非牛顿流体电动力学外文文献翻译@中英文翻译@外文翻译

论文翻译 原文： Electrokinetics of non-Newtonian fluids: A review ABSTRACT This work presents a comprehensive review of electrokinetics pertaining to non-Newtonian fluids. The topic covers a broad range of non-Newtonian effects in electrokinetics, including electroosmosis of non-Newtonian fluids, electrophoresis of particles in non-Newtonian fluids, streaming potential effect of non-Newtonian fluids and other related non-Newtonian effects in electrokinetics. Generally, the coupling between non-Newtonian hydrodynamics and electrostatics not only complicates the electrokinetics but also causes the fluid/particle velocity to be nonlinearly dependent on the strength of external electric field and/or the zeta potential. Shear-thinning nature of liquids tends to enhance electrokinetic phenomena, while shear-thickening nature of liquids leads to the reduction of electrokinetic effects. In addition, directions for the future studies are suggested and several theoretical issues in non-Newtonian electrokinetics are highlighted. 1. Introduction The recently growing interests in electrokinetic phenomena are triggered by their diverse applications in microfluidic devices which could have the potential to revolutionize conventionalways of chemical analysis,medical diagnostics, material synthesis, drug screening and delivery aswell as environmental detection andmonitoring. The prevalent use of electrokinetic techniques in microfluidic devices is ascribed to their several distinctive advantages: (i) the devices are energized by electricitywhich is widely available and ease of control； (ii) the devices involve no moving parts and thus less mechanical failures； (iii) the induced velocity of liquid or particle is independent of geometric dimensions of devices； (iv) the devices can be readily integrated with other electronic controlling units to achieve fully-automated operation. In addition to its useful applications in microfluidics, electrokinetics is also a basis for understanding various phenomena, such as ionic transport and rectification in nanochannels 1,2, thermophoresis in aqueous solutions 3,4, electrowetting of electrolyte solutions 5,6 and so on. When a solid surface is brought into contact with an electrolyte solution, the solid surface obtains electrostatic charges. The presence of such surface charges causes redistribution of ions and then forms a charged diffuse layer in the electrolyte solution near the solid surface to naturalize the electric charges on solid surface. Such electrically nonneutral diffuse layer is usually dubbed electric double layer (EDL) which is responsible for two categories of electrokinetic phenomena, (i) electrically-driven electrokinetic phenomena and (ii) nonelectrically-driven electrokinetic phenomena. The basic physics behind the first category is as follows: when an external electric field is applied tangentially along the charged surface, the charged diffuse layer experiences an electrostatic body force which produces relativemotion between the charged surface and the liquid electrolyte solution. The liquid motion relative to the stationary charged surfaces is known as electroosmosis (Fig. 1a), and the motion of charged particles relative to the stationary liquid is known as electrophoresis (Fig. 1b). The classic electroosmosis occurs around solids with fixed surface charges (or, equivalently, zeta potential ) for given physiochemical properties of surface and solution, and then the effective liquid slip at the solid surface under the situation of thin EDLs is quantified by the well-known Helmholtz Smoluchowski velocity, i.e., us = E0/ ( is the electric permittivity of the electrolyte solution, is the zeta potential of the solid surface, E0 is the external electric field strength and is the dynamic viscosity of electrolyte solution). When a charged particle with a thin EDL is freely suspended in a stationary liquid electrolyte solution, electroosmotic slip motion of solution molecules on the particle surface induces the electrophoretic motion of particle with a velocity given by the Smoluchowski equation, U = E0/ (Note that here denotes the zeta potential of particle). One typical behavior of the second category is the generation of streaming potential effect in pressure-driven flows (Fig. 1c). There are surplus counterions in EDLs adjacent to the channel walls, and the pressuredriven flow convects these counterions downstream to gives rise to a streaming current. Simultaneously, the depletion (accumulation) of counterions in the upstream (downstream) sets up a streaming potential which drives a conduction current in opposite direction to the streaming current. At the steady state, the conduction current exactly counter-balances the streaming current, and the streaming potential built up across the channel under the limit of thin EDLs is given by Es = P/(0) (P is externally applied pressure gradient and 0 represents the bulk conductivity of electrolyte solution). More fundamental and comprehensive descriptions of electrokinetic phenomena are given in textbooks and reviews 7 13. Previous description of electrokinetics usually assumes Newtonian fluids with constant liquid viscosity, and most studies of electrokinetics in literature adopt such assumption. But in reality, microfluidic devices are more frequently involved in analyzing and/or processing biofluids (such as solutions of blood, saliva, protein and DNA), polymeric solutions and colloidal suspensions. These fluids cannot be treated as Newtonian fluids. Therefore, the characterization of hydrodynamics of such non-Newtonian fluids relies on the general Cauchy momentum equation in conjunction with proper constitutive equations which generally define the viscosity of liquid to vary with the rate of hydrodynamic shear, rather than the Navier Stokes equation which is only applicable to Newtonian fluids. Since electrokinetics results from the coupling of hydrodynamics and electrostatics, it is straightforward to believe that non-Newtonian hydrodynamics would modify the conventional Newtonian electrokinetics. In this review, non-Newtonian effects on electrokinetics are comprehensively summarized and discussed. This review is organized as follows: Section 2 provides a review on the most widelystudied electroosmosis of non-Newtonian fluids. Section 3 presents a review for the electrophoresis of particles in non-Newtonian fluids, and Section 4 discusses the streaming potential effects of non-Newtonian fluids. Other non-Newtonian effects of particular interest on electrokinetics are given in Section 5. Lastly, Section 6 concludes the review and identifies the directions for the future studies. 2. Electroosmosis of non-Newtonian fluids The pioneering contribution to this field is probably attributed to Bello et al. 14 who experimentally measured an electroosmotic flow of a polymer (methyl cellulose) solution in a capillary. Their investigation showed that the electroosmotic velocity of such polymer solution is much higher than that predicted with the classic Helmholtz Smoluchowski velocity. It was then proposed that the shear-thinning induced by polymermolecules lowers the effective fluid viscosity inside the EDL. About a decade later, more interests were paid to such phenomenon both experimentally and theoretically. Chang and Tsao 15 conducted an experiment similar to that of Bello et al. 14 to investigate an electroosmotic flowof the polyethylene glycol solution and observed that the drag aswell as the effective viscositywas greatly reduced due to the sheared polymericmolecules inside the EDL. On theoretical aspects, recent efforts have resulted in a great deal of information on electroosmotic flows of non-Newtonian fluids. Specifically, non-Newtonian effects are characterized by proper constitutive models which relate the dynamic viscosity and the rate of shear. There has been a large class of constitutive models available in the literature for analyzing the non-Newtonian behavior of fluids, such as power-law model, Carreau model, Bingham model, Oldroyd-B model, Moldflow second-order model and so on. Power-law fluid model is certainly the most popular because it is simple and able to fit awide range of non-Newtonian fluids. One important parameter in the power law fluid model is the fluid behavior index (n) which delineates the dependence of the dynamic viscosity on the rate of shear. If n is smaller (greater) than one, the fluids demonstrate the shear-thinning (shear-thickening) effect that the viscosity of fluid decreases with the increase (decrease) of the rate of shear. If n is equal to one, the fluids then exactly behave as Newtonian fluids. Das and Chakraborty 16 obtained the first approximate solution for electroosmotic velocity distributions of power-law fluids in a parallel-plate microchannels. However, their analysis did not clearly address the effect of non-Newtonian effects on electroosmotic flows. Zhao et al. 17,18 carried out theoretical analyses of electroosmosis of power-law fluids in a slit parallel-plate microchannel and fully discussed the non-Newtonian effects on electroosmotic flow. Their analyses revealed that the fluid rheology substantially modifies the electroosmotic velocity profiles and electroosmotic pumping performance. Particularly, they derived a generalized Helmholtz Smoluchowski velocity for power-lower fluids in a similar fashion to the classic Newtonian Smoluchowski velocity and further elaborated the influencing factors of such velocity. Similar analyses were later extended to a cylindrical microcapillary by Zhao and Yang 19,20. Recently, an experimental investigation was performed by Olivares et al. 21 who measured the electroosmotic flow rate of a non-Newtonian polymeric (Carboxymethyl cellulose) solution, and their experimental measurements agree well with the theoretical results predicted from the generalized Helmholtz Smoluchowski velocity of power-law fluids. Paul 22 conceptually devised a series of fluidic devicesemploying electroosmosis of shear-thinning fluids. These devices included pumps, flow controllers, diaphragmvalves and displacement systemswhichwere all claimed to outperform their counterparts employing Newtonian fluids. Berli and Olivares 23 addressed the electrokinetic flow of non- Newtonian fluids in microchannels with the depletion layers near channel walls. Their analysis essentially considered a combined effect of electroosmosis and pressure-driven flow, and is greatly simplified due to the presence of depletion layers. Berli 24 evaluated the thermodynamic efficiency for electroosmotic pumping of power-law fluids in cylindrical and slit microchannels. It was revealed that both the output pressure and pumping efficiency for shear-thinning fluids could be several times higher than those for Newtonian fluids under the same experimental conditions. Utilizing the Lattice Boltzmann method, Tang et al. 25 numerically investigated the electroosmotic flow of power-law fluids in microchannels. An electroosmotic body force was incorporated in the Bhatnagar Gross Krook collision approximation which simulates the Cauchy momentum equation. These studies of electroosmotic flow of non-Newtonian fluids however all assumed small surface zeta potentials which are much less than the so-call thermal voltage, i.e., kBT/(ze), where kB is the Boltzmann constant, T is the absolute temperature, e is the elementary charge, z denotes the valence of electrolyte ion. This assumption could be easily violated when large surface zeta potentials are present. Therefore, investigations of electroosmotic flow of power-law fluids over solid surfaces with arbitrary surface zeta potentials were reported in 26,27. However, the constitutive model for non-Newtonian fluids in abovementioned investigations is just an extreme case of the more general non-Newtonian Carreau fluid model. In comparison with the Newtonian fluid model, Carreau constitutive model includes five additional parameters and can describe the rheology of a wide range of non-Newtonian fluids. Under the limit of zero shear rates, the commonly used power-lawmodelwould predict an infinitely large viscosity for shear-thinning fluids, while the Carreau model does not have such defect but has smoothly transits to a constant viscosity. The Carreau fluid model can well characterize the rheology of various polymeric solutions, such as glycerol solutions of 0.3% hydroxyethyl-cellulose Natrosol HHX and 1% methylcellulose Tylose 28, and pure poly(ethylene oxide) 29. These polymers arewidely used for improving selectivity and resolution in the capillary electrophoresis for separation of protein 30 and DNA 31. Zimmerman et al. 32,33 performed finite element numerical simulations of the electroosmotic flow of a Carreau fluid in a microchannel T-junction. The analyses suggested that the flow field remarkably depends on the non-Newtonian characteristics of fluids, and therefore could guide the design of electroosmotic flow rheometers. Zhao and Yang 34 presented a general framework to address electroosmotic/electrophoretic mobility regarding non-Newtonian Carreau fluids. They concluded that electroosmotic/electrophoretic mobility can be significantly enhanced with shearthinning fluids and large surface zeta potentials. Due to the nonlinear dependence of the dynamic viscosity on the rate of shear, equations governing electroosmotic flows of non-Newtonian fluids also become highly nonlinear and then most of theoretical analyses rely on either approximate solutions or numerical simulations. Exact solutions are valuable because they not only can provide physical insight into the studied phenomena, but also can serves as benchmarks for experimental, numerical and asymptotic analyses. An exact solution for electroosmotic flow of non-Newtonian fluids was presented by Zhao and Yang 18who considered electroosmosis of a power-law fluid in a slit parallel-plate microchannel as illustrated in Fig. 2. The channel is filledwith a non-Newtonian power-lawelectrolyte solution having a flowbehavior index n, anda flowconsistency indexm. The microchannel walls are uniformly charged with a zeta potential . The application of an external electric field E0 drives the liquid into motion because of electroosmotic effect, and the velocity profile was derived for the situation of low zeta potentials as 18 1,c o s hsnG n H G n yu y uH （ 1） where the Debye parameter is defined as = 1/ D = 2e2z 2n /( kBT)1/2 (wherein e is the charge of an electron, z is the ionic valence, n is the bulk number concentration of ions, is the electric permittivity of the solution, kB is the Boltzmann constant, and T is the absolute temperature). The function G(, ) in Eq. (1) is defined as 12 22121 1 1 3, c o s h , ； ； c o s h2 2 2GF （ 2） where 2F11,2；1；z denotes the Gauss hypergeometric function 35. us in Eq. (1) denotes the so-called Helmholtz Smoluchowski velocity for power-law fluids and can be written as 110n nns Eun m （ 3） which was firstly derived by Zhao et al. 17 using an approximate method. The thickness of EDL on the channel wall is usually measured by the reciprocal of the Debye parameter ( 1), so the nondimensional electrokinetic parameter H = H/ 1 characterizes the relative importance of the half channel height to the EDL thickness. Then for large values of electrokinetic parameter H (thin EDL or large channel), the Helmholtz Smoluchowski velocity given by Eq. (3) signifies the constant bulk velocity in microchannel flows due to electroosmosis. In electrokinetically-driven microfluidics dealing with non-Newtonian fluids, the Helmholtz Smoluchowski velocity in Eq. (3) is of both practical and fundamental importance due to two reasons: First, the volumetric flow rate can be simply calculated by multiplying the area of channel cross-section and the Helmholtz Smoluchowski velocity. Second, numerical computations of electroosmotic flow fields in complex microfluidic structures can be immensely simplified by prescribing the Helmholtz Smoluchowski velocity as the slip velocity on solid walls. One can find more detailed derivation and discussion of this generalized Smoluchowski velocity in Refs. 17,18,21. Very recently, Zhao and Yang 20 reported an interesting but counterintuitive effect that the Helmholtz Smoluchowski velocity of non-Newtonian fluids becomes dependent on the dimension and geometry of channels owing to the complex coupling between the non-Newtonian hydrodynamics and the electrostatics. Inmicrofluidic pumping applications, the flow rate or average velocity is usually an indicator of pump performance.With the above derived electroosmotic velocity in Eq. (1), the electroosmotic average velocity along the cross-section of channel can be sought as 01 Hu u y d yH （ 4） where 3F21,2,3；1,2；z represents one of the generalized hypergeometric functions 35. It needs to be pointed out that all the hypergeometric functions presented in this review can be efficiently computed in commercially-available software, such as MATLab and Mathematica. 翻译： 非牛顿流体电动力学：回顾 摘要：本文对关于非牛顿流体电动力学进行了全面的回顾，涵盖大量非牛顿流体电动力学效应，包括非牛顿流体的电渗、非牛顿流体的电泳、流动的非牛顿流体的潜在影响以及其他电动力学中的非牛顿流体影响。通常，非牛顿流体动力学和静电学之间的耦合不仅使 电动力学复杂化，而且使流体及颗粒速度非线性地依赖于外部电场和 Zeta 电位的强度。液体的剪切稀化性质能够提高电动力现象，而液体剪切增稠性质会导致的电动效应的降低。另外，未来的研究重点是非牛顿流体电动力学的若干理论问题。 关键词：非牛顿电动力学；非线性电动力现象；电渗；电泳；粘电效应；电流变液；微流控技术 1引言 最近电动力现象正被越来越关注。其原因是由于微流体装置的多方面应用而引发的。微流体装置的多方面应用可能会潜在地彻底改变对化学分析、医疗诊断、物质合成、药物筛选与输送以及环境检测与监测的常规方法。在 电动力技术中运用微流体装置有如下优点：（ 1）该装置由电力控制，因此具有较好的泛用性和可控性；（ 2）该装置不含可移动部件，因此发生机械故障的可能性较小；（ 3）该装置中的液体或离子运动速度与装置的几何尺寸无关；（ 4）该装置能够很容易地集成其他的电子控制单元，从而实现全自动化操作。除了电动力学在微流体方面的应用，电动力学也是解释各种现象的基础。如离子迁移和整改纳米通道、水溶液热泳现象、电解质溶液的电润湿等。 当固体表明与电解质溶液接触时，固体表面会获得静电电荷。这种表面电荷的存在导致离子的再分配，之后在电解质溶液 中固体表面附近形成一个带电扩散层来吸收在固体表面的电荷。这种带电非中性扩散层通常被称为双电层（ EDL），负责两个类别的电动现象：（ 1）电驱动的电现象；（ 2）非电驱动的电现象。第一类现象的基本物理原理如下：当沿着电场表面切向的施加外部电场时，带电扩散层产生静电力迫使带电表面和电解质溶液之间产生相对运动。液体相对带电表面的运动被称为电渗（图 1a），带电粒子相对于静止液体的运动被称为电泳（图 1b）。典型的电泳发生在拥有固定的表面电荷的固体周围（即 Zeta 电位 ） ，改变固体表面和溶液的理化特性，随后液体滑移将处于以著名的 Helmholtz Smoluchowski 速度方程建立的微观 EDL 情况下。即：0 /suE （ 表示电解质溶液的介电常数， 表示固体表面的 Zeta 电位，0E为外加电场强度， 为电解质溶液中的动态粘度）。当一 个具有微观 EDL 的带电粒子被自由悬浮在静止的液体电解质溶液中时，溶液中的分子在粒子表面的电渗滑动在粒子表面引起电泳运动，其速度由 Smoluchowski 方程给出：0 /UE （注意 表示固体表面的 Zeta 电位）。第二类中的一个典型的行为是在压力驱动的流动泳动电势效应的产生（图 1c）。他们是在相邻的通道壁中 EDL 过剩的抗衡离子，并且压力驱动这些抗衡离子转化产生了流动电流。同时，在上游（下游）的抗衡离子的消耗（积累）形 成一个流动电位，驱动在相反方向上导通电流的流动电流。在稳定状态下，导通电流恰好平衡流体的电流。穿过通道的流动电位根据 0/sEP 给出（ P 为从外部施加的压力梯度，0为电解质溶液的体积电导率）。电动力现象的更为根本和全面的描述将在论文和评论中给出。 图 1 三种类型的电现象 前文中对电动力学的描述通常假定所使用的液体粘度为牛顿液体，电动力学的大多数文献中的研究也采用 了这样的假设。然而在实际中，微流体装置更多的被应用与分析生物流体（如血液、唾液、蛋白质和 DNA 溶液）、聚合物溶液以及胶体悬液。这些液体不能被视为牛顿液体。因此，流体动力学的表示这样的非牛顿流体依赖于常规柯西动量方程与合适的本构方程相结合的方法来大致确定的液体的粘度，以改变与流体动力的剪切速率，而非使用仅适用于牛顿流体的 Navier-Stokes 方程。由于耦合电动力学兼具流体力学和静电力学的功能，因此可以认为非牛顿流体电动力学会改变传统的牛顿电动力学。本文组织结构如下：第 2章对非牛顿流体研究最广泛的电渗进行回 顾；第 3 章对非牛顿流体粒子的电泳进行回顾；第4 章讨论对非牛顿流体电位的影响；第 5 章讨论了其他非牛顿效应在电动力学中的应用；第6 章总结了所进行的回顾并对未来的研究方向进行了阐述。 2非牛顿流体的电渗 贝罗等人在这一领域做出了开拓性的贡献。他以实验测得聚合物（甲基纤维素）溶液在毛细管中的电渗流。他们的研究表明，这种聚合物溶液中的电渗速度比传统的 HelmholtzSmoluchowski 速度高得多。这在当时提出后，表明剪切变稀诱导聚合物分子能有效降低 EDL内流体的粘度。大约十年后，产生了更多的实验和理论来支持 这一现象。 Chang 和 Tsao 进行了一个与贝罗等人所做的类似的实验。他们所研究的聚乙二醇溶液中的电渗流和观察到的拖动以及液体的有效粘度均由于 EDL 的内部剪切的聚合分子而大大减少。在理论方面，最近的努力已经导致了大量的对非牛顿流体电渗流动的信息。具体而言，非牛顿效果的特点是其中涉及适当的本构模型动态粘度和剪切速率。文献中已经提出了一大类用于分析流体的非牛顿特性如幂律模型、 Carreau 模型、 Bingham 模型、 Oldroyd-B 模型以及 Moldflow 二阶模型等。幂律流体模型的应用最为广泛因为它的结构最为简单 ，且能够广泛的适应非牛顿流体的应用。在幂律流体模型中的一个重要参数是流体行为折射率（ n），其描绘了粘度对剪切速率的动态依赖。如果 n 小于（大于） 1，流体将表现出剪切稀化（剪切增稠）影响该流体的粘度随剪切速率的增加（减少）而减小。如果 n 等于 1，流体将恰好表现为牛顿流体。 Das 和Chakraborty 获得了微通道平行板的幂律流体电渗速度分布的第一个近似解。然而，他们的分析没有明确地处理非牛顿效应对电渗流动的影响。 Zhao 等人进行了幂律流体在狭缝微通道平行板电渗的理论分析和电渗流的非牛顿效应的充分讨论。他们的分析显 示，该流体流变大幅改善了电渗剖面速度和电渗泵送性能。特别地，它们派生了以类似的方式广义Helmholtz Smoluchowski 速度为功耗较低的流体，以经典牛顿 Smoluchowski 速度和进一步阐述，例如速度的影响因素。 Yang 和 Zhao 后来将类似的分析扩展到一个微圆柱形。最近的一个实验由 Olivares 等进行，测定非牛顿聚合物（羧甲基纤维素）溶液的电渗流速率。而他们的实验结果与幂律流体广义 Helmholtz Smoluchowski 速度预测的