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The mechanisms and properties of inertial microfluidics: from fundamental models to biomedical applications 惯性微流体的机理和特性:从基本模型到生物医学应用
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-25 DOI: 10.1007/s10404-023-02692-x
Shlok Mishra, Joydeb Mukherjee, Deepa Chaturvedi, Ratnesh Jain, Prajakta Dandekar

With continuous efforts of researchers all over the world, the field of inertial microfluidics is constantly growing, to cater to the requirements of diverse areas like healthcare, biological and chemical analysis, materials synthesis, etc. The scale, automation, or unique physics of these systems has been expanding their scope of applications. In this review article, we have provided insights into the fundamental mechanisms of inertial microfluidics, the forces involved, the interactions and effects of different applied forces on the suspended particles, the underlying physics of these systems, and the description of numerical studies, which are the prime factors that govern designing of effective and practical devices.. Further, we describe how various forces lead to the migration and focusing of suspended particles at equilibrium positions in channels with different cross-sections and also review various factors affecting the same. We also focus on the effect of suspended particles on the flow of fluids within these systems. Furthermore, we discuss how Dean flows are created in a curved channel and how different structures affect the creation of secondary flows, and their application to mixing, manipulating, and focusing particles as fluid. Finally, we describe various applications of microfluidics for diagnostic and other clinical purposes, and discuss the challenges and advancements in this field. We anticipate that this manuscript will elucidate the basics and quantitative aspects of inertial fluid dynamic effects for application in biomedicines, materials synthesis, chemical process control, and beyond.

Graphical abstract

随着世界各地研究人员的不断努力,惯性微流体领域正在不断发展,以满足医疗保健、生物和化学分析、材料合成等不同领域的要求。这些系统的规模、自动化或独特的物理特性不断扩大其应用范围。在这篇综述文章中,我们深入了解了惯性微流体的基本机制、所涉及的力、不同作用力对悬浮颗粒的相互作用和影响、这些系统的基本物理特性以及数值研究的描述,这些都是控制有效和实用装置设计的主要因素。。此外,我们描述了各种力如何导致悬浮颗粒在不同横截面通道中平衡位置的迁移和聚焦,并回顾了影响迁移和聚焦的各种因素。我们还关注悬浮颗粒对这些系统内流体流动的影响。此外,我们还讨论了Dean流是如何在弯曲通道中产生的,不同的结构如何影响二次流的产生,以及它们在混合、操纵和聚焦作为流体的粒子方面的应用。最后,我们描述了微流体在诊断和其他临床目的中的各种应用,并讨论了该领域的挑战和进展。我们预计,这篇手稿将阐明惯性流体动力学效应的基础和定量方面,用于生物医学、材料合成、化学过程控制等领域。图形摘要
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引用次数: 1
Particle separation based on dielectrophoresis force using boundary element method and point-particle approach in a microfluidic channel 微流体通道中基于介电电泳力的边界元法和点粒子法粒子分离
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-24 DOI: 10.1007/s10404-023-02694-9
Mostafa Olfat, Erfan Kadivar

Active sorting of particle in the dielectrophoresis microfluidic channel by applying the boundary element method and point-particle approach is investigated. In this paper, we investigate the dynamics of particle sorting for various particle sizes, electrode potential, electrode spacing, and relative permittivity. The microfluidic device consists a straight mother channel, two inlets, two outlets, and up and down triangular electrodes. The boundary element method is applied to numerically solve the integral equations of the Laplace differential equation of electric potential and Stokes differential equation. In continue, the dynamics of particle separation using the point-particle approach is investigated. Numerical results indicate that there are three different particle sorting regimes. They are called by up-outlet, down-outlet, and trapped regimes. The results illustrate that there are a good agreement between two numerical approaches.

应用边界元法和点粒子法研究了介电电泳微流体通道中粒子的主动分选。在本文中,我们研究了不同颗粒尺寸、电极电势、电极间距和相对介电常数的颗粒分选动力学。微流体装置由一个直的母通道、两个入口、两个出口和上下三角形电极组成。应用边界元法对拉普拉斯电位微分方程和斯托克斯微分方程的积分方程进行了数值求解。在继续,使用点粒子方法研究粒子分离的动力学。数值结果表明,存在三种不同的颗粒分选方式。它们被上行出口、下行出口和受困政权所召唤。结果表明,两种数值方法之间有很好的一致性。
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引用次数: 0
Flow synthesis of 1-ethyl-3-methylimidazolium ethyl sulfate in a PTFE micro-capillary: an experimental and numerical study PTFE毛细管流动合成1-乙基-3-甲基咪唑硫酸乙酯的实验与数值研究
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-23 DOI: 10.1007/s10404-023-02686-9
Nirvik Sen, K. K. Singh, S. Mukhopadhyay, K. T. Shenoy

In this work, we have reported continuous flow synthesis of 1-ethyl-3-methylimidazolium ethyl sulfate ionic liquid in a PTFE micro-capillary. A Y-shaped microfluidic junction is used to mix the incoming reactants. Effects of independent parameters like velocity, reaction temperature, and micro-capillary diameter on product yield, rate of production, and space–time yield are reported. Yield is seen to increase monotonically as reaction temperature is increased, while it reduces with an increase in diameter of the micro-capillary. A maxima in yield is observed as flow velocity is increased. A space–time yield of 1258.4 g/min.L is obtained at a reaction temperature of 80 0C using a 300 µm micro-capillary. A two-dimensional computational fluid dynamics (CFD) model of the reacting system has been developed to confirm and explain the observed experimental trends. The simulations were able to qualitatively predict the experimental trends. The simulations also investigated the effect of shapes of different obstacles placed in the flow path.

在本工作中,我们报道了在PTFE微毛细管中连续流动合成1-乙基-3-甲基咪唑鎓硫酸乙酯离子液体。Y形微流体接头用于混合进入的反应物。报道了速度、反应温度和微毛细管直径等独立参数对产物产率、产率和时空产率的影响。产率随着反应温度的升高而单调增加,而随着微毛细管直径的增加而降低。随着流速的增加,观察到产量的最大值。使用300µm微毛细管在80℃的反应温度下获得1258.4 g/min.L的时空产率。已经开发了反应系统的二维计算流体动力学(CFD)模型,以证实和解释观察到的实验趋势。模拟能够定性地预测实验趋势。模拟还研究了流动路径中不同障碍物形状的影响。
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引用次数: 0
On the behavior of prolate spheroids in a standing surface acoustic wave field 长椭球体在驻波场中的行为
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-21 DOI: 10.1007/s10404-023-02690-z
Sebastian Sachs, Hagen Schmidt, Christian Cierpka, Jörg König

The active manipulation of particle and cell trajectories in fluids by high-frequency standing surface acoustic waves (sSAW) allows to separate particles and cells systematically depending on their size and acoustic contrast. However, process technologies and biomedical applications usually operate with non-spherical particles, for which the prediction of acoustic forces is highly challenging and remains a subject of ongoing research. In this study, the dynamical behavior of prolate spheroids exposed to a three-dimensional acoustic field with multiple pressure nodes along the channel width is examined. Optical measurements reveal an alignment of the particles orthogonal to the pressure nodes of the sSAW, which has not been reported in literature so far. The dynamical behavior of the particles is analyzed under controlled initial conditions for various motion patterns by imposing a phase shift on the sSAW. To gain detailed understanding of the particle dynamics, a three-dimensional numerical model is developed to predict the acoustic force and torque acting on a prolate spheroid. Considering the acoustically induced streaming around the particle, the numerical results are in excellent agreement with experimental findings. Using the proposed numerical model, a dependence of the acoustic force on the particle shape is found in relation to the acoustic impedance of the channel ceiling. Hence, the numerical model presented herein promises high progress for the design of separation devices utilizing sSAW, exploiting an additional separation criterion based on the particle shape.

通过高频驻波(sSAW)对流体中粒子和细胞轨迹的主动操纵,可以根据粒子和细胞的大小和声学对比度系统地分离粒子和细胞。然而,工艺技术和生物医学应用通常使用非球形颗粒,对其声学力的预测极具挑战性,并且仍然是正在进行的研究的主题。在本研究中,研究了长椭球体在沿通道宽度具有多个压力节点的三维声场中的动力学行为。光学测量揭示了粒子与sSAW的压力节点正交的排列,这在迄今为止的文献中尚未报道。通过对sSAW施加相移,分析了在受控的初始条件下各种运动模式下粒子的动力学行为。为了获得对粒子动力学的详细理解,建立了一个三维数值模型来预测作用在椭球上的声学力和力矩。考虑到颗粒周围的声学诱导流动,数值结果与实验结果非常一致。使用所提出的数值模型,发现了声力对颗粒形状的依赖性与通道顶部的声阻抗有关。因此,本文提出的数值模型有望在利用sSAW的分离装置设计方面取得巨大进展,利用了基于颗粒形状的额外分离标准。
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引用次数: 0
Flow rate variations in microfluidic circuits with free surfaces 具有自由表面的微流体回路中的流速变化
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-19 DOI: 10.1007/s10404-023-02691-y
Taha Messelmani, Isabela Zarpellon Nascimento, Eric Leclerc, Cécile Legallais, Adam Meziane, William César, Rachid Jellali, Anne Le Goff

We investigate analytically and experimentally the flow rate through a biochip in a circuit involving a peristaltic pump and reservoirs with liquid/air interfaces. Peristaltic pumps are a convenient way to achieve recirculation in microfluidic circuits. We consider different cases: reservoirs in contact with ambient air, tight reservoirs, and imperfect tightness leading to air or liquid leaks. We demonstrate that if changes in hydraulic resistance are slow enough, i.e., if cells do not proliferate too fast, the system may reach an equilibrium, with a difference in liquid height between inlet and outlet reservoir compensating the pressure drop in the biochip. We compute the flow rate through the biochip in the transient regime as well as the characteristic time. We also show that depending on the circuit dimensions, this equilibrium may never be reached. We provide guidelines to design tubings and reservoirs to avoid this situation and ensure a smooth recirculation at a desired flow rate, which is a necessary condition for dynamic cell culture.

我们通过分析和实验研究了在包括蠕动泵和具有液体/空气界面的储存器的电路中通过生物芯片的流速。蠕动泵是在微流体回路中实现再循环的一种方便方式。我们考虑不同的情况:储液器与环境空气接触,储液器密封,以及导致空气或液体泄漏的不完全密封。我们证明,如果水力阻力的变化足够慢,即如果细胞增殖不太快,系统可能会达到平衡,入口和出口储液器之间的液体高度差会补偿生物芯片中的压降。我们计算了在瞬态状态下通过生物芯片的流速以及特征时间。我们还表明,根据电路的尺寸,这种平衡可能永远不会达到。我们提供了设计管道和储液器的指南,以避免这种情况,并确保在所需流速下顺利再循环,这是动态细胞培养的必要条件。
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引用次数: 0
A compact modularized power-supply system for stable flow generation in microfluidic devices 一种用于微流体装置中稳定流动产生的紧凑型模块化电源系统
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-19 DOI: 10.1007/s10404-023-02693-w
Weihao Li, Wuyang Zhuge, Youwei Jiang, Kyle Jiang, Jun Ding, Xing Cheng

The miniaturization of microfluidic systems plays a pivotal role in achieving portability and compactness. However, conventional microfluidic systems heavily rely on external bulky facilities, such as syringe pumps and compressed air supplies, for continuous flow, which restricts their dissemination across various applications. To address this limitation, micropumps have emerged as a potential solution for portable power supply in microfluidic systems, with piezoelectric micropumps being widely adopted. Nonetheless, the inherent pulsatile mechanism of piezoelectric micropumps leads to unstable flow, necessitating appropriate mitigation for applications requiring flow stability. This research introduces an innovative hybrid pumping system that integrates a wirelessly controlled micropump with a 3D-printed modular microfluidic low-pass-filter. The primary objective of this system is to offer a portable and stable flow source for microfluidic applications. The system design and characterization are based on a three-element circuit model. Experimental results demonstrate a highly stabilized flow rate of 657 ± 7 µL/min. Furthermore, the versatility of the system is showcased by successfully forming droplets with a polydispersity ranging from 1.5% to 4%, comparable to that of bulky commercial pumping systems. This hybrid pumping system offers a promising solution for applications necessitating portable and stable flow sources, and its reconfigurability suggests potential integration into multifunctional microfluidic platforms.

微流体系统的小型化在实现便携性和紧凑性方面发挥着关键作用。然而,传统的微流体系统严重依赖外部庞大的设施,如注射泵和压缩空气供应,以实现连续流动,这限制了它们在各种应用中的传播。为了解决这一限制,微泵已成为微流体系统中便携式电源的潜在解决方案,压电微泵被广泛采用。尽管如此,压电微泵固有的脉动机制会导致流动不稳定,因此需要对需要流动稳定性的应用进行适当的缓解。本研究介绍了一种创新的混合泵送系统,该系统将无线控制的微型泵与3D打印的模块化微流体低通过滤器集成在一起。该系统的主要目标是为微流体应用提供便携式和稳定的流动源。系统的设计和表征是基于三元件电路模型。实验结果表明,657的流量高度稳定 ± 7µL/min。此外,该系统的多功能性通过成功形成多分散性在1.5%至4%范围内的液滴而得到展示,与大型商业泵送系统相当。这种混合泵送系统为需要便携式和稳定流源的应用提供了一种很有前途的解决方案,其可重新配置性表明有可能集成到多功能微流体平台中。
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引用次数: 0
A mould-free soft-lithography approach for rapid, low-cost and bulk fabrication of microfluidic chips using photopolymer sheets 一种无模软光刻方法,用于使用光聚合物片材快速、低成本和批量制造微流控芯片
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-10 DOI: 10.1007/s10404-023-02688-7
R. Rahul, Nikhil Prasad, R. R. Ajith, P. Sajeesh, R. S. Mini, Ranjith S. Kumar

Most of the existing microfluidic chip fabrication techniques are very complex, time-consuming, costly, and are not amenable to mass manufacturing. Impending commercialization of lab-on-a-chip devices demand development of new microfabrication methods that involve least procedural complexities using cost-effective materials. This paper proposes an inexpensive and time-efficient procedure for constructing microfluidic devices on a flexographic sheet which is available as commercial-off-the-shelf material, using a mould-free soft-lithography approach. Microchannel design is transferred to a negative-resist photopolymer sheet (PPS) using collimated ultraviolet (UV) rays and etching is performed to remove unexposed material. The microchannel network is sealed on the top by a photopolymer sheet of the same material and pressure-assisted bonding is performed in the presence of UV. The cross-linking between photopolymers in the mating surfaces ensures relatively high bond strength and perfect sealing. Simple and complex microchannel network with 100–500 (upmu)m width is created using this method and various characterization tests are performed. A functional leakage test ensured that the fabricated chip could withstand 200 kPa pressure at a maximum flow rate of 12 mL/min. Cell culture, biomolecule visualization, and droplet mixing dynamics are studied in the microchip to demonstrate its practical utility. Moreover, a large-area chip with 260 (times) 190 mm(^2) is created using PPS with this three-step method. Most importantly, this method could mass produce 24 microchips with multiple designs within a span of 2 h. In other words, the average time incurred for the fabrication of a single microchip (50 (times) 30 mm(^2)) is less than 5 min. Results suggest that it is a promising method flexible enough to create large-sized chips and to bulk-fabricate microchips having versatile channel designs with high fidelity. Since flexographic infrastructure and materials are very cheap and common in resource-limited settings, the proposed method assumes more importance in the context of rapid commercialization of lab-on-a-chip devices.

现有的微流控芯片制造技术大多复杂、耗时、成本高,不适合批量生产。即将商业化的芯片实验室设备需要开发新的微加工方法,这些方法涉及的程序复杂性最小,使用成本效益高的材料。本文提出了一种廉价且省时的方法,用于在柔性版片上构建微流体装置,该柔性版片可作为商业现成材料使用,使用无模软光刻方法。微通道设计被转移到负阻光敏聚合物片(PPS)使用准直紫外线(UV)射线和蚀刻进行去除未暴露的材料。微通道网络在顶部由相同材料的光聚合物片密封,并在紫外线存在下进行压力辅助键合。配合表面的光聚合物之间的交联确保了相对较高的结合强度和完美的密封性。使用该方法创建了100-500 (upmu) m宽度的简单和复杂微通道网络,并进行了各种表征测试。通过功能泄漏测试,确保制作的芯片能够承受200 kPa的压力,最大流量为12 mL/min。细胞培养,生物分子可视化和液滴混合动力学在微芯片的研究,以证明其实际用途。此外,还利用该三步法制作出了260 (times) 190 mm (^2)的PPS大面积芯片。最重要的是,这种方法可以在2小时内批量生产24个具有多种设计的微芯片。换句话说,制造单个微芯片(50 (times) 30 mm (^2))的平均时间不到5分钟。结果表明,这是一种有前途的方法,足够灵活,可以制造大尺寸芯片,并批量制造具有高保真度的多通道设计的微芯片。由于柔版基础设施和材料在资源有限的环境中非常便宜和常见,因此所提出的方法在芯片实验室设备快速商业化的背景下更为重要。
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引用次数: 0
Synthesis of tunable gold nanostars via 3D-printed microfluidic device with vibrating sharp-tip acoustic mixing 基于尖端振动混音的3d打印微流控装置合成可调谐金纳米星
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-08 DOI: 10.1007/s10404-023-02687-8
Kathrine Curtin, Toktam Godary, Peng Li

Gold nanostars are valuable materials for nanomedicine, energy conversation, and catalysis. Microfluidic synthesis offers a simple and controlled means to produce nanoparticles as they offer precise fluid control and improve heat and mass transfer. 3D-printed microfluidics are a good alternative to PDMS devices because they are affordable to produce and can be more easily integrated with active mixing strategies. 3D-printed microfluidics has only been applied to the production of silver and gold nanospheres, but not complex structures like gold nanostars. Synthesis of gold nanostars requires highly effective mixing to ensure uniform nucleation and growth. In this work, we present a 3D-printed microfluidic device that utilizes an efficient vibrating sharp-tip acoustic mixing system to produce high-quality and reproducible gold nanostars via a seedless and surfactant-free method. The vibrating sharp-tip mixing device can mix three streams of fluid across ~ 300 μm within 7 ms. The device operates with flow rates ranging from 10 μL/min to 750 μL/min at low power requirements (2–45 mW). The optical properties of the resulting nanotars are easily tuned from 650 to 800 nm by modulating the input flow rate. Thus, the presented 3D-printed microfluidic device produces high-quality gold nanostars with tunable optical and physical properties suitable for extensive applications.

金纳米恒星是纳米医学、能量转换和催化等领域的宝贵材料。微流控合成提供了一种简单而可控的方法来生产纳米颗粒,因为它们提供了精确的流体控制,并改善了传热和传质。3d打印微流体是PDMS设备的一个很好的替代品,因为它们生产成本低廉,并且可以更容易地与主动混合策略集成。3d打印的微流体只应用于生产银和金纳米球,而不是像金纳米星这样复杂的结构。金纳米恒星的合成需要高度有效的混合,以确保均匀的成核和生长。在这项工作中,我们提出了一种3d打印的微流体装置,该装置利用有效的振动尖尖声学混合系统,通过无籽和无表面活性剂的方法产生高质量和可重复的金纳米星。振动尖尖混合装置可在7ms内混合~ 300 μm范围内的三股流体。该装置在低功率要求(2-45 mW)下的流量范围为10 μL/min至750 μL/min。通过调节输入流量,可以很容易地在650 ~ 800 nm范围内调节纳米晶的光学特性。因此,所提出的3d打印微流体装置可生产具有可调光学和物理特性的高质量金纳米星,适合广泛应用。
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引用次数: 0
Stiffness influence on particle separation in polydimethylsiloxane-based deterministic lateral displacement devices 刚度对聚二甲基硅氧烷确定性侧向位移装置中颗粒分离的影响
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-10-05 DOI: 10.1007/s10404-023-02685-w
Julius Marhenke, Tobias Dirnecker, Nicolas Vogel, Mathias Rommel

Polydimethylsiloxane (PDMS) is a popular material to rapidly manufacture microfluidic deterministic lateral displacement (DLD) devices for particle separation. However, manufacturing and operation challenges are encountered with decreasing device dimensions required to separate submicron particles. The smaller dimensions, notably, cause high hydraulic resistance, resulting in significant pressure even at relatively low throughputs. This high pressure can lead to PDMS deformation, which, in turn, influences the device performance. These effects may often be overlooked in the design and operation of devices but provide a systematic source of error and inaccuracies. This study focuses in detail on these effects and investigates pillar deformation in detail. Subsequently, we discuss a potential solution to this deformation using thermal annealing to stiffen the PDMS. We evaluate the influence of stiffness on the separation performance at elevated sample flow rates with submicron particles (0.45 and 0.97 µm diameter). An excellent separation performance at high throughput is successfully maintained in stiffer PDMS-based DLD devices, while the conventional devices showed decreased separation performance. However, the increased propensity for delamination constrains the maximal applicable throughput in stiffer devices. PDMS deformation measurements and numerical simulations are combined to derive an iterative model for calculating pressure distribution and PDMS deformation. Finally, the observed separation characteristics and encountered throughput constraints are explained with the iterative model. The results in this study underline the importance of considering pressure-induced effects for PDMS-based DLD devices, provide a potential mitigation of this effect, and introduce an approach for estimating pressure-induced deformation.

聚二甲基硅氧烷(PDMS)是快速制造微流体确定性侧向位移(DLD)颗粒分离装置的常用材料。然而,随着分离亚微米颗粒所需的设备尺寸不断减小,制造和操作面临挑战。值得注意的是,较小的尺寸会产生较高的水力阻力,即使在相对较低的吞吐量下也会产生显著的压力。这种高压会导致PDMS变形,进而影响器件性能。这些影响在设备的设计和操作中可能经常被忽视,但却提供了错误和不准确的系统来源。本研究详细地研究了这些影响,并详细地研究了矿柱的变形。随后,我们讨论了使用热退火来加强PDMS的变形的潜在解决方案。我们评估了刚度对亚微米颗粒(直径0.45和0.97µm)在高流速下分离性能的影响。刚性pdms DLD器件在高通量下保持了优异的分离性能,而传统器件的分离性能下降。然而,在较硬的器件中,分层倾向的增加限制了最大适用吞吐量。PDMS变形测量与数值模拟相结合,导出了计算压力分布和PDMS变形的迭代模型。最后,用迭代模型解释了观察到的分离特性和遇到的吞吐量约束。本研究的结果强调了考虑基于pdm的DLD器件的压力诱导效应的重要性,提供了一种潜在的缓解这种效应的方法,并介绍了一种估计压力诱导变形的方法。
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引用次数: 0
Viscous and thermal velocity slip coefficients via the linearized Boltzmann equation with ab initio potential 用从头算势线性化玻尔兹曼方程求解粘速和热速滑移系数
IF 2.8 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Pub Date : 2023-09-30 DOI: 10.1007/s10404-023-02681-0
Thanasis Basdanis, Dimitris Valougeorgis, Felix Sharipov

The viscous and thermal velocity slip coefficients of various monatomic gases are computed via the linearized classical Boltzmann equation, with ab initio potential, subject to Maxwell and Cercignani–Lampis boundary conditions. Both classical and quantum interatomic interactions are considered. Comparisons with hard sphere and Lennard–Jones potentials, as well as the linearized Shakhov model are performed. The produced database is dense, covers the whole range of the accommodation coefficients and is of high accuracy. Using symbolic regression, very accurate closed form expressions of the slip coefficients, easily implemented in the future computational and experimental works, are deduced. The thermal slip coefficient depends, much more than the viscous one, on the intermolecular potential. For example, in the case of diffuse scattering, the relative differences in the viscous slip coefficient data between HS and AI potentials are less than 4%, whilst the corresponding ones in the thermal slip coefficient data are about 6% for He, reaching 15% for Xe. Quantum effects are considered for He, at temperatures 1–104 K to deduce that deviations from the classical behaviour are not important in the viscous slip coefficient, but they become important in the thermal slip coefficient, where the differences between the classical and quantum approaches reach 15% at 1 K. The computational effort of solving the linearized Boltzmann equation with ab initio and Lennard–Jones potentials is the same. Since ab initio potentials do not contain any adjustable parameters, it is recommended to use them at any temperature.

在Maxwell和Cercignani-Lampis边界条件下,利用线性化的经典玻尔兹曼方程计算了各种单原子气体的粘性和热速度滑移系数。考虑了经典和量子原子间的相互作用。与硬球势和Lennard-Jones势以及线性化的Shakhov模型进行了比较。所建立的数据库密度大,涵盖了调节系数的全部范围,精度高。利用符号回归,推导出滑移系数的精确封闭表达式,便于以后的计算和实验工作实现。热滑移系数比粘滑移系数更多地取决于分子间势。例如,在漫射散射情况下,HS势和AI势的粘性滑移系数数据的相对差值小于4%,而He势的热滑移系数数据的相对差值约为6%,Xe势的相对差值达到15%。在1 - 104 K的温度下,He考虑了量子效应,以推断出与经典行为的偏差在粘性滑移系数中并不重要,但它们在热滑移系数中变得重要,其中经典方法和量子方法之间的差异在1 K时达到15%。用从头算和Lennard-Jones势解线性化玻尔兹曼方程的计算量是相同的。由于从头算电位不包含任何可调参数,因此建议在任何温度下使用。
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Microfluidics and Nanofluidics
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