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用于计算各种半月板形状的贝塞尔曲线法。

Bézier Curve Method to Compute Various Meniscus Shapes.

作者信息

Lewis Kira, Matsuura Takeshi

机构信息

Horace Mann School, 231 West 246th Street, Bronx, New York 10471, United States.

Department of Chemical and Biological Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa K1N 6N5, Ontario, Canada.

出版信息

ACS Omega. 2023 Apr 18;8(17):15371-15383. doi: 10.1021/acsomega.3c00620. eCollection 2023 May 2.

Abstract

This paper is an extension of our earlier paper in which it was shown that the meniscus shape in a cylindrical capillary could be computed by solving the Young-Laplace equation via optimization of a Bézier curve. This work extends the previous work by demonstrating that the method is applicable to predict the meniscus shape not only in a cylindrical capillary but also in other cases, such as at a tilted plate, between two plates, and for a sessile drop. Numerous works have attempted previously to solve the Young-Laplace equation, and their results all agree with this paper's validating its method. All the preceding approaches, however, used special techniques to solve the differential equation, while the Bézier curve method proposed in this work is more simple, which allows it to maintain greater computational simplicity. Moreover, the Bézier curve method can be applied to solve many other different differential equations in the same way as shown in this work. The effect of the Bézier curve degree on the precision of prediction was also thoroughly investigated. It was found that the 4th degree Bézier curve was required to predict the meniscus shape precisely in a cylindrical capillary, against a tilted plate, and between two plates, while the 5th degree was required for the shape of the sessile drop.

摘要

本文是我们早期论文的扩展。在早期论文中,我们表明通过对贝塞尔曲线进行优化来求解杨 - 拉普拉斯方程,可以计算圆柱形毛细管中的弯月面形状。这项工作扩展了先前的研究,证明该方法不仅适用于预测圆柱形毛细管中的弯月面形状,还适用于其他情况,如倾斜平板上、两平板之间以及对于静止液滴的情况。此前已有许多工作尝试求解杨 - 拉普拉斯方程,其结果均与本文一致,验证了本文的方法。然而,所有先前的方法都使用特殊技术来求解微分方程,而本文提出的贝塞尔曲线方法更为简单,这使其在计算上保持更高的简便性。此外,贝塞尔曲线方法可以像本文所示的那样以相同方式应用于求解许多其他不同的微分方程。本文还深入研究了贝塞尔曲线次数对预测精度的影响。结果发现,在圆柱形毛细管中、倾斜平板上以及两平板之间精确预测弯月面形状需要 4 次贝塞尔曲线,而对于静止液滴的形状则需要 5 次贝塞尔曲线。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e35f/10157662/8bcdb9bb0cf5/ao3c00620_0002.jpg

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