微粒間作用力與表面張力的研究

Study of Colloid Interaction Due to Surface Tension

廖祿友(Lu-Yu Liao)

指導教授 ： 施文彬

共同指導教授 ： 陳俊杉

國立臺灣大學/工學院/機械工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.10311

摘要

本篇論文一開始先分析單一微粒與水面交互作用的情形，在力學分析的過程中我們發現如果微粒本身為親水 , 將微粒拉出水面所需之力會大於將之完全壓入水面所需之力。如果換做是一斥水微粒則會得到相反的結果。進而我們分析兩個同在水氣界面上的微粒，藉由水氣界面之表面張力交互作用的現象。其中兩微粒位置等高時，微粒間之作用力為吸引力。兩微粒位置皆在無限遠處水平面之上但它們之間高度不等的時候，則會造成微粒間作用力由原本的吸引力在微粒間距為某臨界值時轉變為排斥力的效應，並且微粒間距在此臨界值時，微粒間處於作用力為零並且總能量最低的穩定狀態。兩微粒位置其一在無限遠處水平面之上，另一在無限遠處水平面之下的時候，微粒間的作用力則是為排斥力。這一切之現象皆跟微粒間的水面曲線形狀有著密切的關係。本論文由Young-Laplace equation 出發，成功地求得微粒間水面曲線方程式的解析解並分析各種情形下微粒間作用力以及總能量的變化趨勢。最後並搭配實驗，量測微粒間的水面曲線，將量測之實驗數據與理論部份的解析解比較，並藉由所拍攝之水面曲線影像來分析微粒間之作用力。

關鍵字

微粒 ； 表面張力 ； 作用力 ； 能量 ； 水面曲線 ； Young-Laplace equation

並列摘要

At the beginning of this article, the situation of single colloid interacting with liquid is concerned. It is found that when the colloid is hydrophilic, the vertical force necessary to pull the colloid away from liquid is larger than that necessary to put the colloid into liquid. The reverse is true when the colloid is hydrophobic. The interaction between two colloids is also discussed. When two colloids are on the liquid-air interface, they attract or repel each other due to surface tension on the liquid-air interface. When the two colloids are at the same height above the far-field-liquid level, they attract each other. If their positions are both higher than far-field-liquid level but they are not at the same height, the interaction between them is attractive at long distance, and turns to be repulsive at some critical distance with a stable equilibrium. When one colloid is above the far-field-liquid level and the other is below this level, the interaction between the two colloids is repulsive. In other word, two colloids attract or repel each other depends on the elevations of colloids and the meniscus shape between colloids. Besides, this study successfully got the analytical solution of meniscus shape between colloids from Young-Laplace equation, and analysis variation of interaction between colloids and total energy in all situation. Finally, a experiment of measuring shape of meniscus between colloids is set up. We compared the experiment data with the analytical solution. By taking image of meniscus shape, we can also analysis interaction between colloids.BY taking image of meniscus shape, we can analysis interaction between colloids .

並列關鍵字

colloids ； surface tension ； interaction ； energy ； meniscus shape ； Young-Laplace equation

參考文獻

[1] W. Adamson & Alice P.Gast , “Physical Chemistry of Surface,” Sixth edition,

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[3] Gifford et al.(1971) ,”On the attraction of floating particles,” Chem. Engng Sci.

[4] Mansfield et al. ,”Equilibrium and mutal attraction or repulsion of objects supported by surface tension,” Phil. Trans. R. Soc. Lond. A Phys. Sci. Engng

Vol. 355, pp. 869-919.