液滴潤濕行為之研究:曲率效應

Curvature Effects on Drop Wetting

梁祐恩(Yu-En Liang)

指導教授 ： 諶玉真

國立臺灣大學/工學院/化學工程學研究所/博士(2016年)

https://doi.org/10.6342/NTU201602042

摘要

潤溼現象經常出現在日常生活中，其相關研究在工業、 科學、微流體控制等應用上都有所助益。本文將探討液固面之曲率效應對潤溼行為的影響，分為下列四個部分：
(1)液滴潤溼在纖維上是常見的，而液滴潤溼於垂直纖維底部與平板交界面的行為，與沾筆式奈米微影技術習習相關。我們將結合數值模擬與實驗來探討液滴於纖維底部與平板交界面之平衡形態。當使用超疏水板時，液滴的平衡形態將呈現軸對稱的barrel 狀或不對稱的clam-shell。相對的，當使用親水板時，液滴的平衡形態將呈現軸對稱的bell-like狀或不對稱的half-bell-like狀。介於兩種形態之間，兩種形態可以共存，也表示了有多重穩定態。在這個研究中，藉由有限元素的數值模擬，建立出固定平板接觸角下，液滴體積對液滴與纖維之間的接觸角之相圖。我們建立了兩張相圖，其平板之接觸角分別為70°和165°。其相圖特徵在重力存在下，與液滴於纖維上在無重力存在的相圖相似。其存在著三種區域:單獨barrel(bell-like)、單獨clam-shell(half-bell-like)、與兩者共存。然而，在超疏水板，單獨clam-shell區相較之下是比較小的，是因為同狀態下barrel狀的重力位能較低。另一方面，在親水板，由於親水板使液滴傾向增加與板的接觸面積，使得單獨bell-like的區域主導整個相圖，相較之下共存區明顯的縮小。
(2)在研究圓柱體外圍的潤溼行為之後，液滴於圓柱體內(管內)的相態是我們所關心的。了解液滴於水平管內的相態將對於在毛細力主導時二相流於微流體裝置內的流動提供有用的資訊。液滴於管子內的系統可以和液滴在纖維上(圓柱體外)之系統有所類比。利用Surface Evolver數值模擬與實驗對照，我們一樣發現了兩種形態，adhered drop和liquid slug。Adhered drop傾向存在於小體積，而liquid slug傾向存在於大體積。介於兩者中間的體積時，兩種形態可共存。實驗的觀察與我們的模擬符合。藉由數值模擬，我們建立了液體在管內的體積對接觸角之相圖。其存在著三種區域:單獨adhered drop、單獨liquid slug、與兩者共存。在重力的存在之下，相較於無重力的狀況，adhered drop形態是較為傾向存在的。因此，相圖的共存區明顯上升。
(3)了解並控制液滴於錐狀纖維上的平衡位置與形態將對於沾筆式奈米微影技術提供有用的資訊。在這個研究，藉由Surface Evolver數值模擬，我們探討了液滴於垂直的錐狀纖維之平衡形態。相似於液滴於柱狀纖維之相態，我們得到了兩種形態(barrel狀與clam-shell狀)。在無重力的狀態下，液滴會一直往上(低曲率)的方向移動，並且隨著其上升，總表面能持續的下降。無論液滴模擬的初始狀態為何，向上移動著的液滴最終都會是clam-shell形態，並且沒有平衡位置。然而，在重力存在時，液滴將會停止移動在平衡位置。對於一個已知的接觸角，clam-shell傾向存在於小體積，而barrel傾向存在於大體積。在特定的體積區段，我們發現了兩者的共存態。在足夠大的體積下，液滴將掉落而不在系統中。
(4)最後，我們研究在一個錐和板之間的液橋的潤溼行為，其與沾筆式奈米微影技術更加相關。藉由Surface Evolver數值模擬、多體耗散粒子動力學法、與實驗，我們探討了於錐和板間的液橋形狀與其斷裂過程。取決於錐的幾何形狀(錐的張開角)、錐間與板的距離、與錐和板的潤溼性(接觸角)，我們可以觀察到在斷裂前，有三種液橋形態，並且在斷裂後，錐和板之間競爭的結果會有兩種。有趣的是，在斷裂後，大部份的液橋體積不一定會留在較為親水的錐上。事實上，雖親水但尖銳的錐(錐的張開角小)在潤溼的競爭上經常會輸給疏水板。為了解釋我們的發現，錐之“表觀”接觸角的概念將被提出與介紹，並且我們也發現，在錐板之液橋系統與在兩平行板之間的液橋系統，根據這個概念，是可以類比的。

關鍵字

液滴 ； 潤溼 ； 接觸角 ； barrel ； clam-shell ； Surface Evolver ； 多體耗散粒子動力學 ； 液橋 ； 沾筆式奈米微影技術

並列摘要

Wetting phenomenon is easily seen in our daily life. The research about wetting can provide useful information for industry, science, and microfluidics applications. In this dissertation, there are four major parts to investigate the effects of solid-liquid surfaces’ curvature on drop wetting.

For the first part, droplet-on-fiber is commonly seen and the drop at the bottom of a rigid fiber standing vertically on a flat surface is closely related to dip-pen nanolithography. A combined approach of numerical simulation and experimental observation is conducted to investigate the equilibrium shape of a drop-on-fiber/plane system. For superhydrophobic surfaces, the equilibrium geometrical shape of the drop adopts either axisymmetric barrel or asymmetric clam-shell conformation. In contrast, for hydrophilic surfaces, the equilibrium drop shape adopts either axisymmetric bell-like or asymmetric half-bell-like conformation. At the transition between the two conformations, both conformations can coexist and the multiple steady states are indicated. In this study, the phase diagrams of drop-on-fiber/plane, that is, the plots of droplet volume against liquid-fiber contact angle, are established on the basis of the finite-element simulation for liquid-plane contact angle 70° and 165°. The general features of phase diagrams for drop-on-fiber/plane systems in the presence of gravity are similar to those of drop-on-fiber in the absence of gravity. Three regimes, barrel only (bell-like only), clam-shell only (half-bell-like only), and coexistence, can be identified. However, on superhydrophobic surfaces, the regime of clam-shell only is deflated, since the gravitational energy benefits barrel more than clam-shell. On the other hand, on hydrophilic surfaces, the regime of bell-like only prevails owing to the spreading tendency of the drop and the coexistent regime diminishes significantly.

For the second part, the equilibrium morphology of a drop in a horizontal tube can provide useful information for two-phase flow in microfluidics devices in which the capillary force dominates. A drop-in-tube system is analogous to a drop-on-fiber one and two conformations are obtained, adhered drop and liquid slug, by the approaches of experiments and Surface Evolver simulations. The adhered drop conformation tends to exist at small volume, whereas the liquid slug conformation is favored at larger volume. Around the transition volume between the two conformations, both morphologies can coexist. The experimental results are consistent with those of simulation outcomes. The morphological phase diagram of the drop-in-tube system is constructed via SE simulations by varying the drop volume and contact angle. Three regimes can be identified through the upper and lower boundary curves: adhered drop only, liquid slug only, and coexistence. Compared to the case with negligible gravity, the adhered drop is more favored than the liquid slug in the presence of gravity. As a result, the coexistence regime expands substantially.

For the third part, controlling the droplet equilibrium location and shape on a conical fiber is essential to industrial applications such as dip-pen nanolithography. In this study, the equilibrium conformations of a drop on a vertical, conical fiber has been investigated by the finite element method, Surface Evolver simulations. Similar to the morphology of a drop on a cylinder, two different types (barrel shape and clam-shell shape) can be obtained. In the absence of gravity, the droplet moves upwards (lower curvature) and the total surface energy decays as the drop ascends. Whatever the initial conformation of the drop on a conical fiber is, the rising drop exhibits the clam-shell shape eventually and there is no equilibrium location. However, in the presence of gravity, the drop can stop at the equilibrium location stably. For a given contact angle, the clam-shell shape is generally favored for smaller drops but the barrel shape is dominant for larger drops. In a certain range of drop volume, the coexistence of both barrel and clam-shell shapes is observed. For large enough drops, the falling-off state is seen.

For the fourth part, the formation of a liquid bridge between a cone and a plane is related to dip-pen nanolithography. The meniscus shape and rupture process of a liquid meniscus between a cone and a plane are investigated by Surface Evolver, many-body dissipative particle dynamics, and macroscopic experiments. Dependent on the cone geometry, cone-plane separation, and wetting properties of cone and plane, three types of menisci can be observed before rupture and two types of wetting competition outcomes are seen after breakup. It is interesting to find that after rupture, the bulk of the liquid bridge volume is not necessarily retained by the cone which is more wettable. In fact, a sharp hydrophilic cone often loses wetting competition to a hydrophobic plane. To explain our findings, the “apparent” contact angle of the cone is introduced and the behavior of drop-on-cone/plane system is analogous to that of a liquid bridge between two parallel planes based on this concept.

並列關鍵字

droplet ； wetting ； contact angle ； barrel ； clam-shell ； Surface Evolver ； MDPD ； liquid bridge ； dip-pen nanolithography

參考文獻

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[4] Berthier, J. Microdrops and digital microfluidics. William Andrew Publishing 2008.

[5] Wenzel, R. Resistance of Solid Surfaces to Wetting by Water. Ind. Eng. Chem. 1936, 28, 988-994.

[6] Cassie, A.; Baxter, S. Wettability of Porous Surfaces. T. Faraday Soc. 1944, 40, 546-551.