爬升常数$\hatβ=0.5Ψ_{1,0}+2Ψ_{2,0}$可以测量。通过考虑弹性和惯性效应之间的竞争而得出的爬升条件准确地预测了流体是否会经历杆爬升或杆下降。在这项研究中提出的分析和观察建立旋转棒流变仪作为一个主要的候选人，用于测量聚合物流体在低剪切速率，通常低于商业流变仪的灵敏度限制的法向应力差异。
英文摘要：
The rod-climbing or Weissenberg effect in which the free surface of a complex fluid climbs a thin rotating rod is a popular and convincing experiment demonstrating the existence of elasticity in polymeric fluids. The interface shape depends on the rotation rate, fluid elasticity, surface tension, and inertia. By solving the equations of motion in the low rotation rate limit for a second-order fluid, a mathematical relationship between the interface deflection and the fluid material functions, specifically the first and second normal stress differences, emerges. This relationship has been used in the past to measure the climbing constant, a combination of the first ($Ψ_{1,0}$) and second ($Ψ_{2,0}$) normal stress difference coefficients from experimental observations of rod-climbing in the low inertia limit. However, a quantitative reconciliation of such observations with the capabilities of modern-day torsional rheometers is lacking. To this end, we combine rod-climbing experiments with both small amplitude oscillatory shear flow measurements and steady shear measurements of the first normal stress difference from commercial rheometers to quantify the values of both normal stress differences for a series of polymer solutions. Furthermore, by retaining the oft-neglected inertial terms, we show that the climbing constant $\hatβ=0.5Ψ_{1,0}+2Ψ_{2,0}$ can be measured even when the fluids, in fact, experience rod descending. A climbing condition derived by considering the competition between elasticity and inertial effects accurately predicts whether a fluid will undergo rod-climbing or rod-descending. The analysis and observations presented in this study establish rotating rod rheometry as a prime candidate for measuring normal stress differences in polymeric fluids at low shear rates that are often below commercial rheometers' sensitivity limits.
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