Recently, aperture total internal reflection (A-TIR) was proposed to characterize the microdroplet patterns, such as the coverage fraction of the droplet, by placing the aperture just in front of the detector in classical total internal reflection (TIR). However, the reflection from the curved liquid-air interface was simulated using simple two-dimensional modeling, causing inaccuracy in A-TIR measurement. In addition, the reflectance dependency on the aperture size and the working distance of the aperture was not investigated, hindering its applications. In this study, the simulation based on three-dimensional (3-D) ray tracing with Fresnel equation modeling was successfully developed and verified to explain the internal reflection from the curved droplet liquid-air interface. With this developed 3-D modeling, A-TIR characteristics were explored using the parameters of the aperture size and the working distance of the aperture as well as the droplet surface coverage fraction, which shows a good agreement between the experiment and the simulation. Furthermore, it was for the first time demonstrated that the droplet contact angle can be effectively determined by obtaining the droplet thickness from the analytic quadratic solution by subtracting the measured reflectance at the two different sized apertures and using the spherical profile relation. Low contact angles in the range of 1∼ 15° were determined experimentally for the micro- and macro-sized droplets with a droplet diameter of 70 ∼ 7000 µm by the measured thickness of 1 ∼ 450 µm using A-TIR and compared with Fizeau interferometry and side-view imaging to show a good agreement. The simulation shows that A-TIR can be a new optical diagnostic tool to measure the contact angles 0 ∼ 90° regardless of the droplet diameter by adjusting the aperture size and the working distance. In addition, A-TIR can effectively determine the small contact angles less than 5°, even ultrasmall contact angles less than 1° for the submicron thickness, not requiring the complicated microscope setup. Thus, we can observe a sessile droplet's drastic contact angle change during wetting phenomena from 90° to 0° on the same A-TIR setup. Additionally, A-TIR can be used for a single or an array of micro or nanodroplets with a microscope objective by reducing the laser beam size and scanning methodology.

中文翻译：

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用于接触角测量的孔径全内反射 (A-TIR)

最近，提出了孔径全内反射 (A-TIR) 来表征微滴模式，例如液滴的覆盖率，方法是将孔径放置在经典全内反射 (TIR) 检测器的正前方。然而，弯曲的液-气界面的反射是使用简单的二维模型模拟的，导致 A-TIR 测量不准确。此外，没有研究反射率对孔径大小和孔径工作距离的依赖性，阻碍了其应用。在这项研究中，基于三维 (3-D) 射线追踪和菲涅耳方程建模的模拟得到成功开发和验证，以解释弯曲液滴液体-空气界面的内部反射。有了这个开发的 3-D 建模，使用孔径大小和孔径工作距离以及液滴表面覆盖率等参数探索了 A-TIR 特性，这表明实验与模拟之间具有良好的一致性。此外，首次证明可以通过从解析二次解中减去测量的两个不同尺寸孔径的反射率并使用球面轮廓关系获得液滴厚度来有效确定液滴接触角。通过使用 A-TIR 测量的 1 ∼ 450 µm 厚度，通过实验确定了液滴直径为 70 ∼ 7000 µm 的微米和宏观尺寸的液滴在 1∼15° 范围内的低接触角，并与 Fizeau 干涉法进行了比较和侧视成像显示出良好的一致性。模拟表明，A-TIR 可以作为一种新的光学诊断工具，通过调整孔径大小和工作距离来测量 0 ∼ 90° 的接触角，而与液滴直径无关。此外，A-TIR 可以有效地确定小于 5° 的小接触角，甚至是小于 1° 的亚微米厚度的超小接触角，不需要复杂的显微镜设置。因此，我们可以在相同的 A-TIR 设置上观察到在润湿现象从 90° 到 0° 期间固着液滴的剧烈接触角变化。此外，通过减小激光束尺寸和扫描方法，A-TIR 可用于具有显微镜物镜的单个或一组微液滴或纳米液滴。