Oldroyd-B 流体径向流动：超稀极限下的理论与模拟结果
Radial flow of an Oldroyd-B fluid: theoretical and simulation results in the ultra-dilute limit
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中文总结 AI 辅助
针对 Oldroyd-B 流体径向流动，提出超稀极限下的理论框架与有限元模拟，推导闭式压降表达式，揭示压降随 Deborah 数单调增加，并验证理论在阶数为 1 时的准确性。
中文摘要 AI 辅助
粘弹性流体的压力驱动径向流动在各种工业应用中普遍存在，例如注塑成型和挤出工艺。众所周知，粘弹性流变学可显著影响非牛顿流体的水动力学特征。然而，与牛顿流体中观察到的现象相比，这些水动力学特征仍未得到充分理解。我们分析了平行板之间 Oldroyd-B 流体的压力驱动径向流动，并提出了一个理论框架以及有限元数值模拟，用于确定流量-压降关系。与先前仅限于低 Deborah（$De$）数的弱粘弹性极限的理论研究不同，我们应用润滑理论并考虑超稀极限，这使我们能够在阶数为 1 的 Deborah 数下研究粘弹性径向流动。利用牛顿速度剖面与弹性应力之间的单向耦合，我们推导了超稀极限下构象张量和压降的闭式表达式。我们表明压降随 $De$ 单调增加，识别了控制这种增加的物理机制，并描绘了超稀近似的有效范围。我们进一步揭示，低 $De$ 渐近分析可能无法准确捕捉有限元模拟结果，即使在低 Deborah 数下也是如此，因为它无法满足入口弹性应力。相比之下，我们基于超稀极限的理论预测与有限元模拟结果高度一致，从而能够阐明阶数为 1 的 Deborah 数下的压降行为。
英文摘要
Pressure-driven radial flows of viscoelastic fluids are common in various industrial applications, such as injection molding and extrusion. It is well known that viscoelastic rheology can significantly impact the hydrodynamic features of non-Newtonian flows. However, these hydrodynamic features remain not fully understood compared to those observed in Newtonian flows. We analyze the pressure-driven radial flow of an Oldroyd-B fluid between parallel plates and present a theoretical framework together with finite-element numerical simulations for determining the flow rate-pressure drop relation. Unlike previous theoretical studies restricted to the weakly viscoelastic limit of low Deborah ($De$) numbers, we apply lubrication theory and consider the ultra-dilute limit, which allows us to study viscoelastic radial flows at order-one Deborah numbers. Using the one-way coupling between the Newtonian velocity profile and elastic stresses, we derive closed-form expressions for the conformation tensor and pressure drop in the ultra-dilute limit. We show that the pressure drop monotonically increases with $De$, identify the physical mechanisms governing this increase, and delineate the range of validity of the ultra-dilute approximation. We further reveal that the low-$De$ asymptotic analysis of the pressure drop may fail to accurately capture finite-element simulation results, even at low Deborah numbers, owing to its inability to satisfy the inlet elastic stresses. In contrast, our theoretical predictions based on the ultra-dilute limit are in excellent agreement with the finite-element simulation results, enabling us to elucidate the pressure drop behavior for order-one Deborah numbers.
发表机构
- Technion – Israel Institute of Technology（以色列理工学院）
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