以多體耗散粒子動力學法研究氣泡及液滴沿垂直平板之運動行為

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姓名

阮澄信(Cheng-Hsin Juan) 查詢紙本館藏

畢業系所

化學工程與材料工程學系

論文名稱

以多體耗散粒子動力學法研究氣泡及液滴沿垂直平板之運動行為
(Sliding Motion of Bubble and Liquid Droplet along a Vertical Surface: Many-body Dissipative Particle Dynamics Simulation)

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摘要(中)

當汽水倒入玻璃杯時，杯壁上那些微小的小氣泡會因為接觸角遲滯的影響而黏滯於杯壁上不動。若氣泡要能在表面上移動，則需克服接觸角遲滯所造成的毛細阻力，因此通常自由浮升的氣泡速度，會遠比在杯壁上的氣泡速度來的大很多。本研究透過多體耗散粒子動力學法，模擬於穩態層流系統中，極小氣泡在垂直表面上的運動行為(Reynolds Number，Re ~ O(1))。分別討論表面潤溼性、滑移邊界條件、以及接觸角遲滯的改變對氣泡運動的影響。結果顯示，氣泡的形狀會因流體與固體表面之間的潤濕性質不同而改變。表面潤溼性越差會使氣泡的接觸角減小，即形狀越扁，進而導致參考面積及阻力係數的顯著下降，因此其滑移速度能夠超越自由浮升之氣泡的速度。此外，在固體邊界條件有無滑移，對氣泡移動速度的影響小於10%。接觸角遲滯對氣泡移動有極大的影響，模擬結果顯示，當表面具有粗糙度而產生接觸角遲滯時，於氣泡三相接觸線的位置將會產生毛細阻力進而阻礙氣泡的移動，導致氣泡的移動速度會比其在平滑表面上時顯著變慢。實際上，當外力(即浮力)扣除毛細阻力後，所剩下的作用力才是真正使氣泡移動的有效驅動力。
另外，液滴沿垂直平板運動的結果也和氣泡相同，當液滴潤濕性質越疏水時，液滴會因為和固體接觸面積減少而速度越快。比較體積及形狀相同的液滴和氣泡，發現潤濕性質將主導其速度大小，即氣泡和液滴皆為低接觸角時，氣泡速度較快；反之，兩者皆為高接觸角時，液滴速度較快。表面粗糙度同樣會對液滴產生接觸角遲滯，且對液滴影響大於對氣泡的影響，但在潤濕性質變很差時，液體傾向不潤濕粗糙表面上的孔洞，因此接觸角遲滯趨近於0。

摘要(英)

Tiny bubbles readily stick onto substrates due to contact angle hysteresis (CAH). A tiny bubble can slide slowly on a surface with ultralow CAH once buoyancy overcomes pinning force. In this study, the sliding motion of bubbles at Re~O(1) is investigated by many-body dissipative particle dynamics simulation. The influence of the bubble shape is studied by varying the fluid-solid wettability. As the wettability is reduced, the bubble shape becomes more flat and the sliding velocity grows accordingly. The sliding bubble on a CAH-free surface can rise faster than a freely rising one owing to the decrease of both the frontal area and drag coefficient. Moreover, less than 10% reduction of the sliding velocity is obtained if the slip boundary condition is replaced with the no-slip boundary condition. The CAH induced by surface roughness results in the adhered bubble. As a result, the velocity of the bubble on the rough surface is much slower than that on the CAH-free smooth surface. Actually, the effectively driving force for the bubble motion is the difference between the buoyancy and the pinning force originated from the CAH.
In addition, similar phenomena are observed for the motion of the sliding drop motion on the vertical surface. It shows that the sliding velocity for the drop on the hydrophobic surface is faster than that on the hydrophilic surface due to the small contact area between solid and liquid interface. Comparing the bubble and liquid drop of the same shape, it is found that when both contact angle are small, the sliding velocity of the bubble is faster than that of the drop due to the hydrophobicity of the bubble. In contrast, as both contact angle are large, the sliding velocity of the drop is faster than that of the bubble because of the hydrophobicity of the drop. Moreover, the CAH induced by surface roughness has a strong effect on the drop motion. However, as liquid wettability becomes poorer, liquid beads tend not to impregnate the surface grooves. Thus, CAH induced by surface roughness is absent.

關鍵字(中)

★ 氣泡運動
★ 接觸角遲滯
★ 多體耗散粒子動力學

關鍵字(英)

★ Bubble sliding
★ contact angle hysteresis
★ many-body dissipative particle dynamics

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章、緒論 1
1-1 前言 1
1-2 文獻回顧 1
1-2-1 氣泡於傾斜板上之運動行為 1
1-2-2 粗糙表面上的潤濕行為 4
1-3 研究動機 8
第二章潤濕現象基本原理 9
2-1 潤濕現象的理論定義 9
2-1-1 楊氏方程式 ( Young’s equation ) 9
2-1-2 溫佐方程式 ( Wenzel’s equation ) 11
2-1-3 卡西方程式 (Cassie equation) 13
2-2 接觸角遲滯 ( Contact Angle Hysteresis, CAH) 14
2-2-1 接觸角遲滯的定義 14
2-2-2 接觸角遲滯的成因 15
2-2-3 接觸角遲滯的量測方法 17
2-3 粗糙表面對潤濕現象的影響 18
第三章模擬原理與方法 24
3-1 多體耗散粒子動力學(Many-body Dissipative Particle Dynamics) 24
3-2 MDPD原理 26
3-2-1 MDPD作用力 26
3-2-2 噪訊與時間尺度 30
3-2-3 弗洛里-哈金斯理論(Flory-Huggins Theory) 31
3-2-4 長度、速度、時間尺度的無因次化 33
3-2-5 積分法求解 34
3-2-6 週期性邊界條件 36
3-2-7 Cell List 表列法 37
3-3 模擬系統與參數 38
3-3-1 系統基本參數設定 38
3-3-2 粒子的設定 39
3-4 滑移邊界條件(Slip Boundary Condition) 41
第四章氣泡於垂直平板的運動行為 45
4-1 外力對氣泡運動的影響 45
4-2 表面潤溼性對氣泡運動之影響 52
4-3 滑移邊界條件對氣泡運動之影響 58
4-4 粗糙表面對氣泡運動之影響 62
第五章液滴於垂直平板的運動行為 68
5-1 液滴於平滑表面上的運動行為 68
5-2 液滴於粗糙表面上的運動行為 77
第六章結論 82
第七章參考文獻 84

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指導教授

曹恆光(Heng-Kwong Tsao)

審核日期

2016-6-23

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