液滴產生及其引致振盪對融合過程現象與力學機制之探討

Abstract

二十世紀以來，隨著高速攝影技術的蓬勃發展，液滴撞擊液面的瞬時景象，這些原本肉眼不可見的美麗成像可以被凍結或以慢速撥放，瞬時吸引住人們的目光，並以其自然、純淨、無暇的象徵，時常伴隨著美妝產業的廣告放送；此自然界現象不僅深具藝術內涵，更為重要的是啟發眾多科學家對於液滴融合過程現象的物理機制探討，以此知識基礎帶來多元的科學發展與多樣的工業應用，影響所及橫跨氣象學、印刷技術、農漁經濟、食藥以及電子工業等。惟以往大部分研究為將問題簡化，多半假設液滴的初始形狀為一正圓形，並且著重於從能量轉換的觀點上進行液滴融合過程之研究；以典型實驗觀測作為例子，當液滴於低速下與液面融合後，常會引致水下渦環(vortex ring)的生成，但其渦度(vorticity)與穿透深度卻不隨融合時刻液滴擁有的動能隨之增長，此非線性的結果不可避免地為科學家帶來另一維度思考的要求，即液滴振盪行為。然而即使已知液滴融合時的外型變化將改變質/熱傳表現，百年來的研究仍對何種液滴形狀與撞擊條件將引致最大渦環穿透深度之問題，始終無法達成共識，於是本研究藉尋求此懸宕百年問題的答案之機會，從液滴生成開始乃至融合後各現象終了，進行全面且系統化的力學分析，根據液滴的生命週期可以將此論文架構分為三大部分: I. 液滴生成 此部分首先藉由83組不同尺寸與3種相異材質的滴頭進行懸垂液滴的生成實驗，並藉由比較理論分析與實驗結果，獲得輸入液體流率大小對液滴生成尺寸的影響範圍，接著探討生成液滴直徑與滴頭尺寸的關聯性，從中證實滴頭的特徵直徑宜採用潤濕直徑(wetting diameter)而非慣用的滴頭內/外徑，最後於論文中首次提出一個簡單卻精準的半理論公式，可以廣泛地實際應用於液滴實驗之中。 II. 液滴振盪 此部分研究重新檢視液滴振盪理論，配合實驗結果的擬合分析，求得液滴各振盪模態的振幅大小與運動特性，不僅成功以線性理論預測液滴的振盪行為，並且掌握住各振盪模態在振盪週期中所持有的權重，研究發現透過懸垂斷裂生成的液滴之振盪，至少(或只)須綜合考量第二與第三振盪模態，可以適切合理的描述出真實的液滴振盪行為，主因在於第二振盪模態僅提供液滴軸對稱的擴張與壓縮，但真實液滴的外型變化多呈不對稱之貌，且當其尺寸愈大，振幅大小與不對稱程度將為之更甚，是故提供液滴進行不對稱運動行為的第三模態便無法如同過往文獻一樣，將其忽略而過度簡化物理模型；另外，本研究首次成功藉由液滴振盪參數化分析，賦予新提出的振盪指數(oscillation index, Oi)具有能描述液滴整體振盪運動的物理意義，即液滴存在多重高階模態的特性，因而改善傳統使用的形狀參數(axis ratio, e)只具描述第二振盪模態的能力，此項成果將對接踵而至的液滴融合現象提供更為透徹的力學闡釋。另一方面，此部分研究亦延伸至液滴受彈性板限制下的振盪行為，探究液滴於彈性板不同位置上所對應的振盪模態，並發現液滴於彈性板上在適當條件下可激發其徑向之運動。 III. 液滴-液面交互作用 承襲液滴振盪章節的結論，透過液滴形狀參數化進行系統且定量化的分析，由實驗發現當液滴為振盪指數峰值(Oi,m)之時，其外形似倒立式的西洋梨(inverted pear-shaped)；更值得注意的是研究證實最大水下渦環穿透深度傾向由具振盪指數峰值的液滴融合後演化生成。同時從實驗中亦發現當具Oi,m的液滴撞擊至深液後將引致一特殊的水窪發展型態，水漥上半部形成顯著的頸部區段且最後斷裂以生成大氣泡，藉由液滴振盪與水窪發展的關聯性分析，可以有效說明大氣泡捲入的物理生成機制。另一方面，此部分延伸至當液滴於高速下與液面進行融合過程的現象，首次於實驗中發現液滴噴濺行為有二階段的臨界現象(Double splashing)，意即當液滴撞擊至同一深度之液膜，隨著撞擊速度小至大的發展將有非噴濺至噴濺，而後再次產生非噴濺的速度區域，最後有別過往認知中，噴濺現象皆屬於二次液滴的生成(droplet splashing)，而可以是產生氣泡的噴濺現象(bubble splashing).

Since the twentieth century, with the rapid development of high-speed imaging technology, the scenarios of drop impact upon the liquid surface that originally cannot be observed with the naked eye, is able to be frozen or displayed in slow motion. These beautiful images have drawn public attention instantly and are often shown in the cosmetic/beverage advertising owing to its natural, pure and immaculate symbols. Except the artistic connotation of this visualization, more importantly, it inspires more and more scientists to probe into the physical mechanism of the drop coalescence processes. With exploring the fundamental knowledge, it brings about a wide range of scientific development and industrial applications such as the printing technology, agriculture and fishery, food and medicine and electronic industry. However, for simplicity, most previous studies have assumed that the shape of a droplet is initially spherical, and focused on the process of drop coalescence based on the viewpoint of energy alone. Taking a typical observation of experiment as an example, after a drop completely coalesces with the liquid surface with low energy, the drop will turn into a vortex ring that propagates into the deep pool. Unexpectedly, the vorticity and penetration depth of vortex ring do not increase with the kinetic energy of the drop. Such a nonlinear result inevitably forces the scientists to extend an additional consideration; namely, the drop oscillation. Even though it is known that the oscillatory behaviors will affect the performance of mass/heat transfer, a century-long investigation still fails to reach a consensus on what kind of drop shape/impact conditions will produce the maximum penetration depth of vortex ring, Therefore, this thesis starts with seeking the answer to the long-standing problem, and then carries out a comprehensive and systematic analysis to understand the mechanics from drop generation, oscillation and drop-surface interactions. According to the life of a drop, i.e., generation, falling and hitting, this thesis is divided into three parts: I. Drop generation In this study, dripping drops of water and glycerol/water mixtures from 83 nozzles (in the range of 0.065 mm ≤ Do ≤ 40 mm and 0.043 mm ≤ Di ≤ 35 mm, where Do and Di are outer and inner diameter, respectively) were systematically investigated for four low-viscosity fluids, three wettable nozzle materials, and various liquid feeding rates under the simple dripping mode condition into ambient gas, i.e. air. It is important to point out that no single characteristic length scale mentioned in the literature can be used to satisfactorily predict all experimental data. A new characteristic parameter, i.e. the wetting diameter (Dw), has been introduced and its usefulness in predicting drop size by a simple relation in the whole nozzle range is shown for the first time. The critical wetting diameter (Dc), which is related to the wettability (or advancing contact angle) of the dripping liquid and nozzle material, is theoretically derived and its dimensionless value (Dc*), normalized by the capillary length (λ), shows excellent agreement with experimental results. Five characteristic wetting regimes have been further classified. The Dc*-value is important for the dripping drop classification, i.e. above which is Di*-dependent and below which is Di*-independent or mainly Do*-dependent. The characteristics and relationships of the wetting diameter with respect to the nozzle geometry and wettability for dripping drop formation are analysed and compared in different regimes. A method to stably generate large dripping drops with diameters up to approximately three times the capillary length has been also demonstrated. II. Drop oscillation In this part, the drop oscillation theory was re-examined. With the matched results from the experiments and the linear drop oscillation theory, the amplitude and the characteristics of each drop oscillation mode can successfully be recognized. Moreover, the superposition of 2nd and 3rd oscillation modes at least is demonstrated to be the necessary condition that reflects the real oscillation of a drop falling freely in air. We have, for the first time, proposed a new oscillation index that enables the representative of the drop oscillation with multiple modes instead of the commonly-used axis ratio that represents the 2nd oscillation mode alone. Finally, behavior of a sessile drop on a vibrating elastic plate is also investigated. We further focus on the influence of the non-uniform amplitude of the plate oscillation on the dynamics of drop. III. Drop-surface interactions The complicated outcomes of liquid coalescence are found to be well predicted by choosing a single characteristic length from the oscillating liquid, i.e., the oscillation index Oi, which can be used as a guideline for efficient transportation/mixing across free liquid surface. Moreover, the new oscillation index also reveals the excellent prediction of the distribution of large bubble entrainment that is resulted from necking of the upper cavity. The generation mechanism of large bubbles is illustrated based on the quantitative and systematic investigation. Finally, we present the first quantification of the double splash phenomena, i.e., it follows the region of (I) non-splash, (II) splash and surprisingly (III) non-splash, and then splash (IV) again with increasing the impact velocity of drop at the specified liquid film thickness. For high impact energy over the second threshold of splashing, bubbles are possibly ejected from the crown tips instead of commonly observed droplet splash.