AI 中文总结
研究液桥毛细管细化这一复杂流动，将CBR实验输出重述为弹性应变率并整理成皮普金图，单模应力平衡产生有普遍特征的曲线，C2D2模型能整理相关数据，皮普金图框架为聚合物溶液提供主图研究途径。
AI 中文摘要
液桥的毛细管细化是复杂流动的一个范例，其中宏观几何形状与聚合物构象的微观演化紧密耦合。自毛细管破裂流变学（CBR）诞生以来，它一直被视为测量单一弛豫时间的工具。然而实验表明，表观弛豫时间系统地取决于聚合物浓度、装置几何形状和制备方案。我们认为这种变异性并非缺陷，而是表明细化应被视为测试本构模型的基准复杂流动的证据。我们将CBR实验的输出重新表述为通过弹性魏森贝格数Wi_e表示的自选弹性应变率，而不是表观弛豫时间，并将其整理在弹性毛细管皮普金图中——Wi_e与几何控制的德博拉数相对。单模、中丝应力平衡产生了一系列具有普遍特征的皮普金曲线——低De_0平台和有限延伸率约束上升——通过标度分析可将其归结为一条主曲线，其中以弹性起始为参考的德博拉数吸收了未测量的初始预拉伸。构象和浓度依赖阻力（C2D2）模型通过线圈拉伸滞后作用，将平台降低到恩托夫-欣奇值以下，并整理了跨越分子量和浓度数十年、在一系列装置中的数据，而经典的FENE-P模型则无法做到。皮普金图框架为聚合物溶液类别提供了通向主图的途径，阐明了在延伸主导流动中普遍存在的现象。
英文摘要
Capillary thinning of a liquid bridge is an exemplar of complex flow, where the macroscopic geometry couples tightly to the microscopic evolution of polymer conformations. Since its inception, capillary-breakup rheometry (CBR) has been viewed as a tool for measuring a single relaxation time. Yet experiments show that the apparent relaxation time depends systematically on polymer concentration, device geometry, and the preparation protocol. We argue that this variability is not a flaw, but evidence that thinning should be treated as a benchmark complex flow for testing constitutive models. We recast the output of a CBR experiment as the self-selected elastic strain rate, expressed through the elastic Weissenberg number Wi_e, rather than an apparent relaxation time, and organize it in an elastocapillary Pipkin diagram -- Wi_e against a geometry-controlled Deborah number. A single-mode, mid-filament stress balance yields a family of Pipkin curves with universal features -- a low-De_0 plateau and a finite-extensibility-constrained rise -- that a scaling analysis collapses onto a master curve, with an elastic-onset-referenced Deborah number absorbing the unmeasured initial prestretch. The Conformation- and Concentration-Dependent Drag (C2D2) model, acting through coil-stretch hysteresis, lowers the plateau below the Entov-Hinch value and organizes data spanning decades in molecular weight and concentration, across a range of devices, where the classical FENE-P model cannot. The Pipkin diagram framework offers a path toward master plots for classes of polymer solutions, clarifying what is universal in extension-dominated flows.
Comments26 pages, 9 figures. Supplementary information and an experimental-parameters spreadsheet included as ancillary files. Submitted to the Journal of Rheology. C2D2 model code: https://github.com/prabhakarranganathan/C2D2.jl (archived at https://doi.org/10.5281/zenodo.21090147)
