主動流體的輸送現象

Transport Phenomena of Active Fluids

陳彥甫(Yen-Fu Chen)

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(2018年)

https://doi.org/10.6342/NTU201800297

摘要

主動流體為主動粒子如天然微生物或人造Janus膠體粒子所形成的分散液，其伴隨的非平衡現象近年來已引起了許多關注與討論。由於能量耗散，主動流體不遵循熱平衡系統的一般規則，故需要進一步研究。雖然大量的實驗研究已經展現主動流體的行為，但是實驗觀察仍然有局限性。例如，實驗較難捕捉到微觀層面的特徵；另外，實驗中也不方便去精準調控主動粒子的速度或使其呈現不同推進機制。介觀尺度模擬不僅可以補充實驗結果，亦提供一個可行的方法以獲得更多對主動流體的了解，期待對主動流體的發展或潛在應用有所幫助。
　　本論文採用耗散力子動力學模擬Run-and-tumble球狀主動布朗粒子（亦稱奈米泳體）分散液，以研究主動流體的輸送性質。藉由調整主動粒子的特性與系統的限制條件（牆或障礙物），可以確認這些主動流體展現的現象背後之根本原因。本文將會分成四個議題來探討：
　　在第一部分（第三章）中，探討了奈米泳體於漏斗型閘門隔開的兩腔室中展現的整流現象。根據穿越漏斗區之主動膠體粒子的軌跡，確定了兩種整流機制：幾何輔助擴散和陷阱受阻擴散。一般來說，幾何輔助擴散在小的主動力（F_a）和運行時間（τ）中占主導地位，而陷阱受阻擴散則在大的F_a和τ成為主要影響。整流比也受到漏斗閘門形狀影響，於此討論多種幾何形狀：開口/閉口的三角形、圓形和矩形漏斗。開口漏斗閘門引發的整流比例始終大於閉口漏斗的整流比例。而且，開口的圓形漏斗閘門性能最好，而三角形的最差。隨著漏斗閘門層數的增加，可以提高整流效果，甚至三層漏斗的整流比可以大大提高到30倍。我們的模擬研究為主動流體的強化整流提供了一個改善的方向。
　　在第二部分（第四章）中，探討了奈米泳體於半圓柱漏斗閘門所隔出的周期性腔室微流體通道中，所呈現的穩定棘輪輸送。每個腔室可區分為兩個區塊進行傳輸：整流和主動擴散區。濃度在整流區得到躍升（濃度梯度），而棘輪流動則受到主動擴散區中的擴散速率控制，這其中又可分為正常和努森（Knudsen）類型。前者擴散符合菲克（Fick）定律，與v_a^2 τ成正比（v_a是推進速度，τ是運行時間）。另外，與細菌地毯的機制類似，流體因為與漏斗附近聚集之奈米粒子交互作用（反向且對齊的力偶極），而被誘發出自主泵送。流體流動之方向與主動粒子之棘輪流動方向相同，但前者比後者小一個數量級。總體而言，流體速度取決於奈米泳體的特性。
　　在第三部分（第五章）中，探討了兩種主動膠體粒子—自泳動粒子（力偶極）和外場驅動粒子（單點力）—之主動擴散行為，其中被標記之流體粒子（溶劑）的自擴散也一併被研究。此研究歸結主動粒子的主動力、運行時間和濃度的影響。對於自泳動粒子而言，主動粒子及其溶劑皆展現正常擴散，且前者的擴散性明顯大於後者。對於外場驅動的粒子而言，主動粒子和溶劑皆進行超擴散，且前者的反常擴散指數（anomalous diffusion exponent）略小於後者。此反常擴散推論是由多體且遠距離的流力交互作用（hydrodynamic interactions）引起的。儘管存在超擴散，以沉降平衡測試外場驅動粒子分散液，密度分佈照常呈指數衰減；外場驅動粒子的沉降特徵長度總是大於自泳動粒子的沉降特徵長度。
　　在最後一部分（第六章）中，探討了泳體誘發主動流體的機械壓力增值。相對於沒有泳體的系統，主動流體的增量壓力（Π）包括泳體的直接貢獻（π）和流力交互作用的間接貢獻。壓力可以從內部總體與限制邊界來計算，對於主動流體，前者總是小於後者。稀薄條件下，π與泳體的主動擴散成正比，而Π隨著主動力和運行時間非線性增長。然而，由於流力交互作用對壓力的負貢獻，Π總是遠小於π。壁面壓力與泳體和壁面的相互作用有關，驗證了即使無力矩的主動流體，流力交互作用也可讓壓力不再是狀態函數。另外，在高濃度，相同Run-and-tumble參數的情況下，不同的流動模式（泳動類型：如推體和拉體）也會隨之造成Π的改變。

關鍵字

主動流體 ； 自泳動粒子 ； Run-and-tumble ； 耗散粒子動力學 ； 整流 ； 棘輪輸送 ； 擴散 ； 流力交互作用 ； 壓力

並列摘要

Active fluids, dispersions of active particles such as natural microorganisms or artificial Janus colloids, have attracted an extensive attention due to their out-of-equilibrium phenomena. Due to dissipation of energy, the active systems do not follow the general rules of thermal equilibrium systems and need further investigation. Numerous experimental studies have been shown to explore the behaviors of active fluids. However, experimental observations still possess the limitations. For instance, it is difficult to capture the features at microscopic level. Also, it is not convenient to manipulate the active particles exhibiting different speed or different propulsion mechanisms. Mesoscale simulations can complement the experimental results and provide a feasible method to obtain helpful insight for the development and possible applications of active fluids.
This dissertation adopts dissipative particle dynamics (DPD) to explore transport properties of active fluids by simulating dispersions of spherical run-and-tumble active particles (also viewed as nanoswimmers due to significant thermal fluctuations). By tuning the characteristics of active particles and the confining wall (or barriers), the fundamental causes of the phenomena of those fluids can be identified. There are four issues considered in this thesis:
In the first part (Chapter 3), rectification of run-and-tumble nanoswimmers in two chambers separated by a strip of funnel gates is explored. According to the trajectories of active colloids across the funnel zone, two rectification mechanisms are identified: the geometry-assisted diffusion and trap-hindered diffusion. In general, geometry-assisted diffusion dominates at small active force (F_a) and run time (τ) while trap-hindered diffusion governs at large F_a and τThe rectification ratio is affected by the funnel shape and various geometries are considered: open/closed triangular, circular and rectangular funnels. The rectification ratio of open funnels is always greater than that of closed funnels. Moreover, the open circular funnel has the best performance while the triangular one is the worst. The rectification can be enhanced as the number of the funnel layer is increased. It is found that rectification ratio of self-propelled colloids can be dramatically augmented by triple-layer funnels to be as high as 30. Our simulation study offers an efficient approach for the rectification enhancement.
In the second part (Chapter 4), the steady ratchet transport of run-and-tumble nanoswimmers in a 3D microfluidic channel constructed by periodic chambers separated by half-cylinder funnels is explored. Two regions in a chamber are identified: rectification and active diffusion. While the concentration gradient is driven by the concentration jump in the rectification region, the ratchet current is dominated by the diffusion rate in the active diffusion region, which is classified into normal and Knudsen types. The former obeys Fick’s law and is proportional to v_a^2 τ, where v_a is the propulsion velocity and τ the run time. In addition, autonomous pumping of fluids is induced by aligned force dipoles associated with nanoswimmers accumulated near funnels, similar to the mechanism of bacteria carpet. The direction of fluid flow is the same as that of the ratchet current but the former is one order of magnitude smaller than the latter. Thus, the fluid velocity depends on the characteristics of nanoswimmers.
In the third part (Chapter 5), the diffusive behaviors of active colloids with the run-and-tumble movement are explored for self-propelled particles (force dipole) and external field-driven particles (point force). The self-diffusion of tracers (solvent) is investigated as well. The influences of the active force, run time, and concentration associated with active particles are studied. For the system of self-propelled particles, the normal diffusion is observed for both active particles and tracers. The diffusivity of the former is significantly greater than that of the latter. For the system of field-driven particles, the superdiffusion is seen for both active particles and tracers. In contrast, it is found that the anomalous diffusion exponent of the former is slightly less than that of the latter. The anomalous diffusion is caused by the many-body, long-range hydrodynamic interactions. In spite of the superdiffusion, the sedimentation equilibrium of field-driven particles can be acquired and the density profile is still exponentially decayed. The sedimentation length of field-driven particles is always greater than that of self-propelled particles.
In the final part (Chapter 6), Mechanical pressure of active fluids in which swimmers are modeled by soft run-and-tumble spheres is investigated. The incremental pressure (Π) with respect to the system pressure without swimmers comprises direct contribution of swimmers (π) and indirect contribution of fluids associated with hydrodynamic interactions (HIs). The pressure can be determined from the bulk and confining wall and the former is always less than the latter. π of dilute active dispersions is proportional to their active diffusivity while Π grows generally with propulsive force and run time. However, Π is always substantially less than π because of negative contributions to pressure by HIs. The wall pressure depends on the swimmer-wall interactions, verifying that pressure is not a state function for torque-free active fluids due to HIs. Owing to distinct flow patterns, Π varies with the swim-type (pusher and puller) subject to the same run-and-tumble parameters at high concentrations.

並列關鍵字

Active fluid ； Self-propelled particle ； Run-and-tumble ； Dissipative particle dynamics (DPD) ； Rectification ； Ratchet current ； Diffusion ； Hydrodynamic interactions ； Pressure

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