自驅動紊流之多重碎形動力學及紊流抑制

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劉國安(Kuo-An Liu) 查詢紙本館藏

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物理學系

論文名稱

自驅動紊流之多重碎形動力學及紊流抑制
(Multifractal Dynamics and Turbulence Reduction in Self-propelled Turbulence)

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摘要(中)

大腸桿菌是一種藉由轉動其鞭毛束以達成自我泳動之微生物。其長條形的細胞體使得兩個菌體在非彈性碰撞後可以有同方向排列及運動。在高菌數濃度下，此機制可造成非線性強耦合並且形成集體運動之細菌團簇。細菌團簇的運動可帶動背景液體，產生如同流體紊流(hydrodynamic turbulence)般多重尺度旋渦(vortex)及噴射流(jet)，此流場亦被稱為細菌紊流(bacterial turbulence)。
流體紊流的能量從大尺度運動方式被動注入，並藉由尺度不變(scale-invariant)定律一級一級往更小尺度運動傳遞，功率頻譜密度呈現冪次分佈;相反地，細菌紊流的能量從單細胞尺度主動注入，並藉由上述之非線性強耦合方式傳遞至群體行為尺度。雖然已有大量的文獻證明被動(passive)流體紊流擁有多重碎形(multifractal)或多重尺度率(multiscaling)動力學，以及利用聚合物長鏈分子可有效抑制流體紊流及降低液體輸送阻力，自驅動紊流是否擁有類似行為依然是個未知且重要的議題。在此論文中，我們以高濃度大腸桿菌液體做為平台，探討上述兩個議題。
一、自驅動紊流之多重碎形動力學：我們首次在類二維薄液中探究兩種不同菌數濃度下的多重碎形動力行為。增加細菌濃度可增加整體驅動功率及增加非線性強耦合，使得細菌團簇有機會形成較大尺寸，能量等效地可傳遞到較大尺度，因此旋渦變得較大、較低頻也較強。這也使得流場的速度及空間中距離為r兩點的速度差ν_r都有較寬的機率分佈。ν_r的q級結構函數（q-order structure function, S_q）與r展現冪次關係，即$S_q(r)~r^{ζ_q}。濃度較高下的較強耦合可延伸此冪次關係到較大的r，這再次證明能量可藉由較強耦合傳遞到較大尺度的運動。ζ_q和q在兩種不同濃度下皆展現非線性關係，表示多重碎形或多重尺度率動力行為的存在，而這種動力行為在較高濃度下更為明顯。此外，我們發現延伸自我相似性(extend self-similarity ESS)亦存在於此兩種不同濃度的細菌紊流中。
二、自驅動紊流之抑制與調控：我們亦實驗證明利用被動順磁性微米尺度粒子可以調控細菌紊流。將直流電通入線圈中產生垂直於觀察面的外加磁場，順磁粒子(磁珠)被磁化產生磁偶極矩，磁珠間的縱向吸引力及橫向排斥力造成垂直於觀察面的磁珠鏈。縱向吸引力強到使磁珠鏈不被流場破壞，外加場施於磁珠鏈的回復力矩亦強到使其維持垂直方向而不被流場傾斜，再加上其長條形狀造成較大的拖曳阻力，磁珠鏈因此如同阻礙物般不易被細菌流場給推動。展現群體運動行為的細菌流場擁有長距離相關性，當某細菌團簇遇到運動較慢之磁珠鏈時，此局部阻礙資訊可藉由此長距離相關性快速傳播至整體團簇，造成團簇結構的破壞，於是能量較難傳遞至大尺度，使得較小波數及較低頻率的群體運動有較強的抑制。此研究提供一個方便的方法快速地控制細菌紊流。

摘要(英)

Bacterial suspension is a fundamental nonequilibrium system. At high cell concentration, the strong interplay of bacterial self-propelling force and the nonlinear bacterial couplings from the anisotropic excluded volume, chemical, and hydrodynamic interactions causes self-organized bacterial clusters. The coherent motion of clusters induces multiscaled flows with fluctuating vortices, which is so called {it bacterial turbulence} (BT). Opposite to inertia-dominated hydrodynamic turbulence (HT) and wave turbulence (WT), the energy in BT is injected from the cell level and transported to collective large scales. Whether BT exhibits similar dynamic behaviors to HT and WT is an important and open issue. In this thesis, using {it Escherichia coli} suspension at high cell concentration as a platform, for the first time, we experimentally address two important issues well studied in HT and WT: multifractal dynamics and turbulence reduction by passive additives.
The multifractal dynamics is investigated in thin liquid film at two different cell concentrations. The bacterial flow has fluctuating vortices with a broad range of scales and intensities through the nonlinear interaction of the swimming bacteria. Increasing cell concentration increases the total propelling power and the nonlinear interaction. It causes the generation of vortices with larger scale, lower frequency, and higher intensity. It also widens the histograms of the flow velocity and the velocity increment ν_r between two points separated by a distance r. The q-order structure functions S_q(r) of ν_r can be fitted by a power law function S_q(r)~r^{ζ_q}. Stronger intercell interaction at higher cell concentration can extend the power law relation toward larger r, indicating that the self-propelled energy can cascade to the larger scale. The nonlinear relation between the scaling exponent ζ_q and q are found for both cell concentrations, which manifests the multifractal dynamics. The multifractality can be enhanced by increasing cell concentration. It is also found that the extended self-similarity (ESS) exists in BT for both runs.
We also experimentally demonstrate BT reduction by passive magnetic chain additives. The micron-sized paramagnetic particles are added into bacterial suspensions. Applying an external magnetic field induces magnetic dipoles and causes the formation of chain bundles of magnetized particles. The larger effective drag from connected particles along chains, the anisotropic chain shape, and the chain alignment along the magnetic field reduce chain motion. Chains in turn form obstacles to slow down BT. The criticality feature due to the strong network of intercell interaction causes quick information propagation of local flow retardation. It causes the interruption of the upward energy flow from individual self-propelling bacteria to the larger scale in BT with multiscaled coherent flow, leading to more severe suppression in the low frequency (wave number) regimes of the power spectra. The study provides a new convenient method of quickly controlling BT for the various possible applications, through quickly turning on/off the $B$ field.

關鍵字(中)

★ 生物物理
★ 生物流體
★ 自驅動液體
★ 大腸桿菌
★ 群體運動
★ 紊流
★ 複碎形
★ 多重碎形
★ 紊流抑制
★ 阻力抑制

關鍵字(英)

★ bio-physics
★ bio-fluid
★ self-propelled fluid
★ E. coli
★ collective motion
★ turbulence
★ multifractal
★ multiscaling
★ turbulence reduction
★ drag reduction

論文目次

中文摘要 ............................................................ i
Abstract .......................................................... iii
Contents ............................................................ v
List of Figures ................................................... vii
1 Introduction ...................................................... 1
2 Background ........................................................ 6
2.1 Turbulent ow . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Bacterial ow . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Structure of E. coli . . . . . . . . . . . . . . . . . . . 9
2.2.2 Motion of single bacterium . . . . . . . . . . . . . . . . 9
2.2.3 Collective bacterial motions . . . . . . . . . . . . . . . 11
2.3 Structure function analysis . . . . . . . . . . . . . . . . . 14
3 Experimental Method .............................................. 17
3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . 17
3.2 System setup . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 System setup for freestanding liquid lm . . . . . . . . . 18
3.2.2 System setup of the concave glass slide . . . . . . . . . 20
3.3 Particle image velocimetry (PIV) . . . . . . . . . . . . . . . 21
4 Result and Discussion............................................. 25
4.1 Multifractal dynamics . . . . . . . . . . . . . . . . . . . . 25
4.1.1 Flow eld and time evolution . . . . . . . . . . . . . . . 26
4.1.2 Correlation and spectrum . . . . . . . . . . . . . . . . 28
4.1.3 Non-Gaussian velocity distribution functions and structure
functions . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Bacterial turbulence reduction . . . . . . . . . . . . . . . . 36
4.2.1 Flow eld and particle motions . . . . . . . . . . . . . . 37
4.2.2 Estimation of magnetization eect . . . . . . . . . . . . . 48
5 Conclusion ....................................................... 55
Bibliography ....................................................... 58

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指導教授

伊林(Lin I)

審核日期

2013-7-9

推文