有界面活性劑之軸對稱界面在不同黏滯性之流體模擬

本論文把 Immersed boundary method 發展到軸對稱圓柱座標系中來模擬液滴在不可壓縮流中，液滴內外不同的黏滯度是我們所關心的。為方便分佈界面所產生的力至流體以及內插流體流速至界面的移動速度，須藉由Dirac delta function 將 Eulerian 流體和Lagrangian界面變數合併。我們使用 semi-implicit second-order projection method 來解 Navier-Stokes方程式並且利用Indicator function來更新密度和黏滯度。把液滴放入流場中，觀察有加表面活性劑與沒加表面活性劑的差異性。表面活性劑會分佈在界面中，並且影響表面張力的大小。上述的方程式，我們皆加入人工速度去調整界面上網格的位置，使其分佈均勻。

關鍵字

不同黏滯性；有界面活性劑；軸對稱

並列摘要

In this study, the simulation of drop deformation in incompressible flow was executed by developing an immersed boundary method in the axisym metric cylindrical coordinates. The viscosity difference between two sides of drop interface was particularly considered in this paper. We implemented a semi-implicit second-order projection scheme to solve Navier-Stokes equations. Various viscosity between two sides of drop were tested on simulation, as well as the effect of the surfactant on drop, which affect the surface tension. In addition, the distribution of marker positions were stabilized by imposing the artificial velocity and compared to the original manner without imposition of artificial velocity.

並列關鍵字

Navier-Stokes ； different viscosity ； interfaces ； insoluble surfactant ； Axisymmetric

參考文獻

[1]David L. Brown, Ricardo Cortez, and Michael L. Minion, " Accurate projection methods for the incompressible NavierVStokes equations." Journal of Computational Physics, Vol. 168, (2001), pp. 464-499.

[2] Charles D. Eggleton, Tse-Min Tsai, and Kathleen J. Stebe, " Tip streaming from a drop in the presence of surfactants." Physical Review Letters, Vol. 87,

[3] Wei-Xi Huang, Soo Jai Shin, and Hyung Jin Sung, " Simulation of flexible filaments in a uniform flow by the immersed boundary method." Journal of

[4] Ming-Chih Lai, Wen-Wei Lin, and Weichung Wang, " A fast spectral/differnce method without pole conditions for Poisson-type equations in cylindrical and spherical geometries." IMA Journal of Numerical Analysis, Vol. 22, (2002),pp. 537-548.

[5] Ming-Chih Lai, Yu-Hau Tseng, and Huaxiong Huang, " An immersed boundary method for interfacial flows with insoluble surfactant." Journal of Computa-

延伸閱讀

Tseng, Y. H. (2009). 不可溶界面活性劑之流體模擬數值方法 [doctoral dissertation, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2009.00863
邱宇政（2005）。利用分散粒子動力學探討界面活性劑添加兩溶劑時之相行為〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2005.00447
吳偉宏（2010）。界面活性劑之生物分解、界面相關性質之研究〔碩士論文，國立臺北科技大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0006-2807201014034800
Lin, M. C., & Cheng, P. J. (2021). 廣義型黏滯流體薄膜具弱非線性效應於旋轉垂直圓柱穩定性分析. 中國機械工程學刊, 42(1), 33-41. https://www.airitilibrary.com/Article/Detail?DocID=02579731-202102-202103050014-202103050014-33-41
Maestro, A., Santini, E., Zabiegaj, D., Llamas, S., Ravera, F., Liggieri, L., Ortega, F., Rubio, R. G., & Guzman, E. (2015). Particle and Particle-Surfactant Mixtures at Fluid Interfaces: Assembly, Morphology, and Rheological Description. Advances in Condensed Matter Physics, 2015(), 935-951. https://doi.org/10.1155/2015/917516

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有界面活性劑之軸對稱界面在不同黏滯性之流體模擬

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