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文章编号: 190907  

文献标识码: A

综述

黏弹性流体在微粒被动操控技术中的应用

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  • 1.南京林业大学机械电子工程学院 南京 210037
  • 2.南京师范大学电气与自动化工程学院 江苏省三维打印设备与制造重点实验室 南京 210023

收稿日期:2019-09-09

  修回日期:2019-11-11

  网络出版日期:2020-02-20

基金资助

国家自然科学基金项目(51805270)

国家自然科学基金项目(51805272)

江苏省重点研发计划项目资助(BE2018010-1)

江苏省重点研发计划项目资助(BE2018010-2)

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版权所有,未经授权,不得转载、摘编本刊文章,不得使用本刊的版式设计。

Application of Viscoelastic Fluid in Passive Particle Manipulation Technologies

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  • 1.School of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China
  • 2.School of Electrical and Automation Engineering, Jiangsu Key Laboratory of 3D Printing Equipment and Manufacturing, Nanjing Normal University, Nanjing 210023, China
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Received:9 Sept. 2019

  Revised:11 Nov. 2019

  Online:20 Feb. 2020

Fund

National Natural Science Foundation of China(51805270)

National Natural Science Foundation of China(51805272)

Key Technology R&D Program of Jiangsu Province(BE2018010-1)

Key Technology R&D Program of Jiangsu Province(BE2018010-2)

Copyright

Copyright reserved © 2020.

摘要

因能实现微米尺度粒子的精确操控,微流控技术已被广泛运用于医学、制药、生物和化学等领域,其中无需外场作用的被动操控技术由于其简单性和自主性更是成为研究热点。与其他被动操控技术相比,黏弹性聚焦技术更易实现微粒的三维聚焦且能操控微粒的尺度跨度大、流体流量范围广。因此,本文综述了黏弹性流体在微粒被动操控应用中的最新研究进展。首先,介绍了微粒在不同结构流道内的黏弹性流体中进行迁移的受力机理,进一步详细阐述了黏弹性聚焦、黏弹性分选、黏弹性混合以及其他黏弹性微粒操控应用研究进展,最后对研究黏弹性流体流动特性和在其内微粒迁移运动规律的数值模拟方法进行了介绍,并在分析现有问题的基础上对黏弹性微流控技术未来的发展作出了展望。

关键词: 黏弹性流体 ; 微流控 ; 粒子聚焦 ; 粒子分选 ; 数值模拟

中图分类号: TQ21.1 ()  

本文引用格式

倪陈 , 姜迪 , 徐幼林 , 唐文来 . 黏弹性流体在微粒被动操控技术中的应用[J]. 化学进展, 2020 , 32(5) : 519 -535 . DOI: 10.7536/PC190907

Chen Ni , Di Jiang , Youlin Xu , Wenlai Tang . Application of Viscoelastic Fluid in Passive Particle Manipulation Technologies[J]. Progress in Chemistry, 2020 , 32(5) : 519 -535 . DOI: 10.7536/PC190907

Abstract

Microfluidics, which can precisely manipulate micron-sized particles, has been widely used in medical, pharmaceutical, biological and chemical fields. The passive manipulation technologies without external field effect have become a research hotspot because of their simplicity and autonomy. Compared with other passive manipulation technologies, viscoelastic focusing technology makes it easier to achieve three-dimensional focusing of particles, and can manipulate particles with a large-scale span and a wide range of fluid flow. Therefore, this paper reviews the latest research on viscoelastic fluids in particle passive manipulation applications. Firstly, the force mechanism of particles in viscoelastic fluid in different microchannel structure is introduced. Then, the research progress of viscoelastic focusing, sorting, mixing and other viscoelastic particle manipulation applications is further elaborated. Finally, the numerical simulation method for studying the flow characteristics of viscoelastic fluids and the movement law of particles in it are introduced, and some prospects for the future development of viscoelastic microfluidics are made based on the analysis of existing problems.

Contents

1 Introduction

2 Viscoelastic focusing

2.1 Viscoelastic focusing in straight microchannels

2.2 Viscoelastic focusing in curved microchannels

3 Viscoelastic sorting

3.1 Sheath-flow sorting

3.2 Sheath-free sorting

4 Other applications

5 Numerical simulation

6 Conclusion and prospects

1 引言

微流控技术是在微尺度下精确操控流体和粒子的科学,因其具有样品量少、成本低廉、操作简单、检测快速和精度较高的优点[1, 2],相比传统实验室粒子分析检测方法优势明显,因此被广泛运用于医疗诊断、化学分析、生物技术、制药工业和环境监测等领域[3,4,5,6]。对于单细胞分析、干细胞培养、癌细胞筛选和抗体分选等,微流控技术更是成为不可或缺的重要工具[7,8,9,10]
微流控粒子操控技术包括主动操控与被动操控技术。主动操控技术利用电场[11,12,13]、声场[14,15,16]、磁场[17,18,19]、光场[20,21,22]等外加力场对不同物理特性的粒子进行聚焦及分选。而被动操控技术则通过水动力[23]控制粒子的迁移行为,具有操控简单等优点[24]。其中基于牛顿流体惯性效应[25,26,27]的微流控芯片由于其能将粒子稳定聚焦于流道中心与壁面之间的某一平衡位置[28, 29]实现粒子聚焦[30,31,32]和分离[33, 34],且能高通量地处理大量样品,一度成为研究的热点。1963年,Karnis等首次发现了黏弹性流体中粒子在圆管中流动时向流道中心迁移的现象[35],这种黏弹性流体的黏弹性力作用于粒子使其在流道截面中心单一位置聚焦,有利于粒子计数检测等工作的进行,且黏弹性流体与牛顿流体相比能在简单流道中更易实现粒子的三维聚焦以及能够操控粒子的尺度跨度大、流体流量范围广[36]。故现阶段黏弹性流体在微流体粒子被动操控的应用研究中受到越来越多的关注。
本文将对黏弹性流体在微粒被动操控应用中的最新研究进展进行综述,主要阐述了不同结构流道中粒子迁移的受力机理、黏弹性微流控的应用方向和数值模拟方法。文章将根据流道结构(直流道和弯流道)和有无鞘流(有鞘分选、无鞘分选)分别对黏弹性聚焦和黏弹性分选进行重点阐述,并对各类聚焦和分选方法存在的优缺点进行分析。随后,介绍了对研究黏弹性流体流动特性和在其内微粒迁移运动规律的数值模拟方法。最后,在此基础上对黏弹性微流控技术未来的发展作出展望。

2 黏弹性聚焦

粒子聚焦是指微流道中粒子在溶液中受力迁移至流道中心平面或者中心流线处,从而形成粒子的平面聚焦或三维线聚焦。黏弹性聚焦即粒子在黏弹性溶液中的聚焦。在很多微流控应用中,粒子聚焦是实现粒子检测、计数和分选的先决条件[37, 38],是流式细胞仪[39]和粒子分选器[40]等装置的关键环节。在大多数研究中所采用的微流道结构一般为:圆形直流道、矩形(含方形)直流道和矩形截面弯流道。因此,本节将按不同的流道结构进行分类,分别阐述粒子的黏弹性聚焦。

2.1 直流道中的黏弹性聚焦

2.1.1 粒子受力迁移现象
粒子在黏弹性溶液的直流道中通常受到惯性升力FL 和弹性力FE 的作用,这两种力会对粒子产生不同的迁移效果。通常惯性升力FL 可以表示为[41, 42]:
F L = ρ V m a 4 D 2 h C L
Re = ρ V m D h μ f
其中,ρ为流体密度,Vm 为流道内平均速度,a为粒子直径,CL 为无量纲的升力系数,Dh 为流道的水力直径,Re为雷诺数,μf 为动力黏度。惯性升力本质上是由壁面诱导惯性升力FLw 和剪切诱导惯性升力FLs 组成[42,43,44],其中壁面诱导惯性升力FLw 会将粒子推离壁面[45],而剪切诱导惯性升力FLs 会将粒子推离流道中心[41]。在这两个力的共同作用下,流体中的粒子会横向迁移至合力为零的某个平衡位置[30, 32]。如Segre和Silberberg在第一次发现惯性迁移现象时,发现圆柱管中的粒子由于受惯性效应迁移至离圆心0.6倍半径处并形成一个圆环[29],这一惯性原理在微流控中多有运用,其示意图如图1a所示。在矩形截面(用深宽比AR表示截面形状,AR=流道的高度/流道的宽度)流道中粒子的迁移会产生变化。在方形截面(AR=1)微流道中,粒子将迁移至靠近壁面的4个平衡位置,如图1b所示;在深宽比AR较小的矩形截面微流道中,粒子将迁移至靠近长壁面的两个平衡位置,如图1c所示。当雷诺数Re增大时,粒子的平衡位置将向壁面移动,在矩形微流道中原先两个平衡位置将变成4个[31],如图1d所示。
图1 粒子受惯性升力在直流道中的平衡位置示意图:

(a) 圆形截面;(b)方形截面[32];(c)矩形截面[32];(d)增加雷诺数[32];(e)加入黏弹力[61]

Fig. 1 Schematic diagram of the equilibrium position of particles subjected to inertial lift in straight microchannels

(a) circular section;(b) square section[32];(c) rectangular section[32];(d) Reynolds number increased [32];(e) elastic force added[61]

弹性力则通常用无量纲的Weissenberg数Wi或Deborah数De对其表征[44, 46]:
Wi = λ γ · = λ 2 V m D h
De = λ t p
其中,λ为松弛时间, γ ˙ 为平均特征剪切速率, γ ˙ =2Vm/Dh ,tp 为特征时间。事实上弹性力FE 是由于粒子在黏弹性流体中受到不均匀的法向应力差产生的[47, 48],在黏弹性流体中存在两个应力差,分别为第一法向应力差N 1和第二法向应力差N 2,这两个应力差都有助于粒子迁移。其中第一法向应力差N 1=τxx - τ yy [49],第二法向应力差N 2=τyy - τzz [50, 51]τxx τyy τzz 应力的方向分别为平移方向、速度梯度方向和转动方向。但在一般稀释的黏弹性溶液中,N 2将远远小于 N 1 [52,53],此时可以将N 2忽略不计,由此可以假设粒子所受弹性力FE 和粒子上N 1变化成正比[54],弹性力FE 可以表达为[55]:
F E = C eL a 3 N 1 = - 2 C eL a 3 η p λ γ 2
其中,CeL 为无量纲的弹性升力系数,ηp 为聚合物溶解在溶液中产生的黏度。粒子在弹性力作用下产生的迁移与惯性升力不同[56]。在平行板中,粒子随剪切流动会向较近壁面迁移[57, 58];在矩形狭缝(AR≪1)直流道中,一般会形成一个分界线,分界线内的粒子会迁移至中心平面,而分界线外的粒子则会向壁面迁移[59];在方形直流道中,粒子由弹性力主导将会迁移至流道中心和流道四角处[60],如图1e左所示。
若粒子只受惯性升力或弹性力就很难形成流道中心线单一聚焦。Yang等[61]首先提出了弹性惯性粒子聚焦的概念,将弹性力和惯性升力结合起来,实现了粒子在方形直流道流道中心的单一聚焦,如图1e右所示。与此同时,该团队研究发现黏弹性流体中粒子迁移是由弹性和惯性竞争决定的,通常用弹性数El表示弹性对惯性效应相对重要性,El为Weissenberg数与雷诺数之比[62],不同El导致粒子不同的迁移行为。
El = Wi Re
2.1.2 圆形和方形截面直流道中黏弹性聚焦
粒子在圆形和方形截面直流道中具有相似的黏弹性聚焦现象。Yang等[61]在方形直流道中研究发现,在弹性较大时(El=258)时,粒子受到弹性力的主导迁移至中心流线和四角处,如图2a所示。D’avino等[63]利用1%聚氧化乙烯(PEO)溶液,在流速为Q=4.4×10-3μL/min和De≈0.03条件下在圆形直流道进行实验,由于PEO溶液具有较强剪切稀化效应,PS粒子在流道中心线和壁上实现双稳定性聚焦,如图2b所示。
图2 粒子在不同条件下在不同直流道中的聚焦图

(a)0.05 wt% PEO 溶液(左)和8% PVP溶液(右)在方形直流道中[61];(b)1% PEO溶液在圆柱形直流道中[63];(c)1% PEO溶液在圆柱形直流道中[64];(d)5 ppm λ-DNA溶液在方形直流道中[37];(e)0.8 wt% HA溶液在方形直流道中[60]

Fig. 2 Particles focusing in different straight microchannels under different conditions

(a) 0.05 wt% PEO solution(left) and 8% PVP solution(right) in straight square microchannel[61];(b) 1% PEO solution in straight cylindrical microchannel[63];(c) 1% PEO solution in straight cylindrical microchannel[64];(d) 5ppm λ-DNA solution in straight square microchannel[37];(e) 0.8 wt% HA solution in straight square microchannel[60]

此外,基于弹性惯性聚焦,粒子在圆形和方形直流道均能实现流道中心线单一聚焦。但随着弹性力或剪切稀化效应的增强亦均有发散现象的产生。Seo等[64]利用8%聚乙烯吡咯烷酮(PVP)溶液和1% PEO溶液在圆形直流道中进行实验,用全息技术分别测量了不同直径的粒子在不同流速下的聚焦情况。实验表明,在8% PVP溶液中,对较大的粒子在越快的流速下,聚焦的效果越好,而在1% PEO溶液中,粒子随流速的进一步增加却趋于分散,如图2c所示。Del Giudice等[65]在方形直流道中同样发现在具有强剪切稀化效应的PEO溶液(含1.6%)中,粒子随流速的增强(剪切稀化效应增强)从中心流线向四角迁移。以及Kim等[37]在含(5 ppm)λ-DNA的(13.8 wt%)蔗糖溶液中,实现了3种不同直径粒子在中心流线位置聚焦,如图2d所示。DNA分子由于具有较长的松弛时间,因此能实现在较高流速下的有效粒子聚焦,但随着流速的不断增加,剪切稀化效应随之增强(除DNA溶液浓度极低),粒子在聚焦后还是会分散。由此可见,在具有强弹性或强剪切稀化效应时,弹性惯性粒子聚焦的效果其实并不理想。对此,Song等[66]就3种无量纲数(ReWiEl)对弹性惯性粒子聚焦的影响做了全面研究,证明了与ReEl相比,Wi是一个更合适的聚焦效率参数。
现如今微流道一般由光刻技术[67,68,69]、压印技术[70]和直写技术[71, 72]等方法制作而成。矩形截面直流道相对于圆形截面直流道更便于加工,因此对矩形截面流道的研究和运用更加广泛,且粒子在方形截面流道的聚焦研究是迄今为止最多的。Kim等[73]在500 ppm PEO溶液中实现了对亚微米粒子在方形截面直流道中(5 μm×5 μm)多平衡位置聚焦。该研究体现了黏弹性溶液在聚焦细菌等细小微粒方面的潜力,实现了惯性聚焦无法完成的任务。Holzner等[74]利用低浓度PEO溶液首次实现了对哺乳动物细胞和细菌的弹性惯性聚焦,且该方法不会诱导细胞自身的旋转,说明该方法特别适用于疾病感染细胞的形态学分析。另外,Del Giudice等[60]在0.8 wt% 透明质酸(HA)溶液中实现了对Jurkat细胞和NIH 3T3成纤维细胞的聚焦,如图2e所示。Lim等[75]利用HA溶液在方形截面直流道(80 μm×80 μm)中实现了大流量范围内(10<Re<10 000)的粒子聚焦,该团队在确保粒子的弹性惯性聚焦条件下探索了在此之前从未实现的最高流速(Q=50 mL/min)。
2.1.3 矩形截面直流道中黏弹性聚焦
除圆形截面和方形截面直流道外,粒子在狭缝流道(AR≪1)和矩形直流道(AR<1)中可以实现不一样的黏弹性聚焦。在狭缝流道中,弹性力会将粒子推向中心面[76]。Seo等[77]利用这一原理,在高50 μm、宽500 μm的流道中实现了红细胞的二维中心平面聚焦,如图3a所示。随后,他们将溶液改为含3% PVP的磷酸盐缓冲溶液(PBS)。溶液中红细胞受到上下壁面指向流道中心平面的弹性力,当红细胞在中心平面且平行于上下壁面时,红细胞达到受力平衡状态。然后利用全息显微镜对中心平面进行定量相位成像,实现了对红细胞的计数和检测。该二维平面聚焦方法使红细胞深度位置具有高均匀性,减轻了对焦模糊,提高了检测的灵敏度。在矩形直流道中粒子聚焦多为多线聚焦,Liu等[78]比较了不同直径粒子在不同深宽比下的聚焦情况。如图3b所示,较小直径的粒子聚焦在中心流线位置,而较大直径的粒子由于受到靠近流线中心侧增强的法向应力聚焦至两个偏心平衡位置。基于这种现象,实现了MCF-7细胞和红细胞以及大肠杆菌和红细胞两组基于不同尺寸在不同平衡位置的聚焦,如图3c所示,这为实现高质量的粒子分选提供了条件。项楠等[79]随后报道了10 μm的粒子在AR=1/3的流道中三个不同位置的聚焦情况。粒子随流速的逐渐增加,首先聚焦在中心平面上,随后在两个中心对称位置聚焦,然后出现第三个位置(中心线)的聚焦,最后除中心线外,原两个中心对称位置上的粒子出现分散现象。他们对此提出了一种四阶段机制来解释该流道中粒子随流速增加而出现不同的聚焦现象,如图3d所示,但该机制并不能完全解释在AR=1/2或1的流道中的粒子迁移现象。除此之外,Yang等[80]利用一个双入口、AR=1/4的流道结构,在2000 ppm PEO溶液中实现了PS粒子的双线聚焦,如图3e所示。
图3 (a)红细胞的二维聚焦图[77];(b)粒子在不同深宽比矩形直流道中聚焦图[78];(c)两组不同尺寸粒子的聚焦图[78];(d)粒子聚焦四个阶段示意图[79];(e)双入口流道示意图[80]

Fig. 3 (a) Two-dimensional focusing of red blood cells[77];(b) Particle focusing map in straight rectangular microchannels with different aspect ratios[78];(c) Focusing map of two different sizes of particles[78];(d) Schematic diagram of four stages of particle focusing[79];(e) Schematic diagram of double inlet channel[80]

2.2 弯流道中的黏弹性聚焦

粒子在弯流道中除了受惯性升力和弹性力的作用还受到横向拖曳力的影响。黏弹性流体中横向拖曳力会影响粒子在微流道中的迁移,它一般是由流道横截面的二次流引起的。在弯流道中,中心流线处的流体由于受离心力和不平衡的径向压力梯度的影响向外壁面流动,外壁面处的流体则沿着上下底面回流,从而产生两个方向相反的涡流,这种流道横截面上的径向流动现象就称为二次流或Dean流[24]。在具有缩扩结构的直流道中由于横截面积的突变也能诱导二次流,并在收缩区内流体加速时产生类Dean反向旋转流[81]。通常用Dean数Dn表征二次流的流动强度[82]
Dn = Re D h 2 R
其中,R为弯流道的曲率半径。横向拖曳力FD 就是在流道中产生二次流后流体流过粒子时由于粒子速度与流体速度存在差异而产生的力,通常FD 可以表示为[83]:
F D = 3 π μ f a ( v f - v p )
其中,vf 为流体元素的横向速度,vp 为粒子的横向速度。
在弯流道中最常用的是螺旋形流道,其中螺旋形流道又可分为单螺旋流道[84,85,86]、双螺旋流道[87]和多螺旋流道[88]等。Lee等[86]在单螺旋流道中观察到由弹性力和Dean流拖曳力相互作用引起的多重粒子聚焦现象,并提出了“耦合Dean的弹性惯性聚焦”概念,研究中单螺旋流道的第十环处不同直径PS粒子实现单线聚焦,直径较大的粒子更靠近外壁。其后他们进一步采用含直径为1.5 μm和10 μm PS粒子混合溶液进行实验,发现在第十环处两种粒子在不同位置处形成了双线聚焦,且大尺寸粒子更靠近壁外,如图4a所示,为下一步粒子分选提供了条件。项楠等[85]对单螺旋流道中粒子的弹性惯性聚焦行为进行了一系列的实验探索。在AR=1/4、流道半径Ri =1.1 mm的螺旋流道中观察到粒子随流速的不断增加从分散到单线聚焦再到多线分散的现象。对此他们提出了一种六阶段过程模型来解释这一现象,如图4b所示。基于上述研究,他们[84]又提出了一种通过调节黏弹性流体的浓度来控制粒子聚焦位置的方法。粒子在流道截面AR=1/3的单螺旋流道中,在较高浓度(8 wt% PVP)下,能有效聚焦至中心单一位置,如图4c所示。粒子随流速的增加聚焦效果越好,而浓度越低,粒子越靠近外壁。该方法实现了高通量的连续颗粒浓缩,克服了传统离心法耗时长、易损害细胞[89]和对体积小浓度低样品较难处理[90]的缺点。另外,Liu等[87]利用双螺旋流道也实现了多种纳米颗粒的高质量聚焦。
图4 (a)直径为1.5和10 μm粒子的聚焦图[86];(b)粒子聚焦六个阶段示意图[85];(c)螺旋流道中粒子的三维单线聚焦图[84]

Fig. 4 (a) Focusing map of 1.5 and 10 μm diameter particles[86];(b) Schematic diagram of six stages of particle focusing[85];(c) Three-dimensional single-line focusing map of particles in a spiral microchannel[84]

本节详细阐述了不同流道结构下黏弹性聚焦的研究进展以及在各类流道中粒子的受力机理,分析了不同因素(流道截面形状、流速、黏弹性、剪切稀化等)对粒子聚焦的影响。根据介绍,粒子在直流道中的聚焦大致可分为中心线单一聚焦、多线聚焦和中心面聚焦,分别可对应圆形或方形(AR=1)直流道、矩形直流道(AR<1)和狭缝流道(AR≪1)。相比于圆形截面流道,矩形截面流道更易加工制造,运用更加广泛。另外,矩形截面(AR<1)直流道和螺旋流道更是能实现不同直径粒子在不同平衡位置的多线聚集。对于流速的影响,在PVP溶液中,在有效流速范围内,流速的增加将有利于粒子的聚焦,但在强剪切稀化效应下(如在PEO溶液中且流速较快)粒子的聚焦效果并不理想。这些实验研究结论不断丰富着黏弹性聚焦的理论基础,更是为今后的研究与运用提供宝贵的借鉴意义。

3 黏弹性分选

粒子分选在医疗诊断、生化分析、食品处理和环境评估等方面具有重要意义[33]。其中,生物粒子的分选更是医疗检测、临床诊断和细胞生物学等方面的关键[91,92,93,94]。由于依靠外来标记的分选方法[95]具有成本高和操作复杂等缺点,最近,无需标记的声分选、光分选、电分选和水动力分选等新技术[96,97,98,99]成为研究的热门。而相比于依靠外力分选,基于流体内在力实现分选的被动分选更是具有结构简单的优点。黏弹性分选是指利用黏弹溶液将不同物理特性(粒子的尺寸、变形性和抗阻特性等)的粒子进行分选。下面,本节将根据有无鞘流分别对黏弹性分选进行阐述。

3.1 有鞘分选

由上述可知,粒子流道中受到弹性惯性效应会发生迁移。有鞘分选则是在流道中引入鞘流,在鞘流的辅助下,不同尺寸的粒子由于不同的横向迁移速度从而实现分离。Nam等[100]利用鞘流实现了直径为1 μm和5 μm PS粒子的高纯度分离,该流道入口为三叉分流道,如图5所示,带混合粒子的黏弹性溶液样品从两侧入口注入,而黏弹性鞘液则从中间入口注入,使得鞘流将样品溶液挤压至流道两侧,粒子在流道中由于受到壁面诱导惯性升力、剪切诱导惯性升力和弹性力的联合作用将迁移至平衡位置。而粒子所受的惯性力和弹性力都与其尺寸成正比,即较大的粒子具有较大的迁移速度,从而实现了大小粒子的分离。由于考虑到通过微流体中粒子的相互作用和非牛顿特性(如第二法向应力差)可能会进一步提高分离效率,他们又研究了第二法向应力差对类似结构流道中基于粒子尺寸的鞘流分离的影响[101],比较了粒子在100 ppm聚丙烯酰胺(PAA)溶液和500 ppm PEO溶液、AR=1/2流道中的迁移情况(在PAA溶液中产生了第二法向应力差而PEO溶液中没有),发现在PEO溶液中实现了不同直径粒子的分离,而在PAA溶液中直径较小的1 μm粒子在整个流道截面上扩散,证明了第二法向应力差对小颗粒具有较大影响。
图5 利用鞘流分离的流道结构示意图[100]

Fig. 5 Schematic diagram of the microchannel structure using sheath-flow sorting[100]

Lu和Xuan[102]提出了一种弹性惯性挤压分馏(EIPFF)的分离技术。他们在T形微流道(如图6a所示)中利用鞘流实现了不同尺寸粒子的分离。且他们还详细研究了不同因素(PEO浓度、流道深宽比、样品溶液和鞘液流速等)对EIPFF分离法的影响,如图6b所示,实验表明粒子的分离效率不会随着弹性数增加而单调递增,且会受到流道深宽比的强烈影响。随后,他们[103]利用同一流道更是实现了球形粒子和花生形粒子的分离,在1000 ppm PEO溶液中,在鞘液流速为100 μL/h和样品溶液流速为5 μL/h下,球形粒子更加靠近流道中心,如图6c所示。同样地,他们详细研究了不同因素对球形和花生形粒子分离的影响,发现分离效果对流体弹性和流道深宽比都有很大的依赖性,且可以通过调整ElAR的值,实现花生形粒子偏转等于或小于或大于球形粒子的偏转。Xu等[104]利用在流道两侧注入不同黏度的黏弹性流体,实现粒子和粒子的大行程分离,同时证明了鞘流的流速和黏度差对粒子分离的间隔距离有影响。
图6 (a)粒子在T形流道分离示意图[102];(b)混合粒子在不同条件下的迁移情况[102];(c)球形和花生形粒子的迁移情况[103]

Fig. 6 (a) Schematic diagram of particle separation in a T-shaped microchannel[102];(b) Migration of mixed particles under different conditions[102];(c) Migration of spherical and peanut-shaped particles[103]

最近,Liu等[105]利用鞘流和如图7a所示流道,实现了细胞外囊泡(Evs)和外泌体持续的、依据尺寸大小和无标记的分离,最终获得大于90%的分离纯度和大于80%的外泌体回收率。而Zhou等[88]在上述的基础上将流道改为多螺旋结构流道,如图7b所示,实验对比了1 μm、500 nm、300 nm和100 nm的粒子在直流道和多螺旋结构流道中的聚焦效果,发现粒子在多螺旋结构流道中的聚焦效果明显优于直流道,且粒子越大容易聚焦。他们成功分离了MDA-MB-231培养基中外泌体和细胞外囊泡,实现对外泌体高于92%的分离纯度和高于81%的回收率。Li等[106]采用在流道插入阵列障碍物的流道结构,如图7c所示,利用障碍物周围层流非对称分岔,粒子将根据其大小决定其路径,从而实现高效分离。由于流体的弹性强度与剪切速率有关,通过调节微流道内的流量,可以实现了流体的动态控制。另外,Faridi等[107]利用与图5相似的流道结构成功地实现了细菌从未稀释的全血溶液中的分离,细菌在两侧出口达到76%的回收率。
图7 (a)外泌体和细胞外囊泡所在流道结构示意图[105];(b)多螺旋结构流道示意图[88];(c)具有确定性横向位移阵列的流道结构示意图[106]

Fig. 7 (a) Schematic diagram of the microchannel structure in which exosomes and EVs are located[105];(b) Schematic diagram of a multi-spiral microchannel[88];(c) Schematic diagram of a microchannel with deterministic lateral displacement arrays[106]

上述所用的鞘液和样品溶液均为黏弹性溶液,而Ha等[108]将鞘流改用牛顿流体,实现了粒子从黏弹性流体迁移至牛顿流体,如图8a所示,粒子的这种迁移是黏弹性流体侧的弹性力和牛顿流体侧的惯性升力共同作用所导致。他们还利用该装置从原来2 μm和9.9 μm混合粒子溶液中同时洗涤和分离出9.9 μm粒子。该方法实现了无稀释、高通量和高效率的粒子分离,其中9.9 μm粒子的分离纯度大于97%,回收率大于99%。这种粒子先在黏弹性流体中完成所需操作后再转移至牛顿流体的方法也可称为粒子的介质交换,该方法能够解决潜在的生物相容性问题。Yuan等[109]利用相同的原理实现了粒子从PEO溶液迁移至去离子水溶液中,同时还研究了流道长度、流速还有PEO浓度对粒子迁移的影响。随后,他们[110]还提出了利用黏弹性流体和牛顿流体共同流动对Jurkat细胞进行有效颗粒洗涤,且确定了高效洗涤的临界颗粒堵塞率为0.08(当粒子直径小于此值时将无法迁移至牛顿流体内),实现了Jurkat细胞大于92.8%的回收率。该技术有望成为传统繁琐离心方法的有效替代。在另一项研究中,Tian等[111]与上述研究相反,将样品溶液改为牛顿流体而鞘流改为黏弹性流体,如图8b所示,实验证明了小粒子不能通过惯性和黏弹性介质之间的界面。他们还对比了三种不同鞘液/样品(黏弹性流体/牛顿流体、黏弹性流体/黏弹性流体、牛顿流体/牛顿流体)
图8 (a)粒子从黏弹性流体迁移至牛顿流体的微流道示意图[108];(b)粒子从牛顿流体迁移至黏弹性流体的微流道示意图[111];(c)粒子在三种不同(鞘液/样品)条件下的分离示意图[111]

Fig. 8 (a) Schematic diagram of the microchannel of particles migration from viscoelastic fluid to Newtonian fluid[108];(b) Schematic diagram of the microchannel of particles migration from Newtonian fluid to viscoelastic fluid[111];(c) Schematic diagram of the separation of particles under three different conditions(sheath/sample)[111]

条件下的分离情况,如图8c所示,在黏弹性流体/牛顿流体条件下,由于界面阻挡效应将小粒子留在侧壁附近,因此该条件下具有最好的分离效果。最后他们利用该方法实现了金黄色葡萄球菌(1 μm)和血小板(2~3 μm)高效和高纯度的分离,分离纯度分别达97%和100%。

3.2 无鞘分选

在不使用鞘流的情况下,依据粒子的不同特性、不同尺寸、不同的横向迁移速度以及设计所需的流道结构等,直接实现粒子的无鞘分选,这相对于有鞘分选具有操作更简单、成本更低等优点。Yang等[61]尝试了黏弹性流体的无鞘分选,发现在0.025 wt% PEO溶液中,5.9 μm粒子在出口膨胀区域能较好聚焦至中心流线,而2.4 μm粒子却在该区域分散分布。随后,他们[112]在实验中发现了与图1e左不同的现象,在6.8 wt% PVP溶液中,具有可变形性的红细胞在无惯性流动下向流道中心迁移,如图9a所示,这是由于靠近壁面时,可变形性的细胞将会受到额外的壁面升力而远离壁面。利用这一现象实现了从红细胞中分离出PS粒子,如图9b所示,原本在四角处的刚性PS粒子经过膨胀区域时依旧沿着两侧壁面流动,而红细胞虽有扩散但仍位于中间区域,从而实现分离,且PS粒子的分离纯度达98.2%。基于细胞的可变形性,还实现了新鲜红细胞和人工僵化红细胞(可看作刚性粒子)的分离以及白细胞(变形较小)从稀释全血溶液中的分离。Ahn等[113]证明了Yang等[61]提及的无鞘分选,且在此基础上研究了聚合物和粒子浓度以及流速对分离效率的影响。研究中还发现粒子间的相互作用在分离过程中起着重要作用,随着粒子浓度的增加,分离出的粒子纯度将逐渐降低。随后,Li等[114]对流速、溶液黏度、聚合物浓度、聚合物类型和流道深宽比等对二元混合粒子(5 μm和10 μm)分离的影响做了全面的参数研究,实现了两种粒子在1000 ppm PEO溶液中的有效分离,如图9c上图所示。为了解释粒子聚焦位置的移动,提出将弹性力分解为由弹性效应产生的指向中心和由弹性效应和剪切稀化效应产生的指向壁面的两个分量,其中指向中心的弹性分力与粒子尺寸有更强大的函数关系,驱动粒子向中心偏移。此外,他们还实现了在AR=0.5(高25 μm,宽50 μm)直流道中,在1000 ppm PEO溶液中三元混合粒子(3 μm、5 μm和10 μm)的无鞘分离,如图9c下图所示。Giudice等[60]研究粒子在强剪切稀化溶液中从边缘到中心迁移的实验中,同样也实现了10 μm和20 μm粒子在直流道出口膨胀区域内的无鞘分离,且当De=18时达到最佳分离效率,分离效率分别为80%和96%。另外,Lu等在实现球形和花生形粒子的有鞘分离[103]后,利用矩形流道在膨胀区域内实现了球形和花生形粒子的无鞘分离[115],且两种粒子的分离效率都大于95%,这是由于不同形状的粒子在弹性惯性效应下产生不同的迁移速度从而实现分离。但该分离效率强烈依赖于黏弹性溶液的浓度和流速。
图9 (a)可变形性粒子和刚性粒子在流道中的迁移示意图[112];(b)刚性PS粒子和新鲜红细胞的分离快照图[112];(c)混合粒子的分离图[114]

Fig. 9 (a) Schematic diagram of the migration of deformable particles and rigid particles in the microchannel[112];(b) Snapshot of the separation of rigid PS particles and fresh RBCs[112];(c) Separation map of mixed particles[114]

除了在直流道后添加膨胀区域,很多团队利用不同的流道结构同样实现了粒子的分选。Yuan等在采用了一种在流道单侧插入一组直角等腰三角形槽的结构实现粒子的黏弹性聚焦[81, 116]后,使用类似的流道结构实现了高纯度等离子体的无鞘提纯[117],如图10a所示,用该方法对血液样品进行过滤的同时能聚焦不同尺寸的血小板、红细胞和白细胞,过滤后的血浆纯度达99.93%,且经过两次的连续提纯,血浆纯度可提高至99.99%。Liu等[87]利用双螺旋结构流道,如图10b所示,实现了100 nm和2 μm粒子的无鞘分离。100 nm粒子受黏弹性效应聚焦于流道中心,而2 μm粒子由于其尺寸较大,受到靠近流线中心侧增强的法向应力聚焦至两个偏心平衡位置,从而实现大于95%的分离效率。他们利用相同的原理实现了λ-DNA分子和血小板二元混合粒子分离效率大于95%的无鞘分离。而Nam等提出一种二段式的流道结构[118],如图10c所示,第一阶段的流道为圆柱形截面的微毛细管,利用流体的黏弹性效应将两种不同尺寸的粒子聚焦至中心流道处,实现无鞘预聚焦,第二阶段为基于尺寸黏弹性诱导的横向偏移的分离,在该流道中实现了5 μm和10 μm粒子99%的分离效率和99%的纯度。随后,他们又提出一种新型的流道结构[119],在第一阶段中二元混合粒子(5 μm和10 μm)在圆柱形直流道中共同聚焦至流道中心,而在第二阶段中由于不同尺寸粒子在突扩流道中不同的横向迁移,实现粒子99.9%的分离效率。而且发现可以通过改变流体黏弹性和流速来调节分离的粒子尺度以及使用低黏度但高弹性的黏弹性流体(如DNA或HA溶液)来提高设备通量。此外,他们在另一项研究中[120]将第一阶段中圆柱形直流道改为矩形直流道,并对第二阶段微流道的尺寸进行了优化,如图10d所示,在该流道结构下实现了在白细胞和疟原虫混合溶液中疟原虫99%的分离纯度和94%的回收率。
图10 (a)粒子在具有单侧腔阵结构流道中迁移示意图[117];(b)双螺旋流道结构示意图[87];(c)二段式流道结构示意图[118];(d)粒子在二段式结构流道中迁移示意图[119, 120]

Fig. 10 (a) Schematic diagram of particle migration in a microchannel with a single-sided cavity array structure [117];(b) Schematic diagram of a double spiral microchannel[87];(c) Schematic diagram of a microchannel with two-stage structure[118];(d) Schematic diagram of particle migration in a microchannel with two-stage structure[119, 120]

本节主要介绍了有鞘分选和无鞘分选两种被动分选方法。有鞘分选由于鞘流和样品流的流速不同,相比于无鞘分选,流量控制更加复杂。但鞘流加入后,由于鞘流对样品流的挤压,其可快速实现粒子的预对准,且当鞘流为牛顿流体时,在分选的同时可实现对粒子的洗涤。目前,两种分选方式都可以实现较高的分离效率(如表1),但大多数研究仍停留在对不同尺寸粒子的分选,依据粒子形状或其他特性的分选研究相对较少,需进一步探索。
表1 黏弹性微流控中各种粒子分选方法的概括

Table 1 Summary of various particle sorting methods in viscoelastic microfluidics

Authors Particles Sheat flow Sheath/sample flow Sample flow rate Separation purity(the former)
Nam et al[100] 1 μm/5 μm PS
Platelets/blood cells
Yes Viscoelastic/Viscoelastic fluid 30 μL/h 99.9%
>99.8%
Liu et al[105] 0.1 μm/0.5 μm PS
Exosomes/EVs
Yes Viscoelastic/Viscoelastic fluid 200 μL/h >90%
>90%
Zhou et al[88] 0.1 μm/0.3 μm PS
Exosomes/EVs
Yes Viscoelastic/Viscoelastic fluid 25 μL/min >95%
92.8%
Faridi et al[107] 2 μm/5 μm PS
Bacteria/whole blood
Yes Viscoelastic/Viscoelastic fluid 30 μL/h 93%
76%
Ha et al[108] 9.9 μm/2 μm PS Yes Newtonian/Viscoelastic fluid 40 μL/min 97.5%
Yuan et al[110] 5 μm/0.8 μm PS
10 μm/0.8 μm PS
Jurkat cells
Yes Newtonian/Viscoelastic fluid 2 μL/min 94.4%
100%
92.8%
Tian et al[111] Staphylococcus aureus/platelets Yes Viscoelastic/Newtonian fluid 300 μL/h 97%
Yang et al[112] PS/RBCs No - 160 μL/h 98.2%
Li et al[114] 10 μm/5 μm/3 μm PS No - 300 μL/h 95.2%
Del Giudice et al[60] 20 μm/10 μm PS No - 2 μL/min 96%
Lu et al[115] Spherical/peanut shaped particles No - 150 μL/h 95.2%
Yuan et al[117] Plasma/blood cells No - 50 μL/min 99.93%
Liu et al[87] 0.1 μm/2 μm PS
λ-DNA/platelets
No - 1.4 μL/h 95%
96%
Nam et al[119] 5 μm/10 μm PS No - 0.05~0.14 μL/min 99.9%
Nam et al[120] Malaria parasites/WBCs No - 400 μL/min 99%
Nam et al[118] 5 μm/10 μm PS
MCF-7 cells/WBCs
No - 20 μL/min
200 μL/min
99%
97%

4 其他应用

混合是大多数医学诊断、基因测序、化学生产、药物发现和环境监测等微流控装置的主要工艺[121, 122]。如何实现高效混合一直是研究微混合器的重点。黏弹性溶液具有流动不稳定性[123],将黏弹性溶液运用于微流体混合将有利于提高混合效率。Hong等[124]提出了一种基于边井直流道黏弹性流体混沌涡动力学的高效微混合器,如图11a所示,当流体的惯性和弹性达到一定平衡后,在边井处就会出现由黏弹性溶液不稳定性产生的混沌漩涡,从而加强相邻流体的混合。而Julius等[125]更是将膨胀、收缩和齿形等不同结构的流道组合在一起,来改善混合效率,通过两种不同染料的混合实验,验证了模拟的混合效果。Cai等[126]提出了一种在流道中嵌入几个菱形块的高效微混合器,当流体通过菱形块时,使得黏弹性流体流动失稳,产生强剪切力和强扩展力,从而易于混合。还对比了不同雷诺数Re和Weissenberg数Wi下的混合速度和所需的混合流道长度。实验还发现了在三个入口交汇处也会出现黏弹性流道不稳定性的发生。最后他们提出要合理选取ReWi以及菱形块数量,实现成本和效率的最优化。
图11 (a)边井直流道中流体混合示意图[124];(b)十字槽微流道示意图[129]

Fig. 11 (a) Schematic diagram of fluid mixing in a straight microchannel the side channel[124];(b) Schematic diagram of a microchannel with cross-slot region[129]

黏弹性聚焦也可以用来测量粒子的拉伸变形。Cha等[127]提出了一种基于黏弹性粒子聚焦测量细胞变形性的有效方法。他们利用十字槽微流道,在最初的直流道中实现红细胞的黏弹性聚焦,随后95%以上红细胞被成功地输送到十字槽流道的驻点,并被拉伸流拉伸,从而实现了高效的细胞变形性测量,并成功监测了红细胞热变形性的变化。Bae等[128]利用同样的原理实现了对中国仓鼠卵巢(CHO)细胞的拉伸,且提出了一种新的微流体方法来精确地评估细胞在拉伸应力下的机械损伤,发现了损害CHO细胞的临界拉伸应力。该方法若能运用于其他细胞,如红细胞或白细胞等,则将有利于人工心脏等人工器官的设计与操作。最近,Kim等[129]利用十字槽微流道中黏弹性粒子聚焦来测量不同长径比的椭圆形粒子的形状,如图11b所示,该方法打破了光学显微镜等常规方法测量非球形微粒的形状的局限性,也有助于理解黏弹性介质中非球形粒子的动力学。
此外,Hu等[130]提出了一种利用特殊微流道定量分析单个漂浮癌细胞黏弹性的方法,采用HERTZ和TATARA模型将变形的单元形状转换为单元直径和瞬态应力应变比,随后测量了正常乳腺细胞和乳腺癌细胞的黏弹性参数,证明了所测应力应变比与黏弹性参数之间的高相关性。还有Raj 等[131]对黏弹性流体与可变形壁之间相互作用的研究和Yang等[132]利用形状记忆聚合物对微流道中实现可编程智能阀门的研究等等,这些研究虽仍在探索阶段,但也展示黏弹性流体在微流控中的无限魅力。

5 数值模拟

尽管从发现粒子在黏弹性流体中的迁移现象至今已经过去五六十年了,但微尺寸下黏弹性流体的流动以及粒子在黏弹性流体中的迁移机制仍处在探索研究阶段。而数值模拟能够克服实验研究的限制,提供粒子迁移运动的详细信息。为对黏弹性流体流动进行数值模拟,通常采用有限差分法(FDM)、有限元法(FEM)、有限体积法(FVM)、谱法(SM)等对NAVIER-STOKES方程和本构方程进行离散[133]。1993年,Aharonov等[134]尝试使用格子玻尔兹曼方法(LBM)配合幂则法来描述黏弹性流体,该研究体现了LBM处理多相流和复杂边界条件的能力。随后,LBM主要采用幂则法[135, 136]、Casson模型[137]和Carreau-Yasuda(C-Y)模型[138, 139]来计算黏弹性流体。进一步改进的LBM模型可用于多元和多相复杂流体的模拟。与FDM、FEM、FVM相比,LBM是一种介观模拟方法,流体不再被假设为连续介质,LBM只包含与简单碰撞规则耦合的常微分方程的积分。因此,LBM具有良好的局域性和简单性,且适合并行计算。Zou等[133]利用LBM和FVM的优点,提出了一种模拟等温和不可压缩黏弹性流体流动的格子玻尔兹曼有限体积法,LBM可以提高不可压缩NAVIER-STOKES方程的模拟效率和可扩展性,而FVM可以保持本构方程模拟的准确性和通用性。该方法针对典型的二维黏弹性基准能够进行全面的数值模拟,但该方法是基于二维均匀网络,非均匀网络和具有曲线边界的三维领域仍有待探索。对于血液流动的数值模拟,LBM同样有着方便施加血管流动中常见振荡和脉动边界条件以及精确计算血管壁附近剪切速率的优势[140],Bernsdorf等[141]使用LBM(C-Y模型)对脑动脉瘤血液进行了数值模拟,对比不同雷诺数下牛顿流体和黏弹性流体的壁面剪切应力,发现了脑动脉瘤生长过程和破裂风险的一个关键指标是振荡壁面剪切应力。另外,与LBM相同,耗散粒子动力学(DPD)方法也是一种介观模拟方法。该方法结合了分子动力学(MD)和格子气自动机(LDA)的优点,能够模拟复杂流体且具有较高的计算效率[142]。Duong-Hong等[143]利用DPD方法建立了模拟纤维悬浮牛顿流体和黏弹性流体的通用模型,采用线性链对黏弹性流体进行建模,其模拟结果与Oldroyd-B模型较为吻合。许少锋等[144]则在DPD方法下采用有限伸长非线性弹性链(FENE)来模拟高分子链以实现微流道中黏弹性溶液的Poiseuille流动模拟,同时研究了流道宽度以及流场强度对高分子链迁移的影响。
对于粒子在黏弹性流体中迁移的模拟,Lee等[145]采用LBM结合平面轮廓方法(SPM)模拟了黏弹性悬浮液中二维刚性粒子的运输过程。他们先后研究了黏弹性Couette流动中单粒子的迁移和双粒子的动力学特性,为微尺寸粒子在黏弹性流体中的迁移行为的模拟开启了新的大门。面对黏弹性流动中可能出现弹性不稳定的问题,Su等[146]采用双粒子速度耦合格子玻尔兹曼模型研究了该不稳定现象,结果表明,运动黏度比对弹性不稳定性转变具有重要影响。除了LBM之外,Villone等[147]利用三维有限元法对可变形粒子在黏弹性流体在圆管中的迁移进行了数值模拟,研究表明粒子具有向流道中心和壁面两种方向迁移趋向(与图2b类似),且剪切稀化将增强向壁面的迁移。Decoene等[148]采用Oldroyd模型和基于虚拟区域法的数值方法对黏弹性流体中的二维刚性粒子进行直接模拟。该方法中考虑了惯性效应,研究牛顿和非牛顿稠密悬浮液的沉降,还讨论了刚性粒子对黏弹性流体流变特性的影响。另外,Wang等[149]采用虚拟区域法对Giesekus黏弹性流体驱动下的粒子在矩形流道中的迁移进行了数值模拟。研究表明,在惯性很小时,粒子向流道中心线或最近的角移动,该结果与上述粒子在矩形流道中的迁移现象一致,但该方法具有参数范围相对较小等缺点。

6 结论与展望

本文从应用的角度详细地介绍了黏弹性微流控装置中的各种被动微粒操作,包括聚焦、分选、混合和拉伸等,以及简要列举了一些研究黏弹性流体流动特性和在其内微粒迁移运动规律的数值模拟方法。黏弹性流体相比牛顿流体更易实现三维聚焦,且适用于尺寸更小的粒子,但由于对其研究时间较短,尚未形成完整的理论体系,对此在结合本文介绍的基础上提出如下展望:(1)由于低雷诺数的限制,会较为明显地影响装置的通量,虽通过使用低粘度和高弹性的黏弹性溶液(如DNA或HA溶液)能提高通量,但对此的研究仍相对较少,需进一步探索。(2)目前对粒子形状分选的研究仍停留在形状相似的球形和花生形粒子的对比上,但由于生物粒子的多样性,单一形状的研究结果可能对实际应用不具备普遍意义,因此需要系统地研究不同形状特性生物粒子的分选机理。(3)黏弹性流体中三维粒子操控的模拟仿真研究亟待展开,以及黏弹性流体流动不稳定等问题急需解决。(4)将黏弹性微流控芯片与其他元器件进行整合,实现主动操控和被动操控的结合,提高设备效率与能力,解决实际问题。
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Microfluidics has experienced massive growth in the past two decades, and especially with advances in rapid prototyping researchers have explored a multitude of channel structures, fluid and particle mixtures, and integration with electrical and optical systems towards solving problems in healthcare, biological and chemical analysis, materials synthesis, and other emerging areas that can benefit from the scale, automation, or the unique physics of these systems. Inertial microfluidics, which relies on the unconventional use of fluid inertia in microfluidic platforms, is one of the emerging fields that make use of unique physical phenomena that are accessible in microscale patterned channels. Channel shapes that focus, concentrate, order, separate, transfer, and mix particles and fluids have been demonstrated, however physical underpinnings guiding these channel designs have been limited and much of the development has been based on experimentally-derived intuition. Here we aim to provide a deeper understanding of mechanisms and underlying physics in these systems which can lead to more effective and reliable designs with less iteration. To place the inertial effects into context we also discuss related fluid-induced forces present in particulate flows including forces due to non-Newtonian fluids, particle asymmetry, and particle deformability. We then highlight the inverse situation and describe the effect of the suspended particles acting on the fluid in a channel flow. Finally, we discuss the importance of structured channels, i.e. channels with boundary conditions that vary in the streamwise direction, and their potential as a means to achieve unprecedented three-dimensional control over fluid and particles in microchannels. Ultimately, we hope that an improved fundamental and quantitative understanding of inertial fluid dynamic effects can lead to unprecedented capabilities to program fluid and particle flow towards automation of biomedicine, materials synthesis, and chemical process control.

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Separation and sorting of micron-sized particles has great importance in diagnostics, chemical and biological analyses, food and chemical processing and environmental assessment. By employing the unique characteristics of microscale flow phenomena, various techniques have been established for fast and accurate separation and sorting of microparticles in a continuous manner. The advancements in microfluidics enable sorting technologies that combine the benefits of continuous operation with small-sized scale suitable for manipulation and probing of individual particles or cells. Microfluidic sorting platforms require smaller sample volume, which has several benefits in terms of reduced cost of reagents, analysis time and less invasiveness to patients for sample extraction. Additionally, smaller size of device together with lower fabrication cost allows massive parallelization, which makes high-throughput sorting possible. Both passive and active separation and sorting techniques have been reported in literature. Passive techniques utilize the interaction between particles, flow field and the channel structure and do not require external fields. On the other hand, active techniques make use of external fields in various forms but offer better performance. This paper provides an extensive review of various passive and active separation techniques including basic theories and experimental details. The working principles are explained in detail, and performances of the devices are discussed.

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Focusing particles (both biological and synthetic) into a tight stream is usually a necessary step prior to counting, detecting, and sorting them. The various particle focusing approaches in microfluidic devices may be conveniently classified as sheath flow focusing and sheathless focusing. Sheath flow focusers use one or more sheath fluids to pinch the particle suspension and thus focus the suspended particles. Sheathless focusers typically rely on a force to manipulate particles laterally to their equilibrium positions. This force can be either externally applied or internally induced by channel topology. Therefore, the sheathless particle focusing methods may be further classified as active or passive by the nature of the forces involved. The aim of this article is to introduce and discuss the recent developments in both sheath flow and sheathless particle focusing approaches in microfluidic devices.

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Solid-liquid disperse systems are complex fluids, extensively used for a variety of applications. The flow behavior of such materials is strongly dependent on the matrix rheological properties: when the suspending fluid shows viscoelastic behavior, isolated suspended particles in confined flow fields tend to migrate across the streamlines. In this work, we carry out a detailed experimental investigation of such migration phenomenon for a rigid, spherical particle in planar shear flow, and compare the experimental findings with 3D numerical simulations based on finite elements. A highly elastic non-Newtonian fluid is chosen as the suspending medium. The migration is studied by varying the confinement, the external shear rate and the fluid normal stresses. The particle is always found to move towards the closest wall, regardless of its initial position. For a fixed set of geometrical and flow parameters, the trajectories from different initial positions can be shifted in time to overlap on a single curve. Migration dynamics is governed by an exponential law as the particle is in the region around the midgap. Stronger confinements, higher shear rates and higher levels of normal stresses all enhance the migration speed. We found qualitative agreement between predictions from numerical simulations and experimental results.

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Particle focusing in planar geometries is essentially required in order to develop cost-effective lab-on-a-chips, such as cell counting and point-of-care (POC) devices. In this study, a novel method for sheathless particle focusing, called "Elasto-Inertial Particle Focusing", was demonstrated in a straight microchannel. The particles were notably aligned along the centerline of the straight channel under a pressure-driven flow without any additional external force or apparatus after the addition of an elasticity enhancer: PEO (poly(ethylene oxide)) (similar to O(100) ppm). As theoretically predicted (elasticity number: El approximate to O(100)), multiple equilibrium positions (centerline and corners) were observed for the viscoelastic flow without inertia, whereas three-dimensional particle focusing only occurred when neither the elasticity nor the inertia was negligible. Therefore, the three-dimensional particle focusing mechanism was attributed to the synergetic combination of the elasticity and the inertia (elasticity number: El approximate to O(1-10)). Furthermore, from the size dependence of the elastic force upon particles, we demonstrated that a mixture of 5.9 and 2.4 mu m particles was separated at the exit of the channel in viscoelastic flows. We expect that this method can contribute to develop the miniaturized flow cytometry and microdevices for cell and particle manipulation.

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We perform 3D numerical simulations, heuristic modeling and microfluidic experiments to demonstrate, for the first time, the presence of a bistability scenario for transversal migration of particles suspended in a viscoelastic liquid flowing in a pipe. Our results show that particle migration, either at the centerline or at the wall, can be controlled by the rheological properties of the suspending liquid and by the relative dimensions of the particle and tube. Proper selection of these parameters can promote strict aligning of particles on a line, i.e., 3-D focusing. Simple design rules are given to rationally control particle focusing under flow in micropipes.

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Much difficulty has been encountered in manipulating small-scale materials, such as submicron colloidal particles and macromolecules (e.g., DNA and proteins), in microfluidic devices since diffusion processes due to thermal (Brownian) motion become more pronounced with decreasing particle size. Here, we present a novel approach for the continuous focusing of such small-scale materials. First, we successfully focused fluorescent submicron polystyrene (PS) beads along equilibrium positions in microchannels through the addition of a small amount water-soluble polymer [500 ppm poly(ethylene oxide) (PEO)]. Lateral migration velocity significantly depends upon the viscoelastic effect (Weissenberg number: Wi) and the aspect ratio of particle size to channel height (a/h). Interestingly, focusing using viscoelastic flows was also observed for flexible DNA molecules (lambda-DNA and T4-DNA), which have radii of gyration (R-g) of approximately 0.69 mu m and 1.5 mu m, respectively. This small-scale material manipulation using medium viscoelasticity will contribute to the design of nanoparticle separation and genomic mapping devices.

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Pure separation and sorting of microparticles from complex fluids are essential for biochemical analyses and clinical diagnostics. However, conventional techniques require highly complex and expensive labeling processes for high purity separation. In this study, we present a simple and label-free method for separating microparticles with high purity using the elasto-inertial characteristic of a non-Newtonian fluid in microchannel flow. At the inlet, particle-containing sample flow was pushed toward the side walls by introducing sheath fluid from the center inlet. Particles of 1 mu m and 5 mu m in diameter, which were suspended in viscoelastic fluid, were successfully separated in the outlet channels: larger particles were notably focused on the centerline of the channel at the outlet, while smaller particles continued flowing along the side walls with minimal lateral migration towards the centerline. The same technique was further applied to separate platelets from diluted whole blood. Through cytometric analysis, we obtained a purity of collected platelets of close to 99.9%. Conclusively, our microparticle separation technique using elasto-inertial forces in non-Newtonian fluid is an effective method for separating and collecting microparticles on the basis of size differences with high purity.

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In this work, we investigated the lateral migration of microparticles suspended in two different viscoelastic fluids with or without the second normal stress difference. For the viscoelastic fluid without the second normal stress difference, competing forces existed between microfluidic inertia and the first normal stress difference (N (1)), which resulted in a synergetic effect of particle focusing. For the fluid with the second normal stress difference (N (2)), particles were greatly affected by a N (2)-induced secondary flow, and the competition among the inertia, N (1), and N (2) determined the lateral migration trajectories of the particles. The obtained results were delineated with the blockage ratio, which showed good agreement with the results of a recent numerical study (Villone et al. in J Non Newton Fluid Mech 195:1-8, 2013). The present study also examined the possibility of particle separation in a size-dependent manner using the N (2)-induced secondary flow in microchannel flow.

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Hemodynamics is a complex problem with several distinct characteristics; fluid is non-Newtonian, flow is pulsatile in nature, flow is three-dimensional due to cholesterol/plague built up, and blood vessel wall is elastic. In order to simulate this type of flows accurately, any proposed numerical scheme has to be able to replicate these characteristics correctly, efficiently, as well as individually and collectively. Since the equations of the finite difference lattice Boltzmann method (FDLBM) are hyperbolic, and can be solved using Cartesian grids locally, explicitly and efficiently on parallel computers, a program of study to develop a viable FDLBM numerical scheme that can mimic these characteristics individually in any model blood flow problem was initiated. The present objective is to first develop a steady FDLBM with an immersed boundary (IB) method to model blood flow in stenoic artery over a range of Reynolds numbers. The resulting equations in the FDLBM/IB numerical scheme can still be solved using Cartesian grids; thus, changing complex artery geometry can be treated without resorting to grid generation. The FDLBM/IB numerical scheme is validated against known data and is then used to study Newtonian and non-Newtonian fluid flow through constricted tubes. The investigation aims to gain insight into the constricted flow behavior and the non-Newtonian fluid effect on this behavior.

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格子玻尔兹曼方法(lattice Boltzmann method,LBM)能够直接计算局部剪切速率并可以达到二次精度,因此在非牛顿流动数值模拟中展现出一定优势。尽管已证实LBM 对于非牛顿流动的适用性,但是LBM 需要通过即时调节BGK(Bhatnagar-Gross-Krook)碰撞项中的松弛时间来实时反映黏度改变,当松弛时间接近1/2 时,迭代会出现数值不稳定现象。该文对LBM 在非牛顿流体研究中的进展进行了总结,介绍了增加数值稳定性的方法并对结果的精度进行了比较,在此基础上对LBM 在非牛顿研究中的进一步发展进行了展望。

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