施文彬臺灣大學：機械工程學研究所廖祿友Liao, Lu-YuLu-YuLiao2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/61132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。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 .致謝......................................................i 摘要.....................................................ii Abstract................................................iii 目錄................................................. ....v 圖目錄..................................................vii 表目錄.................................................xiii 第一章 序……………………………………………………………1 1.1 研究動機與目的...................................1 1.2 論文架構.........................................5 第二章 單一微粒與水面交互作用之分析.....................6 2.1 單一親水微粒拉出及壓入水面的力學分析.............6 2.2 單一斥水微粒拉出及壓入水面的力學分析............10 第三章 表面張力造成兩微粒間交互作用之問題描述..........12 3.1 兩微粒相吸問題描述..................................13 3.2 兩微粒相斥問題描述..................................19 第四章 數學模型..........................................28 4.1 座標系統...................... ..............28 4.2 兩微粒外側水面的效應.........................33 4.3 兩微粒相吸力學分析...........................35 4.4 兩微粒相斥力學分析...........................37 4.5 水面曲線方程式之探討.........................39 4.5.1 微粒外側水面的曲線方程式..............39 4.5.2 兩微粒間水面的曲線方程式..............40 第五章 微粒間作用力與微粒間距之關係......................42 5.1 兩微粒相斥...................................42 5.1.1 兩微粒高度位置上下對稱................46 5.1.2 兩微粒高度位置上下不對稱..............53 5.2 兩微粒相吸...................................57 5.2.1 兩微粒間存在高度差....................58 5.2.2 兩微粒等高............................66 5.3 兩微粒其中之一高度為零.......................68 5.4 總結－微粒間作用力在各種情形下的比較.........71 第六章 微粒周圍水面在各種相互作用情形下的能量............83 6.1 單顆微粒周圍水面的能量.......................84 6.1.1 水氣界面的表面能量.....................84 6.1.2 微粒下方的靜液能量.....................85 6.2 兩顆微粒周圍水面在微粒交互作用下的能量.......88 6.2.1 兩微粒外側水面的能量...................88 6.2.2 兩微粒間水面的能量.....................90 6.3 總能量隨微粒間距離變化的分析.................91 6.3.1 兩微粒相斥之總能量.....................91 6.3.2 兩微粒相吸之總能量.....................95 6.4 總結－各種情形下總能量變化的比較............102 第七章 微粒表面接觸角的影響.............................110 第八章 兩微粒間水面曲線之量測...........................115 8.1 實驗目的...................................115 8.2 實驗裝置...................................116 8.3 實驗方法...................................118 8.4 實驗結果分析...............................137 第九章 結論.............................................173 參考文獻................................................175 附錄....................................................1772332589 bytesapplication/pdfen-US微粒表面張力作用力能量水面曲線Young-Laplace equationcolloidssurface tensioninteractionenergymeniscus shapethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61132/1/ntu-96-R93522519-1.pdf