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防抱死制动系统的执行部件设计

乘用车防抱死制动系统的分析及其关键部件的设计初步【优秀】【带SW三维图及仿真】【word+5张CAD图纸全套】【毕业设计】

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任务书

论文(设计)题目:      乘用车防抱死制动系统的分析及其关键部件的设计初步                      

一、主要内容及基本要求

   查阅相关文献资料,了解乘用车防抱死制动系统的国内外研究动态,完成乘用车防抱死制动系统的分析及其关键部件的设计初步。                                                                                

   要求:                                                                                

   1、查阅相关资料,基本掌握乘用车防抱死制动系统的组成及功能;基本掌握实时道路识别技术。                                                                  

   2、设计一款结构简单、可靠的防抱死制动系统的执行部件。                                

   3、不少于2*A0图纸;                                                                                

   4、撰写毕业设计说明书。                                                                                  

   5、相关外文文献翻译,字数3000字以上。                          

二、重点研究的问题

      防抱死制动系统的执行部件设计                                                                          

三、进度安排

序号各阶段完成的内容完成时间

1查阅资料、调研第1-2周

2开题报告、制订设计方案第3周

3方案(设计)第4-5周

4防抱死制动系统的执行部件设计第6-7周

5写出初稿,中期检查第8-9周

6修改,写出第二稿  第10-11周

7写出正式稿  第12-13周

8答辩第14周

四、应收集的资料及主要参考文献

张秀芹.多轴车ABS制动性能仿真与试验研究[D].武汉理工大学,2012.                                            

贾玉梅.汽车ABS虚拟仿真平台的研究与应用[D].重庆邮电大学,2011.                                            

李文娟,付天雷,陈凤林等.汽车防抱死制动系统的自寻最优控制[J].哈尔滨理工大学  学报,2010.                                                                      

郝茹茹,赵祥模,周洲等.整车防抱死制动系统台架检测与道路对比试验[J].农业机械   学报,2013.  

目录

摘要I

ABSTRACTI

第1章  绪论1

1.1  防抱死制动系统的研究意义1

1.2  国外研究动态1

1.3  国内ABS研究动态2

1.4  ABS系统的设计要求3

1.5  ABS系统的质量准则3

1.6  主要评价指标4

1.7  ABS的展望4

1.8  完成的内容及设计的创新之处5

1.9  研究的主要方法5

第2章  ABS的基本结构和工作原理6

2.1  ABS 的基本分类6

2.2  ABS基本组成及工作过程6

2.3  ABS的执行机构8

第3章  制动器的设计初步10

3.1  盘式制动器的初步了解10

3.2  盘式制动器的机构及其特点10

3.3  制动系统的技术参数及要求11

3.4  浮动钳盘式制动器的设计流程12

3.5  参数的选择12

3.6  摩擦衬块的磨损特性计算13

3.7  比滑磨功的核算14

3.8  制动器的热容量和温升的核算15

3.9  盘式制动器制动力矩的计算16

第4章  盘式制动器主要零部件的结构设计17

4.1  制动盘17

4.2  制动钳18

4.3  制动块19

4.4  摩擦材料20

4.5  制动性能评价指标21

总结23

参考文献24

附录A 外文翻译25

附录B 盘式制动器零件图及装配图43

乘用车防抱死制动系统的认识及其盘式制动器的设计初步

摘要

ABS是英文Anti-lock Brake Syetem的缩写,全文的意思是防抱死制动系统,它作为一种具有防以及防锁死等功能的汽车主动安全控制系统,已被广泛运用于汽车上。ABS主要由微机控制单元(ECU)、车轮转速传感器、制动控制电路和制动压力调节装置等部分组成。汽车在制动过程中,ABS系统能使车轮处于非抱死状态,从而可以防止车辆的甩尾和侧滑,提高了汽车制动过程的方向稳定性。

本文介绍乘用车防抱死制动系统的国内外研究动态,对乘用车防抱死制动系统的工作原理进行分析,解析其基本组成。车轮制动器作为行车制动系的重要组成部件,本次论文将重点研究盘式制动器的制动原理,对ABS的执行制动部件进行合理性探讨,在散热性能及其结构上对盘式制动器进行创新设计和改良。最后通过三维制图软件画出装配图和零件图以更充分地表达设计理念。

关键词:ABS系统   ABS工作原理  基本组成  盘式制动器  结构设计

Understanding and design of passenger car disc brake anti-lock braking system initially

ABSTRACT

ABS is Anti-lock Brake Syetem English abbreviation, the full text mean anti-lock braking system, which as well as having an anti-anti-lock function of vehicle active safety control system has been widely used in the car. ABS Main components of the computer control unit (ECU), a wheel speed sensor, the brake control circuit and the brake pressure regulating devices. Car during braking, ABS system allows the wheels in a non-locking state, which can prevent the vehicle from skidding flick and improves directional stability during braking of the car.

This article describes the passenger anti-lock braking system dynamics studies abroad, for passenger anti-lock braking system works to analyze, parse its basic components. As an important component of the wheel brake components brake system. This paper will focus on the principles of the brake disc brakes, brake parts for ABS implementation of rational discussion on the thermal structure of the disc brake performance is extremely innovative design and improvement. Finally, three-dimensional mapping software to draw assembly drawings and part drawings to more fully express the design concept.

Keyword :Anti-lock Brake Syetem ;  ABS system works basically;  

The basic composition  ; Disc brakes ;Structural design

第1章 绪论

1.1 防抱死制动系统的研究意义

安全,环保和节能是当前汽车技术发展的三大主题。人们在享受车轮上的世界时,汽车的安全也是人们一直在探讨的话题。我国已不知不觉步入了汽车社会,汽车乃是当今中国最主流的交通工具。然而据公安部统计,2010年和2011年,在全国道路交通事故死去的人,数量分别达到了65225和62387,该数字已经连续十余年保持世界首位,车祸已成为中国社会之患。统计发现,汽车紧急制动时发生侧滑或制动距离过长等情况往往是导致重大的道路交通事故的发生的原因。汽车的制动性能已经成为了评价汽车主动安全性的一个非常重要的指标。研究和改善汽车的制动性能有着很大的价值。以ABS刹车防抱死系统为例,如果汽车前轮抱死,车辆将失去方向控制能力,不能实现弯道转向;如果后轮抱死,车辆将发生方向稳定性,发生侧滑或甩尾危险现象。汽车安装ABS后,可以大大缩短刹车距离并且在刹车过程中保持汽车方向可控制,以避免碰撞损伤。总体来看,ABS系统有三大优点:

1.能够增加汽车制动时的方向稳定性。

   在汽车制动过程中,作用在四个轮子上的制动力往往是是不相等的,如果汽车的前轮出现抱死现象,汽车的行驶方向就无法得到控制,这将极大可能造成非常危险的后果;如果汽车的后轮出现抱死现象,则会出现侧滑、甩尾的严重事故,更有甚者会使汽车整个掉头。ABS制动系统可以防止汽车制动时车轮被完全抱死,提高汽车制动的方向稳定性。研究数据表明,装有ABS制动系统的车辆,可以将因车轮侧滑,甩尾等引起的道路交通事故比例降低8%左右。

2.能缩短制动距离。

   研究表明,在同样紧急制动的情况下,防抱死制动系统可以将滑移率控制在20%左右,这样,汽车可获得最大的纵向制动力,起到缩短制动距离的效果。

3. 改善了汽车轮胎的磨损状况,防止出现爆胎情况。

   事实上,车轮抱死会造车轮轮胎局部急剧磨损,降低轮胎使用寿命。

1.2 国外研究动态

ABS装置最早应用在铁路上,在20世纪30年代,德国﹑美国﹑法国等国家提出有关防抱死装置专利的申请,而根据官方记录,最早的汽车防抱死系统是1932年英国人申请的专利“制动时防止车轮压紧转动车轮的安全装置”,该专利号为382241。直到20世纪50年代,ABS才开始应用于汽车工业。1908年,一位叫J. E. Francis的英国工程师提出了关于“铁路车辆车轮抱死滑动控制器”的有关理论,但这些理论实际上无法实用化。在接下来的30年中,包括Richard Trappe的“车轮抱死防止器”、Werner Mhl的“液压刹车安全装置”与Karl Wessel的“刹车力控制器”等尝试都以失败告终。20世纪50年代,Good Year航空公司开始尝试把飞机用ABS应用在载货汽车上,并开发出独具特点的ABS装置,这一时期初期电子计算技术开始应用到ABS装置中。1954年,美国福特汽车公司将法国生产的名航机用ABS装置装用在了林肯牌轿车上。虽然这些尝试都以失败告终,但为汽车应用ABS留下了很好的经验。经过人们长期的努力与尝试,1958年Dounlop公司开发出了 应用在载货车的车用ABS。1968年,美国福特公司与Keslsey Hayes公司合作并最终成功开发了车用ABS装置。随着电子技术的飞速发展,20世纪70年代末,欧洲开始批量生产应用于轿车和商用汽车的ABS系统。进入20世纪80年代末,ABS的发展速度变得越来越快。在发展过程中,ABS的体积不断减少,重量也不断地减轻,其控制盒故障诊断功能也越来越完善。在欧洲,美国和日本等国家,ABS应用在汽车上越来越普及,欧洲和美国在法规的要求下,ABS装车率达到100%。随着计算机技术以及新技术新材料的不断出现,人们开始尝试将ABS﹑4WS和DYC技术结合在一起,在ABS原有的基础上,发展防滑控制系统(ASR)﹑电子制动控制系统(EBS)及车辆动力学控制系统(VDC)。四轮转向技术4WS(Four Wheer Steering)是主动底盘控制的重要组成部分,主要是用来改善汽车操纵稳定性。在国外4WS有着很好的发展前景。相比4WS技术,DYC则对汽车有更高的稳定性控制能力。DYC是Direct Yaw Moment Contrl的缩写,称为横摆力矩控制。20世纪90年代末,本田汽车工程师Shibahata就由轮胎侧向力产生的横摆力矩是如何随汽车质心侧偏角的变化而变化作出了相关讨论。目前,世界第一大ABS装置生产厂家――德国Bosch(博世)公司生产的ABS装置已被广泛用于大众,宝马,通用和奥迪等公司的各系列车型中。此外,日本也生产了大量的ABS装置,广泛安装在本田,日产,丰田及马自达等车系上。

1.3 国内ABS研究动态

我国ABS 的研究起步比较晚。上世纪80 年代初,诸如东风汽车公司、上海汽车制动有限公司、山东重汽集团和重庆公路研究所等企业,还有吉林大学和清华大学等高校开始从事ABS的研制工作。其中清华大学率先搭建了汽车安全与节能国家重点实验室,该实验室在宋健,欧阳明高等多名博导和教授的带领下拥有着很强的科技研发实力, 他们在国内开展了有关汽车碰撞安全的课题研究,自行设计建成了测试分析处理系统和汽车碰撞试验台,这些成果填补了国内在测试分析技术和碰撞试验研究方面的空白,在国内率先开展汽车侧面碰撞、行人碰撞及正面碰撞等安全性研究,形成了一套比较系统的设计理论和方法。该室引进和开发一些先进的仪器设备,比如FEV控制器仿真系统﹑汽车力学参数综合试验台、模拟人及标定试验台、电液振动台、Kodak 高速图像运动分析系统、发动机排放分析仪、ABS车载数据采集系统、发动机电控系统开发装置及工况模拟器、转鼓试验台、汽车底盘测功机、噪声测试系统、汽车操纵稳定性测试仪、汽车弹射式碰撞试验台及翻转试验台、电动车蓄电池试验台、电机及其控制系统试验台等。针对ABS该实验室做了许多方面的研究和探索,比如,在ABS 控制量、轮速信号异点剔除、轮速信号抗干扰处理以及防抱死电磁阀动作响应研究等领域的研究都处于国内领先的地位。吉林大学的汽车动态模拟国家重点实验室,该实验室在轮胎力学模型,人车闭环操作仿真以及汽车操纵稳定性等方面的研究成果均处在世界领先地位。有郭孔辉教授领导的研究小组设计并开发了具有自主知识产权的大型试验设备——平板式轮胎力学特性试验台,该试验台为轮胎力学特性的理论研究和试验研究起到了积极的推动作用。西安的博华公司生产的BH1203-FB型ABS和BH1101-FB型ABS被认为到达了国内领先水平。

1.4  ABS系统的设计要求

一般把转向能力,稳定性和最佳制动距离作为评价ABS的主要指标。一般对ABS的设计能满足以下的要求 :

1)在调节制动过程时,汽车行驶稳定性和转向能力必须得到保证;

2)即使在各个车轮上的附着力系数不相等,不可避免的转向反应也应该尽可能小;

3)必须在汽车的整个速度范围内进行调节;

4)调节系统应该最大程度上利用车轮在路面上的附着性,这时优先考虑保持转向能力,然后再保障缩短制动距离的要求

5)调节装置应该能够快速地适应来自路面传递能力的变化

6)在波状路面上给以任意的强迫制动,汽车都应能被完全地控制住;

7)调节装置必须能够对出覆水路面做出识别,并能对此作出正确的反应;

8)调节装置只能附加在常规制动装置上

9)所有的这些对调节装置的要求,汽车轮胎在路面上行驶时都必须得到满足

1.5  ABS系统的质量准则

每一种ABS产品的出现都是为了能投入市场,应用于实际。ABS产品想要开拓市场,它必须具有高的可靠性能。ABS产品的可靠性必须能够满足苛刻的汽车使用条件的要求。评价一个ABS系统应该遵循的质量准则有以下几点 :

(1)保证良好的行驶稳定性

(2)转向能力满足汽车安全行驶要求

(3)高附着力系数的利用率

(4)舒适性良好

1.6  主要评价指标

对ABS系统性能的评价必须是要综合各项指标,ABS的性能好坏最终是要通过道路试验来验证。每一种ABS产品都必须要通过严格的试验检测后才可以进行装车使用。评价ABS系统主要有以下几个指标 :

(1)良好的抗外界电磁场干扰的能力

(2)基本功能(保证制动车轮不抱死)

(3)附着力系数利用率

(4)对道路条件突变的适应性

(5)当产生电器故障可自行解除ABS的工作

1.7  ABS的展望

   ABS在汽车上的成功应用,说明了防抱死理论的可行性。虽然说ABS的理论及其总体结构方案已趋于成熟,但是随着道路升级以及汽车技术的发展和普及,人们对汽车行驶制动安全性的要求越来越高。国内外的一些研究动态以及高档轿车的实际应用情况表明,ABS技术将会在着以下几个方面进行拓宽发展 :

1.自身控制技术的提高。随着计算机技术的发展,ABS向纵深扩展,比如驱动防滑装置,简称ASR(Anti-slip-regulation)及速度限制器等。基于滑移率的控制算法也有了十分明确的理论指导。在控制生产成本的前提下,ABS防抱死系统将向体积更小,性能更可靠以及功能更加全面实用的方向发展。

2.把ABS和驱动防滑控制装置ASR结合在一起,实现一体化。当汽车行驶时车轮出现滑动现象时,实际上会出现以下两种情况:一种情况是汽车在制动时车轮出现抱死而产生的车轮滑移现象;另一种是车身不动但车轮仍在转动,或者说是汽车的运动速度比转动车轮的轮缘速度小,我们称之为滑转。通常ABS是以防止车轮抱死为目的,而ASR则是为了防止车轮出现过分滑转的现象;ABS的作用是为了缓解制动,而ASR则是对车轮施加制动力。由于这两种装置在技术上比较接近,并且都能在低附着性的地面上充分体现出它们的作用,所以人们将二者有机地结合起来。

3.车辆动力学控制系统VDC(Vehicle Dynamics Control)或电子稳定控制ESP。VDC主要在ABS/ASR基础上通过测量方向转盘,侧向加速度和横摆角速度对车辆的运动状态进行控制。设计车辆动力学控制系统的目的是为了解决汽车转向行驶时出现的方向稳定性问题。能保证车辆处于危险情况下实现自动控制。

4.ABS/ASR与自动巡航系统ACC(Adaptive Cruise Control)集成。作为汽车主动安全的一项新技术,ACC装置能够是汽车主动避免碰撞。ABS/ASR和ACC的运作都是建立在相同的发动机调节装置,制动力调节装置以及轮速采集系统上,因此,把ABS和ACC结合在一起将提高汽车安全性的的同时,会大大降低生产成本。

5.将ABS与电子机械制动EMB结合,或者与电子液压制动EHB结合后,ABS就会有更快的的响应速度,表现出更好的控制效果,而且更容易与其它电子系统实现集成,这也将是在ABS的基础上开发或添加其它制动系统的一个趋势。

6.把电子制动力分配装置(EBD)嵌入到ABS系统中,则构成了ABS+EBD系统。在汽车开始制动压力调节之前,EBD能够高速地计算出汽车四个轮胎与路面间的附着力大小,然后调节各个车轮与附着力的关系,使二者能匹配,更大程度地提高车辆制动时的稳定性能,同时也尽可能地达到缩短制动距离的效果。

1.8 完成的内容及设计的创新之处

本次完成的任务主要是对乘用车防抱死制动系统的工作原理进行了分析,解析其基本组成,掌握汽车防抱死制动工作原理。对ABS的执行制动部件进行合理性探讨,重点研究了盘式制动器的结构,在散热性能及其结构上对盘式制动器进行创新设计和改良。最后通过三维制图软件画出装配图和零件图。完成相关外文文献的翻译。

主要的创新点有:(1)制动盘除了采用盘式通风孔设计,还对通风道的位置做了特殊要求,改善其散热性能;(2)改变原有的保持弹簧形状,设计一款安装定位准确且便于安装的保持弹簧;(3)在结构上对防尘油套进行改进,使其与制动钳嵌合,提高油缸防尘防污能力。

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内容简介:
湘潭大学机械工程学本科毕业设计 论文 开题报告 题目 乘用车防抱死制动系统的分析及其盘式电磁制动器的设计初步姓名 欧嵩干专业 机械制造及其自动化学号 2010500334指导老师 朱石沙时间 2014年3月15日 一 课题背景 意义及国内外研究动态 课题背景及研究意义 安全 环保和节能是当前汽车技术发展的三大主题 人们在享受车轮上的世界时 汽车的安全也是人们一直在探讨和话题 我国已不知不觉步入了汽车社会 汽车乃是当今中国最主流的交通工具 然而据公安部统计 2010年和2011年 全国道路交通事故造成死亡人数分别是65225和62387人 该数字已经连续十余年居世界第一 车祸已成为中国社会之患 汽车的制动性能是表征汽车行驶安全性的一个重要指标 重大的交通事故往往与制动距离过长或紧急制动时发生侧滑等情况有关 研究和改善汽车的制动性能有着很大的价值 以ABS刹车防抱死系统为例 汽车安装ABS后 可以大大缩短刹车距离并且在刹车过程中保持汽车方向可控制 以避免碰撞损伤 ABS是英文Anti lockBrakeSyetem的缩写 全文的意思是防抱死制动系统 简称ABS 汽车在制动过程中 ABS系统能使车轮处于非抱死状态 从而可以防止车辆的甩尾和侧滑 提高了制动过程的方向稳定性 如果汽车前轮抱死 车辆将失去方向控制能力 不能实现弯道转向 如果后轮抱死 车辆将发生方向稳定性 发生侧滑或甩尾危险现象 总体来看 ABS系统有三个优点1 增加了汽车制动时候的稳定性 汽车制动时 四个轮子上的制动力是不一样的 如果汽车的前轮抱死 驾驶员就无法控制汽车的行驶方向 这是非常危险的 倘若汽车的后轮先抱死 则会出现侧滑 甩尾 甚至使汽车整个掉头等严重事故 ABS可以防止四个轮子制动时被完全抱死 提高了汽车行驶的稳定性 汽车生产厂家的研究数据表明 装有ABS的车辆 可使因车论侧滑引起的事故比例下降8 左右 2 能缩短制动距离 这是因为在同样紧急制动的情况下 ABS可以将滑移率 汽车华东距离与行驶的比 控制在20 左右 即可获得最大的纵向制动力的结果 3 改善了轮胎的磨损状况 防止爆胎 事实上 车轮抱死会造 制动器是制动系中产生阻止车辆运动或运动趋向的力的机构 车轮制动器是行车制动系的重要部件 目前各类汽车所使用的车轮制动器可以分为鼓式和盘式两大类 由于盘式制动器散热快 重量轻 构造简单 调整方便 特别是高负载时耐高温性能好 制动效果稳定 热稳定性 水稳定性好 盘式制动器被普遍使用 在盘式制动器中又主要以液压盘式制动器为主 但是目前汽车液压系统存在结构复杂 质量大和能源消耗大等问题 近年来则出现了一些全新的制动器结构形式 如磁粉制动器 湿式多盘制动器 电力液压制动臂型盘式制动器 湿式盘式弹簧制动器等 本文将对乘用车防抱死系统进行分析 并着力在液压盘式制动器以及鼓式电磁制动器的基础上对盘式电磁制动器做一些构想 理论可行性和设计初步 国内外研究动态 ABS装置最早应用在飞机和火车上 而在汽车上的应用比较晚 铁路机车在制动时如果制动强度过大 车轮就会很容易抱死在平滑的轨道上滑行 由于车轮和轨道的摩擦 就会在车轮外圆上磨出一些小平面 小平面产生后 车轮就不能平稳地行驶 产生噪声和挣动 1908年英国工程师J E Francis提出了 铁路车辆车轮抱死滑动控制器 理论 但却无法将它实用化 接下来的30年中 包括KarlWessel的 刹车力控制器 WernerMhl的 液压刹车安全装置 与RichardTrappe的 车轮抱死防止器 等尝试都宣告失败 1954年 美国福特公司首先把法国生产的名航机用ABS应用在林肯牌轿车上 这些尝试虽然以失败告终 但揭开了汽车应用ABS的序幕 经过长期不懈的努力 1958年Dounlop公司开发出了用于载货车的ABS 美国福特公司最终与KeslseyHayes公司合作于1968年成功开发了车用ABS装置 20世纪70年代末 欧洲开始批量生产应用于轿车和商用汽车的ABS系统 进入20世纪90年代末 ABS的发展越来越快 欧洲 美国和日本等国家均在高速普及ABS 目前 德国的博世公司成为世界第一大ABS装置生产厂家 其生产的ABS装置已被用于奥迪 宝马 通用和大众等公司的各系列车型中 另外 日本也生产大量的ABS装置 广泛安装于丰田 日产 本田及马自达等系列车型上 国内ABS研究动态我国ABS的研究开始于80年代初 从事ABS研制工作的单位和企业很多 诸如东风汽车公司 重庆公路研究所 西安公路学院 清华大学 吉林大学 北京理工大学 上海汽车制动有限公司和山东重汽集团等 具有代表性的有以下几个 清华大学汽车安全与节能国家重点实验室有宋健等多名博导 教授 有很强的科技实力 他们还配套有一批先进的仪器设备 如汽车力学参数综合试验台 汽车弹射式碰撞试验台及翻转试验台 模拟人及标定试验台 Kodak高速图像运动分析系统 电液振动台 直流电力测功机 发动机排放分析仪 发动机电控系统开发装置及工况模拟器 计算机工作站及ADAMS IDEAS软件 非接触式速度仪 噪声测试系统 转鼓试验台 电动车蓄电池试验台 电机及其控制系统试验台等 该实验室针对ABS做了多方面的研究 其中 在ABS控制量 轮速信号抗干扰处理 轮速信号异点剔除 防抱死电磁阀动作响应研究等方面的研究处于国内领先地位 二 防抱死制动系统的基本组成 ABS系统主要由传感器 电子控制单元 ECU 和电磁阀三部分组成 其系统原理结构组成图如图3 2所示 传感器一般安装在车轮上以测量车轮的转速 传感器一般为磁电感应式 ABS工作时ECU接收传感器送来的车轮信号 一般为符合ECU电压要求的矩形电压波 然后固化在ECU中的程序根据各个车轮的速度来决定对各个车轮的制动液压力如何调节 并输出相应的控制信号给各个车轮的液压控制单元 液压控制单元接收到信号后对车轮分泵的压力进行调节 传感器的作用是为ECU提供车轮的运动情况 ECU是ABS系统的控制中心 ECU中固化的程序实际上是ABS的控制方法 而液压控制单元是ABS控制方法的执行机构 1 前轮速度传感器2 制动压力调节装置3 ABS电控单元4 ABS警告5 后轮速度传感器 轮速传感器是汽车轮速的检测元件 它能产生频率与车轮速度成正比的近似正弦电信号 ABS控制单元根据处理后的信号计算车轮速度 电子控制单元是整个防抱死制动系统的核心控制部件 它接受车轮速度传感器送来的频率信号 通过计算与逻辑判断产生相应的控制电信号 操纵电磁阀去调节制动压力 定性的来说 就是当车轮的滑移率不在控制范围之内时 ECU就输出一个控制信号 命令电磁阀打开或闭合 从而调节制动轮缸压力 使轮速上升或下降 将汽车车轮滑移率控制在一定范围之内 实现汽车的安全 可靠制动 电子控制单元原理图如图所示 电磁阀是防抱死制动系统的执行部件 在没有控制信号的情况下 该制动系统相当于常规制动系统 直接输出最大制动压力 当ECU向电磁阀 发出控制信号时 电磁阀动作 对轮缸压力进行调节 从而调节车轮的滑移率 使制动力在接近峰值区域内波动 但又不达到峰值制动力 实现最佳制动效率 ABS就是在汽车制动过程中不断检测车轮速度的变化 按一定的控制方法 通过电磁阀调节制动轮缸压力 以获得最高的纵向附着系数 使车轮始终处于较好的制动状态 盘式制动器工作原理大多数现代汽车的前轮上都装有盘式制动器 甚至有些汽车四个车轮上都装有盘式制动器 它是汽车制动系统中真正使汽车停止的部件 盘式制动器的主要部件包括 制动衬块 含有活塞的卡钳 安装在轮毂上的转子它由液压控制 主要零部件有制动盘 分泵 制动钳 油管等 制动盘用合金钢制造并固定在车轮上 随车轮转动 分泵固定在制动器的底板上固定不动 制动钳上的两个摩擦片分别装在制动盘的两侧 分泵的活塞受油管输送来的液压作用 推动摩擦片压向制动盘发生摩擦制动 动作起来就好象用钳子钳住旋转中的盘子 迫使它停下来一样 这种制动器散热快 重量轻 构造简单 调整方便 特别是高负载时耐高温性能好 制动效果稳定 而且不怕泥水侵袭 在冬季和恶劣路况下行车 盘式制动比鼓式制动更容易在较短的时间内令车停下 有些盘式制动器的制动盘上还开了许多小孔 加速通风散热提高制动效率 近年来则出现了一些全新的制动器结构形式 如磁粉制动器 湿式多盘制动器 电力液压制动臂型盘式制动器 湿式盘式弹簧制动器等 根据所给商务车的技术参数及性能参数 并综合考虑制动器的设计要求 如下 1 具有足够的制动效能 2 在任何速度下制动时 汽车都不应丧失操纵性和方向稳定性 3 防止水和污泥进入制动器工作表面 4 制动能力的热稳定性良好 5 操纵轻便 并具有良好的随动性 6 制动时 制动系产生的噪声尽可能小 同时力求减少散发出对人体有还的石棉纤维等物质 以减少公害 7 作用滞后性应尽可能好 8 摩擦衬片应有足够的使用寿命 9 摩擦副磨损后 应有能消除因磨损而产生间隙的机构 且调整间隙工作容易 最好设置自动调整间隙机构 10 当制动驱动装置的任何元件发生故障并是使基本功能遭到破坏时 汽车制动系应有音响或光信号等报警提示 结合以上参数及要求 适当考虑经济因素 设计一款合适的汽车制动器并通过绘图软件将该制动器布置图绘出 本次设计的盘式电磁制动器将用电磁总成替代液压助力系统 用磁动力提供制动所需的摩擦力 并讨论理论可行性和用三维制图会出结构设计初步 完成主要参数的计算与确定 摩擦衬块的磨损特性计算 制动器热容量和温升的核算 制动力矩的计算与校核等 三 主要内容及基本要求 主要内容 查阅相关文献资料 了解乘用车防抱死制动系统的国内外研究动态 完成乘用车防抱死制动系统的分析及其关键部件的设计初步 基本要求 1 查阅相关资料 基本掌握乘用车防抱死制动系统的组成及功能 基本掌握实时道路识别技术 2 设计一款结构简单 可靠的防抱死制动系统的执行部件 3 不少于2 A0图纸 4 撰写毕业设计说明书 5 相关外文文献翻译 字数3000字以上 四 进度安排 序号各阶段完成的内容完成时间1查阅资料 调研第1 2周2开题报告 制订设计方案第3周3方案 设计 第4 5周4防抱死制动系统的执行部件设计第6 7周5写出初稿 中期检查第8 9周6修改 写出第二稿第10 11周7写出正式稿第12 13周8答辩第14周 五 主要参考文献 1 张秀芹 多轴车ABS制动性能仿真与试验研究 D 武汉理工大学 2012 2 贾玉梅 汽车ABS虚拟仿真平台的研究与应用 D 重庆邮电大学 2011 3 李文娟 付天雷 陈凤林等 汽车防抱死制动系统的自寻最优控制 J 哈尔滨理工大学学报 2010 4 郝茹茹 赵祥模 周洲等 整车防抱死制动系统台架检测与道路对比试验 J 农 业机械学报 2013 李果 车辆防抱死制动控制理论与应用 国防工业出版社 2009 6 周志立等 汽车ABS原理与结构 机械工业出版社 2005 龙云梅 林秋逢等 一种汽车盘式电磁制动器的研制 机电工程 2013石固欧 刘威 ABS在液压盘式刹车中应用的可行性研究 石油机械 2013吴剑增 刘关学 气压盘式制动器的性能因素探讨 客车技术与研究 2013 湘潭大学机械工程学本科毕业设计进展报告 题目 乘用车防抱死制动系统的分析及其盘式制动器的设计初步姓名 欧嵩干专业 机械制造及其自动化学号 2010500334指导老师 朱石沙时间 2014年3月15日 根据已给参数并参考已有的同等级汽车的同类型制动器 初选制动器的主要参数 并据以进行制动器结构的初步设计 然后进行制动力矩和磨损性能的验算 并与所要求的数据比较 直到达到设计要求 之后再根据各项演算和比较的结果 对初选的参数进行必要的修改 直到基本性能参数能满足使用要求为止 最后进行详细的结构设计和分析 本制动器是参照广汽本田雅阁的制动器而设计的 广汽本田雅阁轿车是我国与日本合资生产的中高端轿车 雅阁轿车四轮均采用防抱死装置且前后轮均采用盘式制动器 现给出有关雅阁2010款2 4EXNavi的有关参数 行车最高车速 203km h官方加速度 12 4s长 宽 高 4945 1845 1480mm轴距 2800mm前轮距 1590mm后轮距 1585mm最小离地间隙 115mm车重 空载1535kg 满载2000kg前轮胎规格 225 55R17后轮胎规格 225 55R17 1 制动盘直径D制动盘直径D应尽可能取大些 这是制动盘的有效半径得到增大 可以减小制动钳的夹紧力 降低衬块的单位压力和工作温度 受轮辋直径的限制 制动盘的直径通常选择为70 79 而总质量大于总质量大于2t的汽车应取上限 在本设计中 取D 330mmDr为车轮轮毂 由轮胎规格可知雅阁轿车的R17代表轮毂为17英寸 即431mm 2 制动盘厚度h制动盘厚度h直接影响着制动盘质量和工作时的温升 为使质量不致太大 盘厚度又不宜过小 制动盘可以制成实心的 而为了通风散热 又可在制动盘的两工作面之间铸出通风孔道 通常 实心制动盘厚度可取10mm 20mm 具有通风孔道的制动盘的两工作面之间的尺寸 即制动盘的厚度取为20mm 50mm 但多采用20mm 30mm 在本设计中 前制动器采用通风盘 取厚度h 30mm 3 摩擦衬块内半径与外半径推荐摩擦衬块外半径与内半径的比值不大于1 5 若此比值偏大 工作时衬块的外缘与内侧圆周速度相差较多 磨损不均匀 接触面积减小 最终将导致制动力矩变化大 在本设计中 取 110mm 160mm符合要求 4 摩擦衬快工作面积A一般摩擦衬快单位面积占有汽车质量在1 6kg 3 5kg 范围内选取 考虑到现今摩擦材料的不断升级 此范围可适当扩大些 本次设计使用半金属摩擦材料 其摩擦系数优于石棉材料A 5442 摩擦衬块的磨损特性计算摩擦衬片 衬块 的磨损 与摩擦副的材质 表面加工情况 温度 压力以及相对滑磨速度等多种因素有关 因此在理论上要精确计算磨损性能是困难的 但试验表明 摩擦表面的温度 压力 摩擦系数和表面状态等是影响磨损的重要因素 汽车的制动过程是将其机械能 动能 势能 的一部分转变为热量而耗散的过程 在制动强度很大的紧急制动过程中 制动器几乎承担了耗散汽车全部动力的任务 此时由于在短时间内热量来不及逸散到大气中 致使制动器温度升高 此即所谓制动器的能量负荷 能量负荷愈大 则衬片 衬块 的磨损愈严重 制动器的能量负荷常以其比能量耗散率作为评价指标 比能量耗散率又称为单位功负荷或能量负荷 它表示单位摩擦面积在单位时间内耗散的能量 其单位为 汽车制动器的比能量耗散率为 式中 汽车回转质量换算系数 汽车总质量 汽车制动初速度与终速度 制动减速度 m s2 计算时取j 0 6g 制动时间 前制动器衬片 衬块 的摩擦面积 制动力分配系数 比滑磨功磨损和热的性能指标也可用衬块在制动过程中由最高制动初速度至停车所完成的单位衬块面积的滑磨功 即比滑磨功 来衡量 制动器的热容量和温升核算 盘式制动器制动力矩的计算 假设制动液压强为8MP由于所设计的轮直径为45mm故作用在背板上的压紧力为 动块作用于制动盘上的制动力矩为 制动器主要零部件的结构设计 制动盘 制动盘一般用珠光体铸铁制成 或用合金铸铁制成 其结构形状有平板形和礼貌形 制动盘在工作时不仅承受着制动块作用的法向力和切向力 而且承受着热负荷 为了改善冷却效果 钳盘式制动器的制动盘有的铸成中间有径向通风槽的双层盘 这样可大大地增加散热面积 降低温升约20 30 但盘的整体厚度较厚 制动盘的工作表面应光洁平整 制造时应严格控制表面的跳动量 两侧表面的平行度 厚度差 及制动盘的不平衡量 根据有关文献规定 制动盘两侧表面不平行度不应大于0 015mm 盘的表面摆差不应大于0 1mm 制动盘表面粗糙度不应大于0 06mm 本次设计采用的材料为合金铸铁 结构形状为礼帽形 前通风盘 后实心盘 圆弧形状如图2中所示 其中 b1 b2分别为通风道入口角 叶片出口角 1 2分别为通风道高度和冷却片厚度 从冷却片形状来分析 向后通风道 b2 90 的流道较平滑 气流在其中流动时阻力较小 能量损失小 因此选择向后的冷却片 通风道基本形状确定后 计算合理的通风道入口角 b1 出口角 b2和叶片数B 为满足双向散热性能的要求 一般取 b1 90 通风道进风口的截面积S1应大于出风口的截面积S2 其中制动盘外直径为330mm 摩擦环内直径为220mm 经计算 得出 b2 arcsin 110 165 38 制动钳 制动钳由可锻铸铁KTH370 12或球墨铸铁QT400 18制造 也有用轻合金制造的 例如用铝合金压铸 可做成整体的 也可做成两半并由螺栓连接 其外缘留有开口 以便不必拆下制动钳便可检查或更换制动块 制动钳体应有高的强度和刚度 在钳体中加工出制动油缸 为了减少传给制动液的热量 将活塞的开口端顶靠制动块的背板 活塞由铸铝合金制造 为了提高耐磨损性能 活塞的工作表面进行镀铬处理 为了解决因制动钳体由铝合金制造而减少传给制动液的热量的问题 减小了活塞与制动块背板的接触面积 制动钳在汽车上的安装位置可在车轴的前方或后方 制动钳位于车轴前可避免轮胎甩出来的泥 水进入制动钳 位于车轴后则可减小制动时轮毂轴承的合成载荷 因此本次设计采用可锻铸铁 整体式 镀铬处理 前制动钳位于车轴后 后制动钳位于车轴前 制动块由背板和摩擦衬块构成 两者直接牢固地压嵌或铆接或粘接在一起 衬块多为扇形 也有矩形 正方形或圆形的 活塞应能压住尽量多的制动块面积 以免衬块发生卷角而引起尖叫声 制动块背板由钢板制成 为了避免制动时产生的热量传给制动钳而引起制动液汽化和减小制动噪声 可在摩擦衬块与背板之间或在背板后粘 或喷涂 一层隔热减震垫 胶 由于单位压力大和工作温度高等原因 摩擦衬块的磨损较快 因此其厚度较大 许多盘式制动器装有衬块磨损达极限时的警报装置 以便及时更换摩擦衬片 本次设计取衬块厚度12mm 有隔热减震垫 有报警装置 摩擦块 钳体 弹簧 密封圈 油塞防尘套 摩擦背板 摩擦块 制动盘 支撑架 保持弹簧 活塞 油缸 防尘油套 密封圈 活塞 弹簧 支撑架 保持弹簧 湘潭大学机械工程学本科毕业设计进展报告 题目 乘用车防抱死制动系统的分析及其盘式制动器的设计初步姓名 欧嵩干专业 机械制造及其自动化学号 2010500334指导老师 朱石沙时间 2014年3月15日 根据已给参数并参考已有的同等级汽车的同类型制动器 初选制动器的主要参数 并据以进行制动器结构的初步设计 然后进行制动力矩和磨损性能的验算 并与所要求的数据比较 直到达到设计要求 之后再根据各项演算和比较的结果 对初选的参数进行必要的修改 直到基本性能参数能满足使用要求为止 最后进行详细的结构设计和分析 本制动器是参照广汽本田雅阁的制动器而设计的 广汽本田雅阁轿车是我国与日本合资生产的中高端轿车 雅阁轿车四轮均采用防抱死装置且前后轮均采用盘式制动器 现给出有关雅阁2010款2 4EXNavi的有关参数 行车最高车速 203km h官方加速度 12 4s长 宽 高 4945 1845 1480mm轴距 2800mm前轮距 1590mm后轮距 1585mm最小离地间隙 115mm车重 空载1535kg 满载2000kg前轮胎规格 225 55R17后轮胎规格 225 55R17 1 制动盘直径D制动盘直径D应尽可能取大些 这是制动盘的有效半径得到增大 可以减小制动钳的夹紧力 降低衬块的单位压力和工作温度 受轮辋直径的限制 制动盘的直径通常选择为70 79 而总质量大于总质量大于2t的汽车应取上限 在本设计中 取D 330mmDr为车轮轮毂 由轮胎规格可知雅阁轿车的R17代表轮毂为17英寸 即431mm 2 制动盘厚度h制动盘厚度h直接影响着制动盘质量和工作时的温升 为使质量不致太大 盘厚度又不宜过小 制动盘可以制成实心的 而为了通风散热 又可在制动盘的两工作面之间铸出通风孔道 通常 实心制动盘厚度可取10mm 20mm 具有通风孔道的制动盘的两工作面之间的尺寸 即制动盘的厚度取为20mm 50mm 但多采用20mm 30mm 在本设计中 前制动器采用通风盘 取厚度h 30mm 3 摩擦衬块内半径与外半径推荐摩擦衬块外半径与内半径的比值不大于1 5 若此比值偏大 工作时衬块的外缘与内侧圆周速度相差较多 磨损不均匀 接触面积减小 最终将导致制动力矩变化大 在本设计中 取 110mm 160mm符合要求 4 摩擦衬快工作面积A一般摩擦衬快单位面积占有汽车质量在1 6kg 3 5kg 范围内选取 考虑到现今摩擦材料的不断升级 此范围可适当扩大些 本次设计使用半金属摩擦材料 其摩擦系数优于石棉材料A 5442 摩擦衬块的磨损特性计算摩擦衬片 衬块 的磨损 与摩擦副的材质 表面加工情况 温度 压力以及相对滑磨速度等多种因素有关 因此在理论上要精确计算磨损性能是困难的 但试验表明 摩擦表面的温度 压力 摩擦系数和表面状态等是影响磨损的重要因素 汽车的制动过程是将其机械能 动能 势能 的一部分转变为热量而耗散的过程 在制动强度很大的紧急制动过程中 制动器几乎承担了耗散汽车全部动力的任务 此时由于在短时间内热量来不及逸散到大气中 致使制动器温度升高 此即所谓制动器的能量负荷 能量负荷愈大 则衬片 衬块 的磨损愈严重 制动器的能量负荷常以其比能量耗散率作为评价指标 比能量耗散率又称为单位功负荷或能量负荷 它表示单位摩擦面积在单位时间内耗散的能量 其单位为 汽车制动器的比能量耗散率为 式中 汽车回转质量换算系数 汽车总质量 汽车制动初速度与终速度 制动减速度 m s2 计算时取j 0 6g 制动时间 前制动器衬片 衬块 的摩擦面积 制动力分配系数 比滑磨功磨损和热的性能指标也可用衬块在制动过程中由最高制动初速度至停车所完成的单位衬块面积的滑磨功 即比滑磨功 来衡量 制动器的热容量和温升核算 盘式制动器制动力矩的计算 假设制动液压强为8MP由于所设计的轮直径为45mm故作用在背板上的压紧力为 动块作用于制动盘上的制动力矩为 制动器主要零部件的结构设计 制动盘 制动盘一般用珠光体铸铁制成 或用合金铸铁制成 其结构形状有平板形和礼貌形 制动盘在工作时不仅承受着制动块作用的法向力和切向力 而且承受着热负荷 为了改善冷却效果 钳盘式制动器的制动盘有的铸成中间有径向通风槽的双层盘 这样可大大地增加散热面积 降低温升约20 30 但盘的整体厚度较厚 制动盘的工作表面应光洁平整 制造时应严格控制表面的跳动量 两侧表面的平行度 厚度差 及制动盘的不平衡量 根据有关文献规定 制动盘两侧表面不平行度不应大于0 015mm 盘的表面摆差不应大于0 1mm 制动盘表面粗糙度不应大于0 06mm 本次设计采用的材料为合金铸铁 结构形状为礼帽形 前通风盘 后实心盘 圆弧形状如图2中所示 其中 b1 b2分别为通风道入口角 叶片出口角 1 2分别为通风道高度和冷却片厚度 从冷却片形状来分析 向后通风道 b2 90 的流道较平滑 气流在其中流动时阻力较小 能量损失小 因此选择向后的冷却片 通风道基本形状确定后 计算合理的通风道入口角 b1 出口角 b2和叶片数B 为满足双向散热性能的要求 一般取 b1 90 通风道进风口的截面积S1应大于出风口的截面积S2 其中制动盘外直径为330mm 摩擦环内直径为220mm 经计算 得出 b2 arcsin 110 165 38 制动钳 制动钳由可锻铸铁KTH370 12或球墨铸铁QT400 18制造 也有用轻合金制造的 例如用铝合金压铸 可做成整体的 也可做成两半并由螺栓连接 其外缘留有开口 以便不必拆下制动钳便可检查或更换制动块 制动钳体应有高的强度和刚度 在钳体中加工出制动油缸 为了减少传给制动液的热量 将活塞的开口端顶靠制动块的背板 活塞由铸铝合金制造 为了提高耐磨损性能 活塞的工作表面进行镀铬处理 为了解决因制动钳体由铝合金制造而减少传给制动液的热量的问题 减小了活塞与制动块背板的接触面积 制动钳在汽车上的安装位置可在车轴的前方或后方 制动钳位于车轴前可避免轮胎甩出来的泥 水进入制动钳 位于车轴后则可减小制动时轮毂轴承的合成载荷 因此本次设计采用可锻铸铁 整体式 镀铬处理 前制动钳位于车轴后 后制动钳位于车轴前 制动块由背板和摩擦衬块构成 两者直接牢固地压嵌或铆接或粘接在一起 衬块多为扇形 也有矩形 正方形或圆形的 活塞应能压住尽量多的制动块面积 以免衬块发生卷角而引起尖叫声 制动块背板由钢板制成 为了避免制动时产生的热量传给制动钳而引起制动液汽化和减小制动噪声 可在摩擦衬块与背板之间或在背板后粘 或喷涂 一层隔热减震垫 胶 由于单位压力大和工作温度高等原因 摩擦衬块的磨损较快 因此其厚度较大 许多盘式制动器装有衬块磨损达极限时的警报装置 以便及时更换摩擦衬片 本次设计取衬块厚度12mm 有隔热减震垫 有报警装置 摩擦块 钳体 弹簧 密封圈 油塞防尘套 摩擦背板 摩擦块 制动盘 支撑架 保持弹簧 活塞 油缸 防尘油套 密封圈 活塞 弹簧 支撑架 保持弹簧 已完成的工作 1 ABS防抱死制动系统相关文献的收集 以及了解了防抱死制动的工作原理2 盘式制动器结构的设计及改进 工程图的绘制 对盘式制动器进行了相关参数的计算以及校核 另外对其进行了运动仿真3 设计说明书的修改 相关外文文献的翻译 湘潭大学机械工程学院毕业论文(设计)工作中期检查表系 机械工程 专业 机械设计制造及其自动化 班级 一班 姓 名欧嵩干学 号2010500334指导教师朱石沙指导教师职称教授题目名称乘用车防抱死制动系统的分析及盘式制动器的设计初步题目来源 科研 企业 其它课题名称乘用车防抱死制动系统的分析及其关键部件的设计初步题目性质 工程设计 理论研究 科学实验 软件开发 综合应用 其它资料情况1、选题是否有变化 有 否2、设计任务书 有 否3、文献综述是否完成 完成 未完成4、外文翻译 完成 未完成由学生填写从方案制定到现在,我收集并阅读了大量的有关ABS防抱死制动的书籍文献,期间有不懂的地方还请教了研究生学长和老师,现在我完成了ABS系统的分析和制动器的参数选择,并着重对制动器进行设计和校核,目前用solidedge制图正在进行中。虽然对制图软件已掌握,但由于对盘式制动器的结构不了解,导致制图过程缓慢,在设计过程中主要遇到的问题有1)对结构参数的选定上。2)结构的设计与装配上。3)理论可行性的验证方法。完成校核和制图后,我将开始书写设计说明书,翻译外文文献,整理资料,准备好论文答辩的工作。由老师填写工作进度预测(按照任务书中时间计划) 提前完成 按计划完成 拖后完成 无法完成工作态度(学生对毕业论文的认真程度、纪律及出勤情况): 认真 较认真 一般 不认真质量评价(学生前期已完成的工作的质量情况) 优 良 中 差存在的问题与建议: 指导教师(签名): 年 月 日建议检查结果: 通过 限期整改 缓答辩系意见: 签名: 年 月 日注:1、该表由指导教师和学生填写。2、此表作为附件装入毕业设计(论文)资料袋存档。任务书论文(设计)题目: 乘用车防抱死制动系统的分析及其关键部件的设计初步 学号: 2010500334 姓名: 欧嵩干 专业: 机械设计制造及其自动化 指导教师: 朱石沙 系主任: 一、主要内容及基本要求 查阅相关文献资料,了解乘用车防抱死制动系统的国内外研究动态,完成乘用车防抱死制动系统的分析及其关键部件的设计初步。 要求: 1、查阅相关资料,基本掌握乘用车防抱死制动系统的组成及功能;基本掌握实时道路识别技术。 2、设计一款结构简单、可靠的防抱死制动系统的执行部件。 3、不少于2*A0图纸; 4、撰写毕业设计说明书。 5、相关外文文献翻译,字数3000字以上。 二、重点研究的问题 防抱死制动系统的执行部件设计 。 三、进度安排序号各阶段完成的内容完成时间1查阅资料、调研第1-2周2开题报告、制订设计方案第3周3方案(设计)第4-5周4防抱死制动系统的执行部件设计第6-7周5写出初稿,中期检查第8-9周6修改,写出第二稿 第10-11周7写出正式稿 第12-13周8答辩第14周四、应收集的资料及主要参考文献 张秀芹.多轴车ABS制动性能仿真与试验研究D.武汉理工大学,2012. 贾玉梅.汽车ABS虚拟仿真平台的研究与应用D.重庆邮电大学,2011. 李文娟,付天雷,陈凤林等.汽车防抱死制动系统的自寻最优控制J.哈尔滨理工大学 学报,2010. 郝茹茹,赵祥模,周洲等.整车防抱死制动系统台架检测与道路对比试验J.农业机械 学报,2013. Electrokinetics of non-Newtonian fluids: A reviewCunlu Zhao, Chun YangSchool of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Republic of Singaporea b s t r a c ta r t i c l ei n f oAvailable online xxxxKeywords:Non-Newtonian electrokineticsNon-linear electrokinetic phenomenaElectroosmosisElectrophoresisViscoelectric effectElectrorheological fluidsMicrofluidicsThis work presents a comprehensive review of electrokinetics pertaining to non-Newtonian fluids. The topiccovers a broad range of non-Newtonian effects in electrokinetics, including electroosmosis of non-Newtonianfluids, electrophoresis of particles in non-Newtonian fluids, streaming potential effect of non-Newtonian fluidsand other related non-Newtonian effectsinelectrokinetics.Generally, thecoupling between non-Newtonian hy-drodynamicsandelectrostatics not only complicates theelectrokinetics but also causesthefluid/particlevelocityto be nonlinearly dependent on the strength of external electric field and/or the zeta potential. Shear-thinningnature of liquids tends to enhance electrokinetic phenomena, while shear-thickening nature of liquids leads tothe reduction of electrokinetic effects. In addition, directions for the future studies are suggested and severaltheoretical issues in non-Newtonian electrokinetics are highlighted. 2013 Elsevier B.V. All rights reserved.Contents1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .02.Electroosmosis of non-Newtonian fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .03.Electrophoresis in non-Newtonian fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .04.Streaming potential effect of non-Newtonian fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .05.Other non-Newtonian effects in electrokinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .05.1.Viscoelectric effect in electrokinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .05.2.Ion-crowding induced shear-thickening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .05.3.Electrorheological fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .05.4.Electroviscous effect of colloidal suspensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .06.Conclusions and outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .06.1.Criterion for non-Newtonian behavior inside EDL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .06.2.Depletion layer due to non-adsorbing particles and adsorption layer due to adsorbing particles . . . . . . . . . . . . . . . . . . . . . .06.3.Charged particles effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .01. IntroductionThe recently growing interests in electrokinetic phenomena aretriggered by their diverse applications in microfluidic devices whichcouldhavethepotentialtorevolutionizeconventionalwaysofchemicalanalysis,medicaldiagnostics,materialsynthesis,drugscreeningandde-liveryaswellasenvironmentaldetectionandmonitoring.Theprevalentuse of electrokinetic techniques in microfluidic devices is ascribed totheir several distinctive advantages: (i) the devices are energized byelectricity which is widely available and ease of control; (ii) the devicesinvolve no moving parts and thus less mechanical failures; (iii) theinduced velocity of liquid or particle is independent of geometricdimensions of devices; (iv) the devices can be readily integrated withother electronic controlling units to achieve fully-automated operation.In addition to its useful applications in microfluidics, electrokinetics isalso a basis for understanding various phenomena, such as ionic trans-portand rectificationin nanochannels 1,2, thermophoresis in aqueoussolutions 3,4, electrowetting of electrolyte solutions 5,6 and so on.When a solid surface is brought into contact with an electrolytesolution, the solid surface obtains electrostatic charges. The presenceof suchsurface charges causes redistribution of ions andthenforms aAdvances in Colloid and Interface Science xxx (2013) xxxxxx Corresponding author. Tel.: +65 6790 4883; fax: +65 6792 4062.E-mail address: mcyang.sg (C. Yang).CIS-01308; No of Pages 150001-8686/$ see front matter 2013 Elsevier B.V. All rights reserved./10.1016/j.cis.2013.09.001Contents lists available at ScienceDirectAdvances in Colloid and Interface Sciencejournal homepage: /locate/cisPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001charged diffuselayerinthe electrolytesolutionnearthe solid surfaceto naturalize the electric charges on solid surface. Such electricallynonneutral diffuse layer is usually dubbed electric double layer(EDL) which is responsible for two categories of electrokineticphenomena, (i) electrically-driven electrokinetic phenomena and(ii) nonelectrically-driven electrokinetic phenomena. The basicphysics behind the first category is as follows: when an externalelectric field is applied tangentially along the charged surface, thecharged diffuse layer experiences an electrostatic body force whichproduces relative motion between the charged surface and the liquidelectrolyte solution. The liquid motion relative to the stationarycharged surfaces is known as electroosmosis (Fig. 1a), and themotion of charged particles relative to the stationary liquid isknown as electrophoresis (Fig. 1b). The classic electroosmosis occursaround solids with fixed surface charges (or, equivalently, zetapotential ) for given physiochemical properties of surface andsolution, and then the effective liquid slip at the solid surfaceunder the situation of thin EDLs is quantified by the well-knownHelmholtzSmoluchowski velocity, i.e., us= E0/ ( is the elec-tric permittivity of the electrolyte solution, is the zeta potential ofthe solid surface, E0is the external electric field strength and isthe dynamic viscosity of electrolyte solution). When a chargedparticle with a thin EDL is freely suspended in a stationary liquidelectrolyte solution, electroosmotic slip motion of solution mole-cules on the particle surface induces the electrophoretic motion ofparticle with a velocity given by the Smoluchowski equation, U =E0/ (Note that here denotes the zeta potential of particle). Onetypical behavior of the second category is the generation of streamingpotential effect in pressure-driven flows (Fig. 1c). There are surpluscounterions in EDLs adjacent to the channel walls, and the pressure-driven flow convects these counterions downstream to gives rise to astreaming current. Simultaneously, the depletion (accumulation) ofcounterions in the upstream (downstream) sets up a streaming poten-tial which drives a conduction current in opposite direction to thestreaming current. At the steady state, the conduction current exactlycounter-balances the streaming current, and the streaming potentialbuilt up across the channel under the limit of thin EDLs is given byEs= P/(0) (P is externally applied pressure gradient and 0repre-sents the bulk conductivity of electrolyte solution). More fundamentaland comprehensive descriptions of electrokinetic phenomena aregiven in textbooks and reviews 713.Previous description of electrokinetics usually assumes Newtonianfluids with constant liquid viscosity, and most studies of electrokineticsin literature adopt such assumption. But in reality, microfluidic devicesare more frequently involved in analyzing and/or processing biofluids(such as solutions of blood, saliva, protein and DNA), polymericsolutions and colloidal suspensions. These fluids cannot be treated asNewtonian fluids. Therefore, the characterization of hydrodynamics ofsuch non-Newtonian fluids relies on the general Cauchy momentumequation in conjunction with proper constitutive equations whichgenerally define the viscosity of liquid to vary with the rate of hydrody-namic shear, rather than the NavierStokes equation which is onlyapplicabletoNewtonianfluids.Sinceelectrokineticsresultsfromthecou-pling of hydrodynamics and electrostatics, it is straightforward to believeFig. 1. Schematic illustration of mechanisms for three typesof electrokinetic phenomena. (a) Electroosmosis: positively charged EDLs with a thickness of Disformed near the negativelycharged solid channel walls. Then an electric field (E0) applied tangentially along the channels walls exerts an electrostatic body force in the EDLs to drive electroosmotic slip flow (us) inthe microchannel. (b) Electrophoresis: On the surface of a free particle in an electrolyte solution, an applied electric field (E0) induces electroosmotic slip velocity (us) which moves thecharged particle with a velocity (U = us). (c) Streaming potential: The convective transport of ionic charges in the EDLs (E) by a pressure-driven flow (the velocity profile denotedby u is shown on the left of the figure) induces a streaming current (the corresponding current density profile denoted by Eu is shown in the middle of the figure). Simultaneously,such streaming current leads to the accumulation (depletion) of counterions downstream (upstream), thereby setting up a streaming potential which drives a conduction current (thecorresponding current density profile denoted by Esis shown in the right of the figure, where is the local electric conductivity of electrolyte solution and Esis the streaming potential)to counterbalance the streaming current.2C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001that non-Newtonian hydrodynamics would modify the conventionalNewtonianelectrokinetics.Inthisreview,non-Newtonianeffectsonelec-trokinetics are comprehensively summarized and discussed. This reviewis organized as follows: Section 2 provides a review on the most widely-studied electroosmosis of non-Newtonian fluids. Section 3 presents a re-view for the electrophoresis of particles in non-Newtonian fluids, andSection 4 discusses the streaming potential effects of non-Newtonianfluids.Other non-Newtonianeffectsof particularinterestonelectrokinet-icsaregiveninSection5.Lastly,Section6concludes thereviewandiden-tifies the directions for the future studies.2. Electroosmosis of non-Newtonian fluidsThe pioneering contribution to this field is probably attributed toBello et al. 14 who experimentally measured an electroosmotic flowof a polymer (methyl cellulose) solution in a capillary. Their investiga-tion showed that the electroosmotic velocity of such polymer solutionis much higher than that predicted with the classic HelmholtzSmoluchowski velocity. It was then proposed that the shear-thinninginduced bypolymer moleculeslowerstheeffectivefluid viscosityinsidethe EDL. About a decade later, more interests were paid to such phe-nomenon both experimentally and theoretically. Chang and Tsao 15conductedanexperimentsimilartothatofBelloetal.14toinvestigateanelectroosmoticflowofthepolyethyleneglycolsolutionandobservedthatthedragaswellastheeffectiveviscositywasgreatlyreducedduetothe sheared polymeric molecules inside theEDL. On theoretical aspects,recent efforts have resulted in a great deal of information on electroos-motic flows of non-Newtonian fluids. Specifically, non-Newtonianeffects are characterized by proper constitutive models which relatethe dynamic viscosity and the rate of shear. There has been a largeclass of constitutive models available in the literature for analyzing thenon-Newtonian behavior of fluids, such as power-law model, Carreaumodel, Bingham model, Oldroyd-B model, Moldflow second-ordermodel and so on. Power-law fluid model is certainly the most popularbecauseitissimpleandabletofitawiderangeofnon-Newtonianfluids.One important parameter in the power law fluid model is the fluidbehavior index (n) which delineates the dependence of the dynamicviscosityontherateofshear.Ifnissmaller(greater)thanone,thefluidsdemonstrate the shear-thinning (shear-thickening) effect that the vis-cosity of fluid decreases with the increase (decrease) of the rate ofshear. If n is equal to one, the fluids then exactly behave as Newtonianfluids.DasandChakraborty16obtainedthefirstapproximatesolutionfor electroosmotic velocity distributions of power-law fluids in aparallel-plate microchannels. However, their analysis did not clearlyaddress the effect of non-Newtonian effects on electroosmotic flows.Zhao et al. 17,18 carried out theoretical analyses of electroosmosisof power-law fluids in a slit parallel-plate microchannel and fullydiscussed the non-Newtonian effects on electroosmotic flow. Theiranalyses revealed that the fluid rheology substantially modifiesthe electroosmotic velocity profiles and electroosmotic pumpingperformance. Particularly, they derived a generalized HelmholtzSmoluchowski velocity for power-lower fluids in a similar fashion tothe classic Newtonian Smoluchowski velocity and further elaboratedthe influencing factors of such velocity. Similar analyses were laterextended to a cylindrical microcapillary by Zhao and Yang 19,20. Re-cently, an experimental investigation was performed by Olivares et al.21 who measured the electroosmotic flow rate of a non-Newtonianpolymeric (Carboxymethyl cellulose) solution, and their experimentalmeasurements agree well with the theoretical results predicted fromthegeneralized HelmholtzSmoluchowski velocityof power-lawfluids.Paul22conceptuallydevisedaseriesoffluidicdevicesemployingelec-troosmosisofshear-thinningfluids.Thesedevicesincludedpumps,flowcontrollers,diaphragmvalvesanddisplacementsystemswhichwereallclaimed to outperform their counterparts employing Newtonianfluids. Berli and Olivares 23 addressed the electrokinetic flow of non-Newtonian fluids in microchannels with the depletion layers nearchannel walls. Their analysis essentially considered a combined effectof electroosmosis and pressure-driven flow, and is greatly simplifiedduetothepresenceofdepletionlayers.Berli 24evaluatedthethermo-dynamic efficiency for electroosmotic pumping of power-law fluids incylindrical and slit microchannels. It was revealed that both the outputpressure and pumping efficiency for shear-thinning fluids could beseveral times higher than those for Newtonian fluids under the sameexperimental conditions. Utilizing the LatticeBoltzmann method,Tang et al. 25 numerically investigated the electroosmotic flow ofpower-law fluids in microchannels. An electroosmotic body force wasincorporated in the BhatnagarGrossKrook collision approximationwhich simulates the Cauchy momentum equation. These studies ofelectroosmotic flow of non-Newtonian fluids however all assumedsmall surface zeta potentials which are much less than the so-call ther-mal voltage, i.e., kBT/(ze), where kBis the Boltzmann constant, T is theabsolute temperature, e is the elementary charge, z denotes the valenceof electrolyte ion. This assumption could be easily violated when largesurface zeta potentials are present. Therefore, investigations of electro-osmotic flow of power-law fluids over solid surfaces with arbitrarysurface zeta potentials were reported in 26,27.However, the constitutive model for non-Newtonian fluids inabovementioned investigations is just an extreme case of the moregeneral non-Newtonian Carreau fluid model. In comparison with theNewtonian fluid model, Carreau constitutive model includes fiveadditional parameters and can describe the rheology of a wide rangeof non-Newtonian fluids. Under the limit of zero shear rates, the com-monlyusedpower-lawmodelwouldpredictaninfinitelylargeviscosityfor shear-thinning fluids, while the Carreau model does not have suchdefect but has smoothly transits to a constant viscosity. The Carreaufluid model can well characterize the rheology of various polymeric so-lutions, such as glycerol solutions of 0.3% hydroxyethyl-celluloseNatrosol HHX and 1% methylcellulose Tylose 28, and pure poly(ethyl-eneoxide)29. Thesepolymers are widely used for improving selectiv-ity and resolution in the capillary electrophoresis for separation ofprotein 30 and DNA 31. Zimmerman et al. 32,33 performed finiteelement numerical simulations of the electroosmotic flow of a Carreaufluid in a microchannel T-junction. The analyses suggested that theflow field remarkably depends on the non-Newtonian characteristicsof fluids, and therefore could guide the design of electroosmoticflow rheometers. Zhao and Yang 34 presented a general frameworkto address electroosmotic/electrophoretic mobility regarding non-NewtonianCarreaufluids.Theyconcludedthatelectroosmotic/electrophoretic mobility can be significantly enhanced with shear-thinning fluids and large surface zeta potentials.Due to the nonlinear dependence of the dynamic viscosity on therate of shear, equations governing electroosmotic flows of non-Newtonian fluids also become highly nonlinear and then most oftheoretical analyses rely on either approximate solutions or numericalsimulations. Exact solutions are valuable because they not only canprovide physical insight into the studied phenomena, but also canservesasbenchmarksforexperimental,numericalandasymptoticanal-yses. An exact solution for electroosmotic flow of non-Newtonian fluidswaspresentedbyZhaoandYang18whoconsideredelectroosmosisofa power-law fluid in a slit parallel-plate microchannel as illustrated inFig.2.Thechannelisfilledwithanon-Newtonianpower-lawelectrolytesolutionhavingaflowbehaviorindexn,andaflowconsistencyindexm.The microchannel walls are uniformly charged with a zeta potential .The application of an external electric field E0drives the liquid intomotion because of electroosmotic effect, and the velocity profile wasderived for the situation of low zeta potentials as 18u y usG n;HG n;ycosh1nH1where the Debye parameter is defined as = 1/D= 2e2z2n/(kBT)1/2(wherein e is the charge of an electron, z is the ionic valence,3C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001nis thebulknumberconcentrationof ions, istheelectric permittivityof the solution, kBis the Boltzmann constant, and T is the absolutetemperature). The function G(,) in Eq. (1) is defined asG ; 112cosh 2F1212;12;32; cosh2?2where2F11,2;1;z denotes the Gauss hypergeometric function 35.usin Eq. (1) denotes the so-called HelmholtzSmoluchowski velocityfor power-law fluids and can be written asus n1nnE0m?1n3which was firstly derived by Zhao et al. 17 using an approximatemethod. The thickness of EDL on the channel wall is usually measuredby the reciprocal of the Debye parameter (1), so the nondimensionalelectrokinetic parameter H = H/1characterizes the relative impor-tance of the half channel height to the EDL thickness. Then for largevalues of electrokinetic parameter H (thin EDL or large channel), theHelmholtzSmoluchowski velocity given by Eq. (3) signifies theconstant bulk velocity in microchannel flows due to electroosmosis. Inelectrokinetically-driven microfluidics dealing with non-Newtonianfluids, the HelmholtzSmoluchowski velocity in Eq. (3) is of bothpractical and fundamental importance due to two reasons: First, thevolumetric flow rate can be simply calculated by multiplying the areaof channel cross-section and the HelmholtzSmoluchowski velocity.Second, numerical computations of electroosmotic flow fields in com-plex microfluidic structures can beimmensely simplifiedbyprescribingthe HelmholtzSmoluchowski velocity as the slip velocity on solidwalls. One can find more detailed derivation and discussion of thisgeneralized Smoluchowski velocity in Refs. 17,18,21. Very recently,Zhao and Yang 20 reported an interesting but counterintuitive effectthat the HelmholtzSmoluchowski velocity of non-Newtonian fluidsbecomes dependent on the dimension and geometry of channelsowing to the complex coupling between the non-Newtonian hydrody-namics and the electrostatics.Inmicrofluidicpumpingapplications,theflowrateoraverageveloc-ityisusuallyanindicatorofpumpperformance.Withtheabovederivedelectroosmotic velocity in Eq. (1), the electroosmotic average velocityalong the cross-section of channel can be sought asu 1HZH0u y dy ustanh1nH(sinh Hcos h Hn 12F11;2n 12n;3n 12n;sinh2H?nHsinh2Hn 1 2n 13F11;2n 12n;2n 12n;3n 12n;4n 12n;sinh2H?)4where3F21,2,3;1,2;z represents one of the generalized hyper-geometric functions 35. It needs to be pointed out that all thehypergeometric functions presented in this review can be efficientlycomputed in commercially-available software, such as MATLab andMathematica.With the utilization of the above exact solutions, non-Newtonianeffects on electroosmosis of power-law fluids are presented graphicallyin Fig. 3. Fig. 3(a) shows that the electroosmotic velocity profilebecomes flat inside a much larger channel domain as the fluid behaviorindex decreases. For different values of fluid behavior index, the veloci-ties in the central portion of channel are exactly the correspondingHelmholtzSmoluchowski velocities. The ratio of the average velocityto the HelmholtzSmoluchowski velocity is shown in Fig. 3(b). It isseen that the difference between the average velocity and theHelmholtzSmoluchowski velocity diminishes as fluid behavior indexn decreases or H increases. For the extreme case of H , the aver-agevelocitypreciselyreducestotheHelmholtzSmoluchowskivelocity.It also has to be noted that the velocity under such extreme condition isuniform in the whole channel domain with perfectly plug-like profiles.Consequently, extremely large values of H need to be maintained inmost microfluidic applications to produce plug-like velocity profileswhichensures both highresolution and sensitivity of chemical analysesby minimizing the dispersion of analytes in microchannels. However,for microfluidic applications under some circumstances, it should benoted that the large value of H may be not preferred. For example,electroosmotic flows of Newtonian fluids were found to substantiallyaffect the solute transport, and solute transport achieves the maximalenhancement when H = 40 (H is the half channel height) for0E2Hxyou yFig.2.Schematicsofelectroosmoticflowofpower-lawfluidsinaparallel-platemicrochannelwith a height of 2H. Very thin EDLs develop near two channel walls to screen the wall zetapotential,.Thentheinteractionoftheexternalelectricfield(E0)withEDLsproduceselectro-static body force, resulting in electroosmosis. Because of thin EDLs in microfluidics, theelectroosmotic flow profile u(y) is usually plug-like. Reprinted with permission from 18.Copyright 2011 by Elsevier.0.00.81.00.00.81.0u(y)/usy/H23411 n=0.52 n=1.03 n=1.54 n=2.0a0.00.51.01.52.00.91.0432n1 H=52 H=103 H=504 H=1001Hu/usbFig. 3. Non-Newtonian effects onelectroosmoticflowina slit parallel-plate microchannel.(a) Effectof the fluid behavior index n on electroosmoticvelocity profiles (evaluated fromEq. (1) with H = 15. (b) Effects of the fluid behavior index n and the electrokinetic pa-rameter H on the average electroosmotic velocity (evaluated from Eq. (4). The extremecase of H is denoted by the dashed line. Reprinted with permission from 18.Copyright 2011 by Elsevier.4C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001parallel-platechannels36andH = 60(Histheradius)forcylindricaltubes 37. Later, Mondal and De 38 extended the two analyses tonon-Newtonian fluids, and found that the shear-thinning electroosmo-sis is promising to induce more significant enhancement of solutetransport.The above exact solutions are limited to low surface potentials.For a more general situation with arbitrary surface potentials,exact solutions for electroosmosis of a power-law fluid in parallel-plate channels are absent from literature, probably due to highnonlinearity of both the PoissonBoltzmann equation and the non-Newtonian hydrodynamics. However, for electroosmosis of power-law electrolyte liquids over a flat surface charged with arbitraryzeta potentials, the exact solution of velocity distribution becomespossible and was derived as 26u y n1nnE0m4kBTzetan hze4kBT?1nG y;ze4kBT;n?G 0;ze4kBT;n?5where y is the distance measured from the surface and the functionG(,) is defined in the form of an integral as 26G ; 1Zee2tanh2 #1d ecoth2 hi12F112;1;1 22;e2coth2 ?6At first glance, the velocity distribution Eq. (5) derived for theelectroosmosis over a flat surface seems to be of no practical use sincepractical microfluidic channels are bounded by walls. However,microfluidic channels practically have thin EDLs, and thus the velocityprofile in a channel can be estimated as a superposition of velocityprofiles of individual channel walls predicted from Eq. (5).By using Eq. (5), we can obtain the HelmholtzSmoluchowski slipvelocity over the flat surface asus u y jy n1nnE0m4kBTzetanhze4kBT?1n2F112n;1n;1 2n2n; tanh2ze4kBT?7which is the bulk liquid velocity in the electroosmotic flow of a power-lawfluidinamicrochannelwiththinEDLs.Itisobviousthattheelectro-osmotic velocity approaches to usas long as the distance is much largerthantheDebyelength1(note thatitdoes notneedthedistance to beinfinitely far from the surface as suggested by Eq. (7).An examination of Eq. (7) clearly indicates that the HelmholtzSmoluchowski velocity of power-law fluids scales nonlinearly with thezeta potential, external electric field strength and thickness of EDL. Itis also interesting to note that the HelmholtzSmoluchowski velocityis an explicit function of the temperature. Such feature is differentfrom the classic HelmholtzSmoluchowski velocity of Newtonianfluids which only implicitly depends on the temperature due to thetemperature-dependent electric permittivity and viscosity of fluids.Eq. (7) is a general form of HelmholtzSmoluchowski velocity forpower-law fluids and three special cases can be recovered from it26: Case I, for Newtonian fluids (n = 1), Eq. (7) reduces tous E0m8which is the widely-cited HelmholtzSmoluchowski velocity ofNewtonian fluids; Case II, when |ze/(4kBT)| 1, Eq. (7) then can besimplified to Eq. (3) which is the HelmholtzSmoluchowski velocityunder small zeta potentials; Case III, for very large potentials, i.e., |ze/(4kBT)| 1, Eq. (7) approaches tous n1nnE0m2kBTze?1n1ffiffiffip n12n?2n 12n?9where(z)denotestheGammafunction35.(n 1)/(2n)isinfinite-ly large for shear-thinning and Newtonian fluids (n 1), but of finitevalue for shear-thickening fluids. Thus when the zeta potential becomesvery large, the HelmholtzSmoluchowski velocity for shear-thickeningfluids has a limiting value given by Eq. (9). Besides, in order to transformEq. (9) to a more compact form as Eq. (3), an asymptotic zeta potential,s, can be defined ass 2kBTzen12n?2n12n?nn210Similarly, in order to write Eq. (7) in a more compact form given byEq. (3), an effective zeta potential effcan be defined aseff4kBTzetanhze4kBT?2F112n;1n;1 2n2n; tanh2ze4kBT?)n(11Obviously, it is not surprising that s= eff| . Fig. 4 plots thevariation of normalized effective zeta potential, zeeff/(kBT), with theflow behavior index, n, under different values of normalized actualzeta potentials, ze/(kBT). It is clear from the plot that the effectivezeta potential is identical to the actual zeta potential for Newtonianfluids. However, the effective zeta potentials are higher (lower) thanthe actual zeta potentials for shear-thinning fluids (shear-thickeningfluids). For weakly charged surfaces (e.g., ze/(kBT) = 1), the differ-ence between effective and actual zeta potentials is insignificant, andit also depends weakly on the fluid behavior index. For highly chargedsurfaces, the difference between effective and actual zeta potentials be-comes noticeable, and it depends strongly on the flow behavior index.For example, if the actual wall zeta potential becomes infinitely large(i.e., |ze/(kBT)| ), theeffective zeta potential alsobecomes infinite-ly large for shear-thinning and Newtonian fluids, but approaches a limit-ing value for shear-thickening fluids as represented by the solid line withcircles in Fig. 4. Correspondingly, the HelmholtzSmoluchowski velocityfor shear-thickening fluids also reaches an asymptotic limit as the actualzetapotentialgoestoinfinity.Suchashear-thickeninginducedasymptot-ic behavior of the HelmholtzSmoluchowski velocity is a commonfeature of electrokinetics of non-Newtonian fluids. In Section 5, similar0.500.751.001.251.50-90-75-60-45-30-150|ze/(kBT)|zes/(kBT)zeeff/(kBT)nze/(kBT)= -1ze/(kBT)= -5ze/(kBT)= -10ze/(kBT)= -15Fig. 4. Dependence of the normalized effective wall zeta potential zeeff/(kBT) (fromEq. (11) on the fluid behavior index, n, under different values of normalized actual zetapotential (ze/(kBT). The line with circles is the normalized zeta potential of saturationfrom Eq. (10). Reprinted with permission from 26. Copyright 2010 by Wiley.5C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001asymptotic saturation of the HelmholtzSmoluchowski velocity is to bediscussed for another two cases of shear-thickening behaviors.Recently,efforts also have been made to address combined electroosmoticallyand pressure driven flows of non-Newtonian fluids in microchannels39,40andelectroosmoticflowsofnon-Newtonianfluidsovercomplex-wavy surfaces 41 and even in nanochannels 42,43. In addi-tion, aforementioned theoretical studies of electro-osmotic flows ofnon-Newtonian fluids have been limited to simple inelastic constitutivemodels (pure viscous constitutive models), such as the widely usedpower-lawandCarreaumodels.Manycomplexfluidsactuallycoulddem-onstrate both viscous and elastic behaviors which can be described byvarious viscoelastic constitutive models. Characteristics of electroosmoticflows of non-Newtonian fluids of viscoelastic nature were then in-vestigated theoretically 4456. These investigations unanimouslyrevealed a common feature that the flow pattern as well as volumet-ric flow rate of electroosmosis is significantly affected due to the ex-istence of fluid viscoelasticity. Experimentally, Bryce and Freeman57 demonstrated that the viscoelastic nature of polymer solutioncan induce extensional instability in electroosmotically-drivenmicroflows in a microchannel constriction. One evident applicationof electroosmosis of non-Newtonian fluids is to pump (transport)liquid samples in microfluidic analytical systems 38, other applica-tions include the enhancement of micromixing 5860 and heattransfer 19,6167.3. Electrophoresis in non-Newtonian fluidsFor the electroosmotic flow over a charged surface discussed inSection 2, if we change the system of reference by imagining that thefluid from the charged surface is stationary, and then the chargedsurface is expected to move with a velocity equal in magnitude butopposition in direction to the previously discussed HelmholtzSmoluchowski velocity. This scenario effectively represents the electro-phoretic motion of a particle with thin EDL in an infinitely large non-Newtonian fluid domain 17,18,26,34. Apparently, the previouslydiscussed HelmholtzSmoluchowski velocity of electroosmosis can benaturally applicable to analyzing the electrophoretic velocity of aparticle with thin EDL in unbounded non-Newtonian fluid domains,only with the reversion of its sign and the replacement of the zetapotential of charged channel wall with that of charged particle.Actually, the earliest attention paid to electrophoresis of particles innon-NewtonianliquidscouldbetracedbacktoSomlyody68whofileda patent 30 years ago about electrophoretic display which utilizes anon-Newtonian liquid to provide superior threshold characteristics. In1985, VidybidaandSerikov 69 presentedprobably thefirsttheoreticalstudy of the electrophoresis of a spherical particle in a non-Newtoniansolution. They demonstrated an interesting and counterintuitive effectthat the net electrophoretic motion of a particle in non-Newtonianfluids can be induced by an alternating electric field. Then this area ofresearch was left blank for nearly 20 years, and was recently renewedby Hsus group. In 2003, Lee et al. 70 analyzed the electrophoreticmotion of a rigid spherical particle in non-Newtonian Carreau fluidsenclosed by a spherical cavity with assumptions of low zeta potentialandweakappliedelectricfield.Theyspeciallypaidattentiontotheelec-trophoretic characteristicsof a spherical particle located at the center ofthe cavity. Later, the analysis was extended to investigate electrophore-sisofsphericalparticleslocatedatarbitrarypositioninsidethesphericalcavity 71. In addition to single particle electrophoresis, Hsu et al. 72conducted an investigation of the electrophoresis of a concentratedparticle dispersion in a Carreau fluid with assumptions of low zetapotentials, and the analysis with arbitrary potentials was done by Leeet al. 73. To investigate the effect of boundary on electrophoresis innon-Newtonian fluids, Lee et al. 74 considered the electrophoresis ofa spherical particle in a Carreau fluids normal to a uncharged planarsurface, and found that the presence of planar surface enhances theshear-thinning effect and thus the electrophoretic mobility. A similaranalysisbyHsuetal.75waslatercarriedouttoinvestigatetheelectro-phoresis of a spherical particle in a Carreau fluid normal to a largecharged disk. In order to more closely simulate the real applications,Hsu et al. 76 analyzed the electrophoresis of a spherical particle inCarreau fluids bounded by a cylindrical microcapillary under theconditions of low zeta potential and weak applied electric field. Manypractical electrophoretic applications involve biological particles thatare more reasonably represented by rod-like particles, such as protein,and DNA. To this end, Yeh and Hsu 77 extended previous studies onthe electrophoresis of a spherical particle in non-Newtonian fluidsalongtheaxis ofa cylindrical channel tothecaseof a cylindrical particle(a finite rod). The general conclusion from the studies by Hsus group isthat the electrophoretic mobility of a particle is enhanced with a shear-thinning fluid and/or a thinner EDL surrounding the particle. This is inconsistency with the dependence of electroosmotic velocity on thefluid rheology and EDL thickness presented and reviewed in the previ-ous section. Very recently, Khair et al. 78 demonstrated that theelectrophoretic velocity of a uniformly charged particle with a thinEDL in non-Newtonian fluids explicitly depends on shape and size ofthe particle. This behavior is quite contrary to the electrophoresis inNewtonian fluids. Moreover, it was identified that the stresses outsidethe EDL (i.e., inside the bulk electroneutral non-Newtonian fluid) areresponsible for such complicated dependence. Interestingly, such sizeand geometry dependence of electrophoresis in non-Newtonian fluidsqualitatively coincides with electroosmosis of non-Newtonian fluids asreported in Ref. 20.In summary, it can be concluded that the electrophoretic velocity ofparticleinanon-Newtonianfluidscalesnonlinearlywiththeexternalap-plied field and the particle zeta potential, resembling the electroosmoticflows of non-Newtonian fluids. Another notable feature is that use ofshear-thinning liquids would enhance the electrophoretic mobility ofparticles and thus leads to fast motion of particles under electric fields.4. Streaming potential effect of non-Newtonian fluidsThe first attempt made to investigate the streaming effect ofnon-Newtonian fluids was as early as 1960s. Raza and Marsden 79,80reported their experimental measurements of the pressure-driven flowof aqueous foams through Pyrex tubes and the associated streaming po-tential. They observed remarkably high streaming potentials (e.g., 50 V)for nonionic foaming agents. The streaming potential of such largemagnitude generates significant electroosmotic flow which resists thepressure-driven flow, thereby being regarded as the main reason forthe blockage of foam flow in porous mediums. In order to correlate theexperimental results, the foam was assumed to be a non-Newtonianpower-law fluid and a theoretical model was then formulated todescribe the streaming potential across circular tubes. The calculatedstreaming potential favorably agrees with the measured streamingpotential. In next several decades, this effect apparently has been leftunnoticedintheliterature.Recently,Bhartietal.81theoreticallyinves-tigated the pressure-driven flow of a power-law liquid in a cylindricalmicrochannel with electroviscous effects. They numerically estimatedthe streamingpotential field which was shown to decrease as increasingthe fluid behavior index. Furthermore, it was found that due to thestreaming potential effects the flow reduction for shear-thinning fluidsis more significant than that for shear-thickening fluids. Utilizing amore general Carreau liquid model, Bharti et al. 82 carried out a similarinvestigation by considering a pressure-driven flow in a cylindricalmicropipe with a contraction-expansion structure. Zhao and Yang83 analyzed the pressure-driven flow of power-law fluids in slitmicrochannels under the effect of streaming potential. In this analysis,analytical solutions for the streaming potential and velocity field wereobtained for arbitrary fluid behavior indices in terms of incompletegamma functions. Vasu and De 84 studied the similar problem. Exactsolutions of streaming potential were obtained for several special valuesofflowbehaviorindex(suchasn = 1,1/2,1/3),andnumericalsolutions6C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001were sought for arbitrary values of flow behavior index. Additionally,parametric studies were carried out to assess effects of applied pressuregradient, fluid behavior index, EDL thickness and zeta potential on theapparent viscosity, streaming potential and friction coefficient. Fig. 5shows the effects of pressure-gradient and the fluid behavior index onthe streaming potential. The streaming potential increases with increas-ing pressure gradient and/or decreasing fluid behavior index, and thedependence of the streaming potential on the fluid behavior indexbecomes more significant for a larger pressure gradient.Tang et al. 85 numerically investigated the streaming potentialeffect on pressure-driven non-Newtonian fluid flow in microchannelsusing the Lattice Boltzmann method. The proposed Lattice Boltzmannmethod with second-order accuracy was claimed highly efficientfor characterizing flow fields of non-Newtonian fluids with shear-dependent viscosities. The Lattice Boltzmann method was furtherutilized by the same group to investigate the streaming potential effecton pressure-driven flows in microporous structures 86. Aside fromfundamental interests, streaming potential effect of non-Newtonianinelastic fluids was also recently explored to convert mechanical workto electricity83,87. It wasshown that non-Newtonianpolymeric solu-tions of shear-thinning nature can substantially increase the energyconversion efficiency in comparison with Newtonian electrolytesolutions under the same operating conditions. More recently, the useof streaming potential effect for electricity generation was achieved byusing non-Newtonian viscoelastic fluids 88.The above analyses generally predict that shear-thinning fluidsinduce larger streaming potentials than shear-thickening fluids doesunder a same applied pressure gradient, and correspondingly wouldexperience more significant flow reduction due to streaming potentialeffect.Thesefindings can provide more physical insightinto thecharac-teristics of non-Newtonian fluid flows in microchannels, thereby givingrise to better control of the non-Newtonian fluid flows in microfluidicdevices.5. Other non-Newtonian effects in electrokineticsIn this section, non-Newtonian effects in electrokinetics includ-ing (i) viscoelectric effect, (ii) ion-crowding induced thickening,(iii) electrorheological effect, and (iv) electroviscous effect of colloi-dal suspensions will be discussed. Non-Newtonian rheology in thefirst and third cases stems from the electric field dependent dynamicviscosity, and that in the second case refers to the increased viscosityin EDLs dueto highlypacked ions, and that in thefourthcase is due tothe flow-induced deformation of EDLs. The origins of these fournon-Newtonian effects are different from those reviewed in previousthree sections which are due to the dependence of dynamic viscosityon the rate of shear.5.1. Viscoelectric effect in electrokineticsThe phenomenon in which the viscosity of liquid varies with thestrength of external electric field is referred to as viscoelectric effectwhich was first experimentally reported by Andrade and Dodd 89,90and commonly described as E 01 fE2?12where 0is the usual liquid viscosity in absence of external electricfields, E is the strength of local electric field, and f represents theso-called viscoelectric coefficient. For three liquids of chloroform,chlorobenzene and amyl acetate, the viscoelectric coefficients weremeasured to be 1.89 1016, 2.12 1016, and 2.74 1016m2/V2,respectively 89,90. As suggested by Eq. (12), the local viscosity nearhighly charged solid surfaces can increase significantly because of thevery strong electric field normal to the surface inside the EDL. Lyklemaand Overbeek 91, and Lyklema 92 determined experimentallythe value of f for water to be 1.02 1015m2/V2and showed thatviscoelectriceffectwouldmodifytheconventionalHelmholtzSmoluchowski velocity. Here, we show a simple derivation of theHelmholtzSmoluchowski velocity subjected to viscoelectric effect.When a flat surface with a wall zeta potential of is considered, theHelmholtzSmoluchowski velocity over this surface can be derived as91,92us E0Z0d13whereistheelectricpermittivityofsolutiontakentobeaconstantatthemoment, E0is the external electric field tangential to the surface, and isthe potential distribution inside EDL. In order to obtain an analyticalformula for us, an integration of Eq. (13) needs to be carried out. To doso, and should be explicitly correlated. With aid of Eq. (12), thedynamic viscosity of solution inside the EDL can be expressed as 01 fddy?2?14where d/dy is the double layer field strength (wherein y represents thecoordinate normaltotheflatsurface) and canbederived from the GouyChapman solution of EDL potential as (d/dy)2= C sin h2ze/(2kBT).Then Eq. (13) can be transformed asus E00Z0d1 f C sinh2ze2kBT?15where C = 8nkBT/ (all the symbols have the same definitions asthose in Eq. (1), and f C = f/(1/C) can be interpreted as the dimen-sionless viscoelectric coefficient. It should be noted that the contri-bution of externally applied electric field to Eq. (14) is negligiblesince usually |E0| |d/dy|. Finally, one is able to integrateEq. (15) to obtain an exact formula for the HelmholtzSmoluchowskivelocity asus E002kBTzearctanffiffiffiffiffiffiffiffiffiffiffiffifC1ptanhze2kBT?ffiffiffiffiffiffiffiffiffiffiffiffifC1p16Fig. 5. Variation of streaming potential with the flow behavior index (n) under variouspressure gradients (G). a is the channel half height, 1= Dis the EDL thickness, andthen a quantifies the relative thickness of EDL. Reprinted with permission from 84.Copyright 2010 by Elsevier.7C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001When f C 1, one can readily show that Eq. (16) reduces tous E002kBTzetanhze2kBT?17ClearlytheHelmholtzSmoluchowskivelocitynowbecomesnonlinearly dependent on the wall zeta potential because of theviscoelectric effect. When the viscoelectric effect is absent, i.e., f = 0,Eq. (16) naturally reduces to the conventional form of the HelmholtzSmoluchowski velocity given by Eq. (8). For extremely large zetapotentials, i.e., |ze/2kBT| 1, the HelmholtzSmoluchowski velocityin Eq. (16) reaches an asymptotic valueusE002kBTzearctanffiffiffiffiffiffiffiffiffiffiffiffifC1pffiffiffiffiffiffiffiffiffiffiffiffifC1p18Similar to the electroosmosis of non-Newtonian power fluidsover flat surface discussed in Section 2, we also define an effectivezeta potentialeff2kBTzearctanffiffiffiffiffiffiffiffiffiffiffiffifC1ptanhze2kBT?ffiffiffiffiffiffiffiffiffiffiffiffifC1p19Eq. (16) then can be rewritten in the conventional form ofHelmholtzSmoluchowski velocity as in Eq. (8). The results predictedfrom Eq. (19) are shown in Fig. 6. It is interesting to note the effectivezeta potential approaches its asymptotic values at large actual zetapotentials when the viscoelectric effect is present (e.g., fC 0). Thisbehavior is reminiscent of the asymptotic behavior due to the shear-thickening behavior of liquids discussed in Section 2. However, theshear-thickening in this case is induced by the EDL electric field as sug-gested by Eq. (14), while that in Section 2 is induced by the shear-ratedependent viscosity. The asymptotic saturation of effective zeta poten-tial shown in Fig. 6 indicates that the viscoelectric effect tremendouslyenhances the viscosity of the inner part of the EDL so that the innerpart of the EDL looks like immobilized. Lyklema 91,92 assumed thatsuch enhancement of viscosity is attributed purely to the electric field-dependent viscosity of solvent (as suggested by Eq. (14), and is notdependent on the local net charge density. However, this assumptionwas later shown to be in conflict with recent experimental andtheoretical investigations on hydrodynamic slip and electrokinetics innanochannels (see detailed discussion in Section 4.1.2 of Ref. 93).Bazant et al. 93 further argued that the highly charged surface wouldresult in the crowding of counterions inside EDL (to be discussed inSection 5.2), leading to the apparent viscosity near the surface to signif-icantly deviate from the pure bulk solvent.In addition to increasing the viscosity of solvent, the electric fieldalso reduces the dielectric constant of solvent because of the saturationeffect94,95. Consideringthehighelectric fieldstrengthinthe EDL,thedielectric constant of solvent can be modified according to 01Bddy?2?20where 0is the solvent permittivity under the zero electric fieldstrength,andthecoefficientBdescribesthestrengthofdielectric reduc-tion, and is estimated to be 4 1018m2/V for the room-temperaturewater.Underthejointactionoftheviscoelectric effectandthedielectricreduction, one can follow a similar procedure of deriving Eq. (16) toobtain a more generalversion of the HelmholtzSmoluchowskivelocityasus 0E00kBTzezekBTBffiffiffiffiffiffiffiffiffiffiffiffifC1p 2 B farctanffiffiffiffiffiffiffiffiffiffiffiffifC1ptanhze2kBT?fffiffiffiffiffiffiffiffiffiffiffiffifC1p21which clearly includes Eq. (16) as a special case when B = 0.5.2. Ion-crowding induced shear-thickeningIn dilute electrolyte solutions, the concentration of ionic species andthe electric potential in the diffuse part of EDL over a charged surface isrelated bythePoissonBoltzmannequation.Inclassicallinearelectroki-netic phenomena, the potential drop across the EDL (or so-called zetapotential) is typically comparable to the thermal voltage (kBT/(ze).However, practical applications may encounter the situations withlarge zeta potentials. One example is that the induced-charge electroki-netic phenomena under a typical driving voltage of order 100 kBT/(ze)involves large induced zeta potentials significantly exceeding thethermal voltage 93. It is found that under such circumstances thePoissonBoltzmann theory breaks down by predicting ridiculouslyhigh concentrations of counterions on the solid surface. This is attribut-ed to the assumption of point-like ions embedded in the classicPoissonBoltzmann equation. However, ions have finite sizes whichwere already shown to have important implications on EDL charging96 and ACEO pumping 97. For heavily charged solid surfaces, thecounterions in the electrolyte solution become highly packed insidethe EDL. Therefore, the conventional PoissonBoltzmann equationbecomes invalidated, and the local viscosity in the EDL also drasticallyincreases. More advanced models are required to modify the PoissonBoltzmann equation and the viscosity inside EDL. Bazant et al. 98addressed this issue and they hypothesized that the crowding ofcounterionsinaEDLmodifiestheconventionalPoissonBoltzmannthe-ory and thickens the fluids (equivalently increases the local viscosity).To clarify the effects of ionic crowding on the ion distribution insidethe EDL, they employed the simplest modified PoissonBoltzmanntheory of Bikerman and others 99,100. Furthermore, the ratio ofelectric permittivity to viscosity was also postulated to diverge as thecounterions becomes extremely packed. A simple model was thenformulated to describe the shear-thickening of liquids 98001ejja3ze !22where eis the local net charge density, a is the effective diameter ofions, 0and 0are bulk electric permittivity and dynamic viscosity ofthe solution, respectively.02468100246810fC=100fC=10fC=1fC=0.1fC=0.01fC=0ze/(kBT)zeeff/(kBT)Fig. 6. Variation of the effective zeta potential, zeeff/(kBT), with the actual zeta potential,ze/(kBT), for different strength of viscoelectric effect. Nondimensional parameter fC char-acterizes the strength of viscoelectric effect, and fC = 0 corresponds to the case withoutviscoelectric effect such that eff= .8C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001Combining Eq. (22) and the modified PoissonBoltzmann theory ofBikerman, one can derive the effective zeta potential to beeff sgn kBTzeln 1 2sinh2ze2kBT?23where = 2a3c0NA(c0is the bulk molar concentration of electrolyteand NAis Avogadro constant) denotes the volumetric fraction of bulksolvated ions and also can be seen as a characterization of the intensityofioniccrowding.Inthelimitofpoint-likeions( = 0),onecanreadilyobtain the classical result, eff= . Eq. (23) is rather simple withinvolvement of only one additional parameter of the effective ion size,a. Therefore, it is unable to fit some experimental data. With moreadvanced modified PoissonBoltzmann theories and more complexcorrelationsofcharged-induced shear-thickening, it is possible tointro-duce more than one parameter to fit the ion size effect observed inexperiments. For a more detailed review of this aspect, one may referto 93. Fig. 7 presents the results predicted from Eq. (23) in responseto different intensities of ionic crowding. The effective zeta potentialbecomes saturated to an asymptotic value at the large value of actualzeta potential when the effect of finite ion size is important. For largervalues of (more significant ion crowding), the effective zeta potentialattains a lower asymptotic value at a lower actual zeta potential. Theconclusion from this figure is that the chemistry of solution (a, z andc0) affects the effective zeta potential, which is different from the classi-cal behavior of eff= under the limit of point-like ions ( = 0).The soundness of the above concept for ion-crowding inducedshear-thickening is validated by its consistency with previous modelswhich predict an increase of bulk viscosity with increasing bulkelectrolyte concentration 101103. It is promising from Fig. 7 thation-crowding induced shear-thickening could explain the dependenceof the HelmholtzSmoluchowski velocity on solution chemistry,througha,zandc0.Inaddition,alongwithmodifiedPoissonBoltzmanntheories, it also could be applicable to model the behavior of electrolytesolutions confined in nanostructures where the ionic crowding shouldbe of tremendous significance.5.3. Electrorheological fluidsElectrorheological fluids are nonaqueous suspensions of extremelyfine dielectric particles. Under the influence of external electric fields,the enhancement of apparent viscosity of a typical electrorheologicalfluid can reach as high as 5 orders of magnitude 104, thereby leadingto the transformation of electrorheological fluid from the liquid stateto the gel state. Winslow 105,106 first noticed the electrorheologicaleffect in the late 1940s, and found that it was because of the fibrillatedchains of particles formed in electrorheological suspensions. Fig. 8shows the change of microstructure in an electrorheological fluid sub-ject to an external electric field. Without an electric field, the particlesare uniformly suspended in the liquid; while under the effect of anelectric field, the particles form chained structures along the directionof the applied electric field. The change of the system from thedisordered state to an ordered state is responsible for the incredible in-crement of apparent viscosity. It should be mentioned that differentfrom other non-Newtonian effects reviewed in the present work,electrorheological effect is not because of EDLs (free charge); insteadit is purely due to dielectric response (bond charge) of particles andsurrounding liquid medium. Therefore, in the present review electroki-netics may have a more general definition of the motion inducedby electricity, and is not necessarily limited to its classical definitionassociated with EDLs.The rheological response of electrorheological fluids is commonlycharacterized by a constitutive model of Bingham type 107 ;E0? 0E0 pl 0for N 0E0for b0E024where ;E0?istheshearstress, istherateofshear,E0isthestrengthofapplied electric field, 0(E0) is the dynamic yield stress and pldenotesthe plastic viscosity. When subjected to a shear stress higher than0(E0),theelectrorheological fluidsbehaveasliquidsandtheincremen-tal shear stress ( ;E0?0E0) is linearly proportional to the rate ofshear. However, when subjected to a shear stress lower than 0(E0),electrorheological fluids behave as solids. Typically, the yield stress0(E0) varies with the external electric field, while the plastic viscositypllargely does not depend on the external electric field. The responseofshearstresstoelectricfieldsisreversible,andisfastwiththeresponsetime in the order of l100 ms under an electric field of 1 kV/mm.Electrorheological fluids mainly consist of two phases, i.e., a dis-persed phase (solid particles) and a continuous phase (nonaqueous/nonpolar liquids). Occasionally, a third phase (additives) is alsorequired to finely tune the properties of electrorheological fluids. Thecontinuous phase is usually various kinds of insulating oils (silicone oil,vegetable oil, mineral oils and so on), and the material of dispersedphaseincludesmyriadofinorganicoxides/non-oxides,organicandpoly-meric materials 108. It is such rich compositions of electrorheologicalfluids that primarily determine the electrorheological effects. The modu-lation of electrorheological effect can be simply realized by varying thecomposition of fluids. In addition, the electrorheological effect wasfound to be influenced by the geometry of the electrodes. The parallelgrooved electrodes slightly increased the electrorheological effect andthe perpendicular grooved electrodes doubled the electrorheologicaleffect 109; it was believed that these increases in electrorheological ef-fect are achieved by taking advantage of dielectrophoresis of dispersedparticles. With electrodes coated with electrically polarizable materials,electrorheological effect can be significantly increased, and the leakagecurrent in electrorheological fluids was minimized 110. Compared toother non-Newtonian electrokinetics reviewed in the present work,electrorheological fluids not only have well-developed theories but alsonumerousestablishedapplications.Intheliterature,severalexcellentre-views107,108,111,112havebeendedicatedtoelectrorheologicalfluidsin terms of mechanisms, models, materials and applications. The inten-tion of the present review is to summarize various non-Newtonianeffects in electrokinetics, and electrorheological effect is one of themaccording to the aforementioned general definition of electrokinetics.However, in order not to compete with those reviews, we herein onlyprovide a very brief discussion of the mechanisms and applications ofelectrorheological fluids.The major obstacle limiting the use of electrorheological fluids inpractical applications is the low yield stress in the mode of shearflows. One way to increase the yield stress is by applying an additional051015202530051015202530=0=7.710-2=7.710-5zeeff/(kBT)ze/(kBT)=7.710-8Fig.7.Variationoftheeffectivezetapotentialwiththeactualzetapotentialunderdifferentbulk volume fractions of solvated ions. The three non-zero values of = 7.7 108,7.7 105, 7.7 102in the plot represent respectively three bulk electrolyte concen-trations c0= 1 M, 1 mM, and 1 M with a typical value of the effective ion size a = 4 .9C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001compressive stress on the electrorheological fluid 113. In 2003, Wenet al. 114 discovered another new way of increasing yield stress withthe so-called giant electrorheological fluid. The giant electrorheologicalfluid is formedbydispersingurea-coated nanoparticles of BaTiO(C2O4)2in thesiliconeoil. The high dielectric constant of particles,thesmall sizeof particles and the urea coating are identified to be responsible for thehigh yield stress. Another discovery from their investigation is that theyield stress is linearly proportional to the electric field strength whenthe electric field exceeds 1 kV/mm. This feature is advantageousover conventional electrorheological fluids for which the yield stress isusually nonlinearly related to the electric field strength. In addition,for noticeable electrorheological response, giant electrorheologicalfluids require much lower electrical field strength and current densityin comparison with conventional electrorheological fluids.The applications of electrorheological fluids range from hydraulicvalves 115, clutches 116, brakes 117, shock absorbers 118 andhaptic controllers 119 to tactile displays 120. Other novel applica-tions of these fluids also have been proposed. Since electrorheologicalfluidsarecapableofchangingfromtheliquidstatetoahardstatealmostinstantaneouslyundertheactionofelectric fields,theUSarmyhasbeenplanning to use them to make bulletproof armors. Furthermore,electronics giant-Motorola filed a patent in 2006 for utilizing electro-rheological fluids to make a flexible mobile electronic device. Such de-vice becomes rigid when electrically energized, but can be flexiblybendable when not electrically energized. Because of intrinsic superiorelectrorheological response, giant electrorheological fluids naturallyare suitable for all the above-mentioned purposes. Other than conven-tional applications at the macroscale, a group from The Hong Kong Uni-versity of Science and Technology recently utilized electrorheologicalfluids at the microscale for various microfluidic functionalities, such asmicrodroplet manipulations, microfluidic logic gates, microvalving,micropumping, and micromixing. For more detailed discussion ofmicrofluidic applications of electrorheological fluids, the readers are re-ferred to recent reviews 112,121.5.4. Electroviscous effect of colloidal suspensionsGenerally, the effective viscosity () of a liquid suspension of un-chargedsphericalparticlesishigherthanthatofthepureliquidmedium(0). Under the limit of a low volumetric fraction of particles ( 0),the effective viscosity of the particle suspension can be evaluated fromthe well-known Einstein formula 122,123 01 2:525However, the particle suspending in an aqueous electrolyte solutionacquires electric charge on their surface, and then EDLs have to formaroundparticlestoneutralizesuchsurfacecharge.ThebulkfluidmotionrelativetoparticlesmaycausetheEDLsinequilibrium todeform,whichmanifests asan further increaseinboth energy dissipation andviscosity124,125. This effect offically termed the primary electroviscous effectwas firstly brought into public attention by Smoluchowski 126, andthe effective viscosity of liquid suspension can be modified accordingto the following relation 125 01 2:5 1 p ;a=D?fg26where p(, a/D) is the primary electroviscous coefficient, and itdepends on the particle zeta potential and the ratio of the particleradius to the EDL thickness. When the ratio a/Dis extremely large(a/D ), hydrodynamic disturbance because of particle surfacecharge is confined to a thin EDL around the particle and does not affectthebulkfluidfield,andhencetheelectroviscouscoefficientpapproachesto zero. When a/Dis of finite value, the EDL thickness is comparable tothe particle size, and thus hydrodynamic disturbance can substantiallyalter the bulk flow field with large values of p. If the suspension isso concentrated that the EDLs around particles become overlapped(a/D 1), the forces due to EDL repulsion and van der Waals attractionwould come into play, and then the secondary electroviscous effectemerges. Finally, we have the tertiary electroviscous effect which resultsfrom a change in the conformation of soft particles (such as size and/orshape of polymeric particles and biomolecules). The detailed discussionon three categories of electroviscous effects in colloidal suspensionscan be foundin books and reviews 7,125,127,128. It is also worthwhilemaking a comparison between the electroviscous effect and theelectrorheological effect reviewed in the previous section. These two ef-fects are both existent in particle suspensions. However, the continuousphase in electrorheological effect is nonaqueous liquids, while thecontinuous phase in electroviscous effect is aqueous liquids. Theelectrorheological effect usually requires a relatively higher volumetricfraction of particles as compared to the electroviscous effect. The viscos-ity incrementdue to electroviscous effect usually is limited by a factor of2. However, the viscosity increment because of the electrorheological ef-fect can reach up to 5 orders in magnitude.6. Conclusions and outlookWe have presented an extensive review of electrokineticsregarding non-Newtonian fluids. This topic is of high relevancefor electrokinetically-driven microfluidic and nanofluidic systemswhich are routinely used to process and analyze non-Newtonianfluids, such as biofluids, polymeric solutions and colloidal suspen-sions. In particular, Sections 2 to 4 summarize non-Newtonianeffects in EDL-related electrokinetics (electroosmosis, electrophore-sis and streaming potential). Section 5 presents other related non-Newtonian effects in electrokinetics, including viscoelectric effect,shear-thickening induced by finite size of ions, electrorheologicalfluids and electroviscous effect of colloidal suspension. The surveyFig. 8. (a) Homogeneous suspension of dielectric particles without applied electric field. (b) Dielectric particles form chains in the direction of the applied electric field. The size of thedielectric particles is 700 nm. Reprinted with permission from 104. Copyright 1992 by AAAS.10C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001of literature suggests that non-Newtonian effects generally lead to anonlinear dependence of liquid/particle velocity on externallyapplied electric fields and/or zeta potential. Then it is natural to con-sider non-Newtonian electrokinetics as a type of nonlinear electroki-netics. In addition to the nonlinearity, the liquid or particle velocityin EDL-related electrokinetics tends to saturation due to the shear-thickening behavior of liquids that originates from the shear-ratedependent viscosity, viscoelectric effect, and ionic crowding etc.Obviously, non-Newtonian effects enable electrokinetic phenomenato show an explicit dependence on the fluid rheology. There are stillunfilled blanks in this field of research. It is well-known, that electroos-mosis,electrophoresis,streamingpotentialandsedimentationpotentialare four classic EDL-related electrokinetic phenomena. The first threetypes of electrokinetic phenomena have been covered in Sections 2 to4.Clearly,non-Newtonianeffectsonsedimentationpotentialofchargedparticles have been overlooked in the literature. In addition, manyinvestigations 129131 showed that flow enhancement in thepressure-driven flow of non-Newtonian fluids can be achieved byadding an oscillating pressure gradient of small amplitude to a constantpressure gradient. Such flow enhancement is ascribed to reducedeffective viscosity due to the small oscillation of pressure gradient. It isthen expected that the similar concept of flow enhancement can alsobe applicable to the electroosmotic flow of non-Newtonian fluidsunder a combination of a DC field and a small AC field. How would theflow enhancement be? How does such flow enhancement depend onthe fluid rheology (thinning versus thickening)? In addition to the en-hancement of electroosmotic flow, the enhancement of electrophoretictransport of particles in non-Newtonian fluids is also promising underthe combined action of AC and DC electric fields.At last, we put forward some theoretical deficiencies of currenttheoreticalmodelsregardingtheEDL-relatednon-Newtonianelectroki-netics, and point out the directions to which such deficiencies couldbe overcome or alleviated. Admittedly, most studies reviewed inSections 2, 3 and 4 treated non-Newtonian effects by simply using par-ticular constitutive models of non-Newtonian fluids, and the associatednon-Newtonian effect is considered to be homogeneous in the entireliquid domain. Such treatment, however, may not completely reflectthe micro/nano scale physics of non-Newtonian fluids. Practically,non-Newtonian fluids are made from suspensions of particles/macromolecules (polymer, DNA, protein etc.). In addition, the charac-teristic length scales characterizing the interparticle interactions innon-Newtonian fluids and the interactions between the particles inthe fluids and the solid surface are usually in order of micrometers oreven nanometers. When the liquid is confined into a conventionallargescaledomainwhosedimensionsaremuchlargerthantheselengthscales of interactions, the aforementioned interactions do not play sig-nificant roles and the fluid rheology can be assumed to be uniform inthe entire fluid domain. However, when the liquid is confined into amicro- and nano-scale domain whose dimensions are comparable tothese length scales of interactions, the aforementioned interactionsbecome prominent and would introduce several theoretical issueswhich must be further clarified in EDL-related electrokinetics.6.1. Criterion for non-Newtonian behavior inside EDLThe non-Newtonian behavior in complex fluids results from thereorganization of the microstructure of fluid under the influence of animposed shear flow. At sufficiently low shear rates, the reorganizationis weak, and thus the shear stress is linearly proportional to the rate ofshear (Newtonian behavior). When the magnitude of shear ratebecomes large enough (comparable to the inverse of relaxation timecharacterizingatransitionprocessofrestoringtheinitialmicrostructuredistorted by the shear flow), deviation from the Newtonian behaviorbecomesnoticeable.Theslowestmechanismofrestorationisassociatedwith the thermal motion of particles composing the complex fluids.Widely cited estimation based on the above mechanism shows thatthe shear stress leading to the non-Newtonian behavior should satisfythe following inequality 132 N kBT=a327where a is the diameter of dispersed particles and is considered as thecharacteristic dimension of microstructure. If we consider the shearstress that is developed within a thin EDL over a planar surface, anintegration of the Cauchy momentum equation with the far-fieldboundary condition that 0 and d/dy 0 as y yields ddyE028Under the DebyeHckel linear approximation, the potential distri-bution within a thin EDL is expressed as = exp(y), where isthe reciprocal of Debye length and is the zeta potential of the chargedsurface. Using this expression and combining Eqs. (27) and (28), wearrive at the following criteriona=a?3N129In Eq. (29), thelengthscaleparameter a*denotes a critical diameter,above which one can expect the non-Newtonian behaviora?kBTE0?1330For typical values of = 7 1010F/m (water at room tempera-ture), = 50 mV, = 108/m (103M 1:1 aqueous electrolytesolution) and E0= 104V/m, we obtain that a* 50 nm. According tothe above estimation, particles must be larger than 50 nm (definitelylarger than the double layer thickness, D= 1= 10 nm) to allownon-Newtonian effects inside the EDL. Therefore, a question naturallyarises, is it still valid to employ the continuum approach to correlatethe local stress with local shear rate? Furthermore, even though thecontinuum approach is valid here, it is still necessary to find complexfluids with the diameter of dispersed particles satisfying the conditionDN a N a*under which non-Newtonian effect can prevail inside theEDL.6.2. Depletion layer due to non-adsorbing particles and adsorption layerdue to adsorbing particlesMany authors reported the existence of a depletion layer that sepa-rates the complex fluid and the solid surface 133138. Such layer isdue to the depletion of non-adsorbing particles near the solid surfaceand thus is occupied by the pure solvent. Therefore, the viscosity ofdepletion layer is much lower than that of bulk. A typical indicationfor the existence of depletion layer is the hydrodynamic slip observedin flows of many complex fluids (such as polymeric solutions, emul-sions, suspensions of colloid and blood). The thickness of depletionlayerisrelatedtothehardspherewallinteractionsandthusistypicallyof about the gyrationradius of microstructures (polymeric moleculesorparticles). It is imperative to consider the wall depletion since the EDL-related electrokinetic effects take place inside the EDL whose thicknessis comparable to that of the depletion layer. Berli and Olivares 23 onlyaddressed a special case in which the thickness of EDL is assumed tobesmallerthanthatofthedepletionlayerandtheliquidviscosityinsidethe depletion layer is constant (Newtonian liquid). Under theseassumptions, electrokinetic effects inside the EDL essentially exhibitNewtonian characteristics, indicating no effect of the bulk rheology.Practically, the liquid viscosity inside the depletion layer varies due tothe bulk concentration of polymer and the depletion layer also can bethicker than EDL 138,139. A more general model describing the elec-trokinetics of non-Newtonian liquids with arbitrary thicknesses of EDL11C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001anddepletionlayeraswellasavaryingliquidviscosityinsidethedeple-tion layer deserves further efforts. For special cases where the thicknessof EDL is larger than that of depletion layer, one certainly can anticipatethe extension of electrokinetic effects to the bulk of complex fluid andalso the effect of bulk rheology on electrokinetic phenomena.Depletionlayerdiscussedaboveisbecauseofnon-adsorbingparticlesin non-Newtonian fluids. However, there are practically also non-Newtonian fluids composed of adsorbing particles which form anadsorption layer near solid surface 7,140,141. Adsorption of particles(e.g., biological and polymeric molecules) on solid surfaces would alterboth physicochemical and hydrodynamic conditions inside the EDL,such as change of the zeta potential, induced local shear-thickeningand particlewall collisions, which all could modify the EDL-relatedelectrokinetics.6.3. Charged particles effectFor non-Newtonian fluids formed by suspending particles in aque-ous media, it is also quite reasonable to take into account the electricalcharges of constituent particles. We consider the electroosmosis of anon-Newtonian fluid in a slit microchannel shown in Fig. 9 to providea simple picture of the effect of charged particles. Here it is assumedthat the constituent particles of non-Newtonian fluids are non-adsorbing, and then the entire channel domain can be divided intotwo depletion layers near the channel walls and a complex fluid layerin the bulk of channel. For simplifying the analysis, the particles areregarded to be completely depleted from the depletion layers, andthen the depletion layers are purely Newtonian solvents (water) andall the particles are confined in thecomplex fluid layer. Under the effectof the surface charge on channel walls, ions in liquids redistribute toform EDLs which extend from the channel wall into the depletionlayer and even the complex fluid layer. Because of the aqueous particlesuspension,theparticles inside thecomplex fluid layer arealso natural-ly charged. Similar to ions, the charged particles also would redistributeunder the influence of the surface charge on channel walls. However,the redistribution of particles should be much weaker than that ofions since the complex fluid layer is far from the channel wall, andalso the particles are more massive than electrolyte ions. In comparisonwith ions which follow the Boltzmann distribution inside EDL, theparticles in the complex fluid layer can be reasonably assumed to beuniformly distributed. Obviously, the uniformly distributed chargedparticles would introduce an extra charge density in the complex fluidlayer.Withtheaboveconsiderations,theelectricfieldwithinthesystemsketched in Fig. 9 due to the charged channel walls is governed by thefollowing two equationsd2Ddy2 2DDfor H y H31d2Cdy2 2CCqCfor 0 y H32where , and are the electric potential, theDebye parameter and theelectric permittivity, respectively. Parameters with subscript C are asso-ciated with the bulk complex fluid layer, while those with subscript Dare associated with the depletion layer. The term 2 accounts for thefree charge density due to small ions, and q is the charge density insidethe complex fluid layer due to the charged constituent particles.Eqs. (31) and (32) are completed by the following boundary conditionsdCdy?y0 033DjyH CjyHand DdDdy?yH CdCdy?yH34DjyH 35Thesolutionof aboveequationsresults inthe electric fieldinside thefluiddomainwhichwouldberequiredforsolvingthemomentumequa-tion. In this particular case, the depletion layer is Newtonian fluids, andthe non-Newtonian characteristics of complex fluid layer are assumedto be described by thepower-law constitutive model. Then thesolutionof the momentum equation gives rise to the following expressions forthe fluid velocity in the depletion layer and the complex fluid layeruDy DEDD36uCy DEDDjyH?CEm?1nZyHdCdy0?1ndyDEDDjyH?CEm?1nZyHdCdy0?1ndyfordCdyN0fordCdyb 08:37whereDistheNewtoniandynamicviscosityof thedepletionlayer,andn and m are the fluid behavior and consistency indices of the complexfluid layer respectively. A preliminary analysis shows some interestingeffects. For example, when zeta potential and charge density q havethe same signs, an increase of the electric field strength may changethe sign of velocity in the complex fluid layer. Additionally, the abovesimple model does not consider the EDLs formed at the interfacesbetween the complex fluid layer and depletion layers. The existence ofsuch EDLs would exert extra electric stresses on the interfaces, andthus is believed to further alter electrokinetic phenomena.Other than the aforementioned three major theoretical concerns,the application of famous power-law constitutive model to non-Newtonian EDL-related electrokinetics in most reviewed investigationsremains questionable. As is known, an established criterion of goodconstitutive models is that they always should describe the Newtonianbehavior at low shear stresses 142,143. Apparently, the power-lawmodeldoesnotmeetthiscriterion.Forinstance,asthevelocitygradientapproaches asymptotically to zero outside the EDL, the power-lawmodelpredictsanunphysicalinfiniteviscosityforshear-thinningfluids.When addressing the EDL-related electrokinetics of non-Newtonianfluid, one probably should use other constitutive models (such asthe Carreau model) rather than the power-law model to describe therheology of fluids.Fig. 9. Non-Newtonian electroosmosis in a microchannel with the depletion layers nearsolid walls and the charged complex fluid layer in the bulk. The height of the channel is2H, the thickness of the depletion layer is , and the two walls are uniformly negativelycharged with the zeta potential of which induces electric field in the depletion layer,D, and the complex fluid layer, C. Then an externally applied axial electric field Einteracts with the charge densities inside the depletion layer and the complex fluid layerto induce electroosmosis in the depletion layer, uD, and in the complex fluid layer, uC.12C. Zhao, C. Yang / Advances in Colloid and Interface Science xxx (2013) xxxxxxPlease cite this article as: Zhao C, Yang C, Electrokinetics of non-Newtonian fluids: A review, Adv Colloid Interface Sci (2013), /10.1016/j.cis.2013.09.001Certainly, there are burgeoninginterests in electrokinetic phenome-na involving non-Newtonian fluids, especially the EDL-related electro-kinetic phenomena reviewed in Sections 2 to 4. Notably, researches inthe current literature mainly focus on theoretical investigations whichmostly arelack of experimental validations. Moreover, three theoreticalconsiderations described above also need solid experimental verifica-tion. Thus, we have good reasons to expect booming experimentalinvestigations of the EDL-related electrokinetics of non-Newtonianfluids in the near future.At last, it needs to be highlighted that apart from fundamentalaspects of electrokinetics of non-Newtonian liquids discussed above,exploitation of its practical applications also may attract the attentionof future investigations. Apparently from the review, three types ofEDL-related electrokinetics of non-Newtonian fluids (electroosmosis,electrophoresis, and streaming potential effect of non-Newtonianfluids) mainly undergo theoretical investigations at present, becausethey are still in the early stage of development. As a consequence,there are very few established applications for such three effects. Forexample, electroosmosis of non-Newtonian fluids is only suggestedconceptually for pumping, solute transport and heat transport as men-tionedattheendofSection2,buttherearenoexperimentaldemonstra-tions of these applications as far as we know. The electric displaymentioned in the second paragraph of Section 3 could be the onlyestablished application of electrophoresis of non-Newtonian fluids atthe moment, and the established application of streaming potential ef-fect of non-Newtonian fluids is only limited to the power generationas mentioned at the beginning of Section 4. For viscoelectric and ion-crowding effects reviewed in Section 5, at present they do not haveany practical applications yet. These two mechanisms are mainly usedto explain the discrepancy between the experimental observationsand the classical HelmholtzSmoluchowski theory.AcknowledgmentsThe current work greatly benefits from the communication and dis-cussion with Dr. Emilijk Zholkovskij at the Institute of Bio-Colloid Chem-istry of the Ukrainian Academy of Science. The authors also gratefullyacknowledge the financial support of the research grant (MOE2009-T2-2-102) from the Ministry of Education of Singapore to CY.References1 Stein D, Kruithof M, Dekker C. Surface-charge-governed ion transport innanofluidic channels. Phys Rev Lett 2004;93:035901.2 Siwy ZS. Ion-current rectification in nanopores and nanotubes with brokensymmetry. Adv Funct Mater 2006;16:73546.3 Alois W. Thermal non-equilibrium transport in colloids. Rep Prog Phys2010;73:126601.4 Zhao Y, Zhao C, He J, Zhou Y, Yang C. Collective effects on thermophoresis ofcolloids: a microfluidic study within the framework of DLVO theory. 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