液滴在細桿上的平衡型態之研究

Abstract

本篇研究目的在提供液滴的潤濕行為與表面結構之背景知識。在理想的平坦表面上,液滴的潤濕現象可用 Young's方程式描述，但隨者合成與加工技術之進步，微奈米材料的表面圖案與塊材形狀(如圓柱狀)在科學研究中經常被探討。 改變表面與整體形狀對於潤濕行為的影響是界面科學的重要議題。然而，就已知的文獻資料看來，以理論與模擬分析的研究是比較困難，因為形狀是非軸對稱。對於理想(無粗糙度)柱體形狀， Young's 方程式是不足以描述其潤濕行為，目前也無適當的理論方程式(如著名的Wenzel模型或Cassie-Baxter模型)可用於預測液體的形狀。更重要地，柱體形狀與表面接觸角兩者對潤濕現象的影響。以熱力學能量最小化法的觀念，本研究藉由數值軟體(Surface Evolver)探討柱體上的潤濕現象。第三章將研究忽略重力的情況，重新解釋先前文獻的研究結果，並進一步解釋其不完善之處。第四章將計算重力效應的影響。就本研究對於圓柱系統的液滴潤濕行有詳細的研究。將以液滴形狀，體積與表面接觸角等因子來描述並建立對應的相圖。另外，我們發現在相同情況下(同一接觸角及液滴體積)，會有不只一種型態的液滴存在，即共存區，是另一重點。比對過去文獻的結果與本研究的實驗結果可知，該相圖的資訊在定性與定量上有著良好的描述。未來的研究可以延伸至柱體的半徑隨軸變化、柱體的表面有粗糙度和多根柱體(網狀)等情況下的潤濕行為。

The wetting behavior of a droplet on a planar solid surface is well-known. Due to the geometrical constraint of the fiber, however, the equilibrium shapes of a droplet on fibers are more complicated and therefore are less studied. A combined numerical simulation and experimental investigation were employed to examine the conformations of a droplet on a fiber. The energy calculation results were accurately achieved by using a powerful modeling tool, the Surface Evolver, to present the fiber-droplet system in mathematical model taking surface tension, gravity energy, and other geometrical constraints into consideration. In the first part, we simulate our fiber-droplet system with no gravity and compare the results to Carroll’s and McHale’s work. Our results show that the existence of inflection point for barrel shape is a good criterion in determining if a barrel shape droplet could exist. We also find the coexistent region of two configurations. In the second part, we simulate our fiber-droplet system with gravity. Our results demonstrate that several regimes can be found. If the droplets volume is too small to cover the fiber in a barrel shape, the droplets can only exist in shapes of downward and upper clam-shell(Regime I). For droplets where the gravity effect is not too significant, shapes of upper clam-shell, barrel, and downward clam-shell can co-exist (Regime II). As volume increases, the upper clam-shell droplet becomes unstable (Regime III); if the volume grows larger further, the barrel also ceases to exist, leaving only the downward clam-shell one (Regime IV). Finally, gravity turns out to be the most important factor and the droplet can no longer be attached to the fiber (Regime V). Our results also indicate that the intrinsic surface property (e.g. the contact angle) of the fiber has significant effect on these regimes, number of the regimes changes as the contact angle varies. This work can be related to a number of industrial applications regarding fiber-based microfludics such as low-cost medical diagnostic and cell cultivation.