Capillary rise is important in many aspects of physical phenomena from transport in porous media to biotechnology. It is typically described by the Lucas–Washburn–Rideal equation (LWRE), but discrepancy between some experiments and the model still remains elusive. In this paper, we show that the discrepancy is simply from the contact angle change during the capillary rise with no help of any specific models, such as dynamic contact angle (DCA) models. To demonstrate this, we directly measure the contact angle change in the capillary rise for glycerol and carboxymethyl cellulose solutions as examples of Newtonian and non-Newtonian liquids. Unlike previous studies that used DCA models to explain the discrepancy, when the contact angle change is directly applied to the LWRE for all four tested fluids, the model agrees well with experimental data. The estimated contact angle from the capillary rise as a function of time is in good agreement with the directly measured contact angle within a narrow margin of error. To pinpoint the conditions for the discrepancy, we propose a new time scale when contact angle dynamics dominates. The contact angle dynamics that can be obtained from the macroscopic capillary rise may provide useful information for capillary flow in a more complicated geometry such as porous media.

中文翻译：

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直接测量毛细管上升中的接触角变化

从多孔介质到生物技术的传输，毛细管现象在物理现象的许多方面都很重要。它通常由Lucas-Washburn-Rideal方程（LWRE）描述，但某些实验与模型之间的差异仍然难以捉摸。在本文中，我们显示出差异仅来自毛细血管上升过程中的接触角变化，而没有任何特定模型的帮助，例如动态接触角（DCA）模型。为了证明这一点，我们直接测量了甘油和羧甲基纤维素溶液作为牛顿液体和非牛顿液体的毛细管上升中的接触角变化。与以前使用DCA模型解释差异的研究不同，当将接触角变化直接应用于所有四种测试流体的LWRE时，该模型与实验数据非常吻合。由毛细管上升作为时间的函数估计的接触角与直接测量的接触角在很小的误差范围内非常吻合。为了查明差异的条件，当接触角动力学起主导作用时，我们提出了一个新的时标。可以从宏观的毛细管上升中获得的接触角动力学可以为毛细管在更复杂的几何结构（例如多孔介质）中流动提供有用的信息。