在孔洞、圓柱體與傾斜面的液滴潤濕行為

Droplet Wetting on Holes, a Fiber, and a Tilted Plate

周東和(Tung-He Chou)

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(2012年)

https://doi.org/10.6342/NTU.2012.00311

摘要

潤濕的現象經常出現於日常生活中，以液滴附著在器物或植物表面最為常見，如葉面的水珠和滑落玻璃的雨滴。潤濕常指流體在相界面 (至少有兩種流體) 的平衡結果，其為界面科學之基礎。工業上，液滴潤濕於固體表面是很普遍的程序。因此，研究液滴的潤濕將有助於工業應用與科學發展，例如在控制液滴的型態、附著、移動和潤濕度 (Wettability) 等方面。相關的理論分析發軔於18世紀末期，基於材料科學的發展與量測技術的精進，潤濕科學的基礎框架於20世紀時，
幾乎已發展完備。然而，隨著半導體製程技術、電潤濕、微流體晶片 (Microfluidic Chips) 、仿生材料學 (Biomimetics) 等科技的發展，它們所衍生的潤濕現象仍有許多等待探究與闡明，例入考慮重力效應、固體幾何形狀 (Solid Geometry) 與接觸角遅滯 (Contact Angle Hysteresis) 等外在或本質因素時，如何系統地以熱力學模型定量描述液滴型態與潤濕行為。本論文分為三大部分探討不同系統下液滴潤濕的行為：(1) 超疏水表面 (接觸角大於150°) 通常以非潤濕 (Nonwetting)或部分潤濕 (Partial Wetting) 的粗糙結構所構成。研究顯示，表面微溝槽 (Groove) 的表面張力與液氣界面的型態有密切關聯，因此表面微結構經常被視為超疏水現象的主因。我們考慮一個液滴 (體積V) 完全覆蓋一至多個氣孔 (半徑 r)。在最小自由能的狀態方下，取得描述液滴型態的解析解 (包含底部的液氣界面)。透過定義一界面角 (θ1)，將θ1表示為V/r3與本質接觸角 (θ*) 的函數。結果顯示當相對孔洞尺度越小 (r3/V → 0) ，液滴底部會趨於平坦 (θ1 → 0)。此外，θ*越小也會有類似的現象。我們利用數值模擬(基於最小能量法)佐證先前的解析解並得到良好的一致性。若考慮重力效應，則數值模擬與實驗結果相互吻合。此研究結果指出忽略孔洞效應 (Wall-Free) 的毛細現象適用於排除液體，可應用於微流體裝置和燃料電池。(2) Drop-on-fiber是指液滴在圓柱體的潤濕，因表面幾何形狀的改變，潤濕行為不同於在平面的情況。在圓柱體上，液滴的形態可為軸對稱的”barrel-shape”或非對稱的”clam-shell-shape” (無重力狀態下)。型態的轉換過程取決於該狀態的能量大小。然而，實驗顯示兩種形態卻能共存。型態轉換的過程中具有多重穩定態 (Multiple Stable States)。我們以數值模擬建立drop-on-fiber的相圖 (液滴體積對接觸角)。重力效應忽略時存在三種體系：單獨barrel、單獨clam-shell、與兩者共存；以及考慮重力效應時也存在三種體系：單獨朝下clam-shell、barrel與朝下clam-shell共存與液滴掉落。(3) 透過實驗與理論分析，論文的第三部分是研究液滴於平板傾斜過程的潤濕轉變。傾斜液滴模擬的數值計算是基於liquid-induced defect model，透過設定兩個熱力學參數 (潤濕前與潤濕後的固液表面能)，比對一個液滴放置在水平的平坦表面 (初始接觸角為θ) 而後緩慢的傾斜此表面，並細分為兩種情況: (I) 液滴在水平時，θ調整為θa (II) θ調整為θr。在(I)時慢慢增加傾斜程度，液滴上端的接觸角將逐漸下降 (與水平的重力分量方向相反) 而下端的接觸角卻保持定值。當此液滴保持不滾動，後端的三相線將保持不動 (Receding Pinning) 而前端的部份則會前進 (Advancing Depinning)。透過分析液滴傾斜過程的總自由能變化顯示固液界面自由能的減少將補償因氣液接觸面的增加而造成的能量上升，進而形成不對稱的液滴型態。在(II)時慢慢增加傾斜程度，上端接觸角會增加而下端接觸角卻保持定值。透過分析液滴傾斜過程的總自由能變化顯示氣液界面自由能的減少將補償因固液接觸面的減少而造成的能量上升，進而形成不對稱的液滴型態。在考慮傾斜液滴的遲滯效應時，我們的模擬結果與實驗結果有良好的一致性。

關鍵字

潤濕 ； 液滴 ； 接觸角 ； 自由能量最小法 ； Surface Evolver ； 遲滯

並列摘要

Wetting phenomena of a liquid droplet on substrates are ubiquitous in everyday life as well as in industrial practices. The extent of a droplet’s spread over a substrate and its equilibrium shapes in the presence of gravity are important for wetting applications such as coating, self-cleaning surfaces, droplet formation, and microfluidics. In this thesis, there are three major parts: (1) Superhydrophobic surfaces involve completely nonwetting or partially wetting roughness. Since the contact angle is closely related to liquid-gas interfacial tension, the shape of the liquid-gas interfaces within the grooves plays a key role in determining droplet wetting behavior. We consider a droplet with volume V atop holes with radius r and obtain an analytical expression for the bottom liquid-gas shape based on surface free energy minimization. The bottom shape is found in terms of the interfacial angle θ1 to depend on the hole size by V/r3 in addition to the intrinsic contact angle θ*. For a given droplet volume, the smaller the hole size (r3/V → 0), the flatter the interface (θ1 → 0). Furthermore, the flatness of the interface grows with reducing intrinsic contact angle. Numerical simulations are performed to confirm our theory. Moreover, wetting experiments where the gravity effect cannot be neglected are conducted, and the results are consistent with our numerical simulations. Here, these findings indicate that such wall-free capillarity may have potential to extract liquid from microfluidic devices and fuel cells. (2) Drop-on-fiber is also commonly observed in daily life and is closely related to digital microfluidics. The wetting behavior of it differs from that of drop-on-plane due to the global cylindrical shape. The equilibrium geometric shape of a droplet on a fiber is generally believed to take either asymmetric clam-shell or axisymmetric barrel conformation in the absence of gravity. The barrel-to-clam-shell transition is determined by a stable condition. However, experimental observations showed that both barrel and clam-shell conformations can coexist in some situations and thus indicated the existence of multiple stable states. Here, the phase diagrams of drop-on-fiber, that is, the plots of droplet volume against contact angle, are established on the basis of the finite-element simulation. When the gravity effect is absent, there are three regimes including barrel, clam-shell, and the coexistence of both; in contrast, when the gravity effect is considered, there also exist three regimes, including (I) downward clam-shell, (II) coexistence of barrel and downward clam-shell, and (III) falling-off. (3) The wetting behavior of a liquid drop sitting on an inclined plane is investigated experimentally and theoretically. We performed numerical simulations that are based on the liquid-induced defect model, in which only two thermodynamic parameters (solid-liquid interfacial tensions before and after wetting) are required. A drop with a contact angle equal to θ is first placed on a horizontal plate and then the plate is tilted. Two cases are studied: (I) θ is adjusted to the
advancing contact angle (θa) before tilting and (II) θ is adjusted to the receding contact angle (θr) before tilting. In the first case, the uphill contact angle declines and the
downhill contact angle remains unchanged upon inclination. When the tilted drop stays at rest, the pinning of the receding part of the contact line (receding pinning) and the
depinning of the advancing part of the contact line (advancing depinning) are observed. The free energy analysis reveals that upon inclination, the reduction of the solid-liquid free energy dominates the increase of the liquid-gas free energy associated with shape deformation. In the second case, the downhill contact angle grows and the uphill contact angle remains the same upon inclination. Advancing pinning and receding depinning are noted for a tilted drop at rest. The free energy analysis indicates that upon inclination, a decrease of the liquid-gas free energy compensates an increase of the solid-liquid free energy. The experimental results are in good agreement with those of simulations.

並列關鍵字

Wetting ； Droplet ； Contact Angle ； Free Energy Minimization ； Surface Evolver ； Hysteresis

參考文獻

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