Active and passive micromixers: A comprehensive review

Journal Pre-proof Active and passive micromixers: A comprehensive review Morteza Bayareh, Mohsen Nazemi Ashani, Azam Usefian

PII:

S0255-2701(19)30873-6

DOI:

https://doi.org/10.1016/j.cep.2019.107771

Reference:

CEP 107771

To appear in:

Chemical Engineering and Processing - Process Intensification

Received Date:

18 July 2019

Revised Date:

24 November 2019

Accepted Date:

1 December 2019

Please cite this article as: { doi: https://doi.org/ This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

Active and passive micromixers: a comprehensive review Morteza Bayareh*, Mohsen Nazemi Ashani, Azam Usefian Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran *[email protected] Highlights

ro

 

The present review (with 205 refs.) addresses the need for microdevices and presents the basic microfluidic equations. The review describes the relevant numerical and experimental approaches. Various types and designs of passive and active micromixers are discussed.

of



lP

re

-p

Abstract The present review (with 205 refs.) addresses the need for microdevices, presents the basic microfluidic equations and describes the relevant numerical and experimental approaches. Various types and designs of passive and active micromixers are presented. In addition, the relevant effective dimensionless or dimensional parameters and the fabrication technology for different micromixer types are introduced. Different general configurations of lamination, obstacle, convergence-divergence and curved-channel are discussed for passive micromixers. The active micromixers are categorized and described as pressure field driven, acoustic field driven, magnetic field driven, electric field driven and thermal field driven.

ur na

Keywords: Lab-on-a-Chip, Microfluidics, Passive micromixer, Active micromixer, Mixing efficiency

Jo

Nomenclature Species concentration (mol/lit) c Sound velocity (m/s) Cs Diffusion coefficient (m2/s) D Dean number De Hydraulic diameter (m) Dh Energy (J) e Disturbance frequency (Hz) f Body force vector (N) f Fourier number Fo Thermal conductivity (W/m.K) k Knudsen number Kn Characteristic length (m) L Mixing index MI

Heat-flux vector (W/m2) q Mean radius of the channel curvature (m) R Reynolds number Re Time (s) t Temperature (K) T Mean velocity (m/s) U Velocity vector (m/s) V Greek symbols The ratio of specific heats κ Mean free space (m) λ Dynamic viscosity (Pa.s) μ Density (kg/m3) ρ

p Pe Pr

σT σv τ

Pressure (Pa) Peclet number Prandtl number

Tangential temperature coefficient Tangential momentum coefficient Shear stress tensor (Pa)

Jo

ur na

lP

re

-p

ro

of

1. Introduction Lab-on-a-Chip (LOC) or microfluidic chips have been of great interest over the past two decades. Microfluidic has many applications in the fields of engineering, biotechnology and medicine. The history of microfluidics dates back to the 1950s, which was specifically used in the production of inkjet printers [1]. The mechanism of these printers was based on microfluidic devices, because they include very small tubes that carry ink for printing. In the 1970s, with the advancement of silicon technology, this technology was developed into small mechanical machines [2]. In the 1980s, with the advent of micro-valves and micro-pumps, the use of smallscale technology was increased [1, 2]. In these years, several analytical systems were proposed based on micron methods. All of these samples showed the precision and control of microfluidic devices when the volume of fluid was reduced [1]. Microfluidics has reached advanced stages and many achievements. In principle, microfluidics can be used in many engineering, bio and medical sciences especially in Micro-Electro-Mechanical Systems (MEMS). MEMS are combinations of mechanical components, sensors, mechanical arms, and electronic components that are located on a layer of strategic material, such as silicon. Nguyen and Wereley [2] have presented the Fig. 1 for a better understanding of the size of microfluidic devices and the volume of the fluid. Microfluidic technology has specific characteristics such as small-scale particle control, low cost and rapid response time [3]. The development of microfluidic devices has led to a lot of interest in using these devices in medical science and experimental chips [4]. The advantages of these devices include reduction of the consumption of samples (reactants), high controllability and the ability to manipulate samples during the process as well as high surface to volume ratio [4]. The analysis time in microfluidic devices is much shorter than that in milli-scale ones. On the other hand, high surface-to-volume ratio is an ideal property for microfluidic systems [5]. Therefore, application of these devices with laboratory equipment reduces the time required for analysis as well as the required space [6-7].

Fig. 1. Dimensions and sizes of microfluidic devices [2].

In the field of engineering, mixing and separation are of particular importance. These processes (especially particle separation) can be used inside the human body, for example, the drug delivery. Different methods are used for mixing of fluids. There are several reviews on micromixers [8-14]. Since new structures have been proposed to improve the mixing quality, these reviews should be updated. In addition, the mentioned reviews considered the types of micromixers and did not perform a comprehensive review on fabrication of micromixers. In the present work, different mixing techniques, various fabrication methods, different numerical schemes and different design variants are reviewed comprehensively. In addition, the present article addresses recent operating principles and techniques that have not been covered in the other review manuscripts.

ro

of

2. Basic microfluidic equations 2.1. Fluid flow and heat transfer equations In general, the governing equations for the simulation of mixing process of Newtonian and nonNewtonian fluids are continuity, momentum, and energy equations. These equations in conservative form are presented as follows, respectively [15]:

-p

𝜕𝜌 + ∇. 𝜌𝑽 = 0 𝜕𝑡

(2) (3)

lP

𝜕𝜌𝑒 = ∇. (𝜌𝑒𝐕 − 𝛕𝑽 + 𝐪) 𝜕𝑡

re

𝜕𝜌𝑽 = −∇. (𝜌𝑽𝑽) + 𝜌𝐟 + ∇. 𝛕 𝜕𝑡

(1)

ur na

where 𝐕 is velocity vector, 𝜌 is the density, 𝐟 is the body forces, 𝛕 is shear stress tensor, e is the energy, p is the pressure, and q is the heat-flux vector. The shear stress tensor can be expressed for Newtonian and non-Newtonian fluids. 2.2. Convection-diffusion equation The concentration distribution is determined using convection-diffusion transport equation [13]: 𝜕𝐜 + 𝐕. ∇𝐜 = 𝐃∇2 𝐜 𝜕𝑡

(4)

Jo

where c and D are the species concentration and diffusion coefficient, respectively. 2.3. Governing dimensionless parameters Dimensionless parameters that are used to describe the mixing process include Reynolds number (the ratio of inertia to viscous forces), the Peclet number (the ratio of mass transport due to convection to that of diffusion), the Fourier number (the ratio of diffusion to inertia force), Knudsen number, and Dean number. These dimensionless parameters are defined as follows, respectively [8, 9]:

𝑅𝑒 =

𝜌𝑈𝐷ℎ 𝜇

(5)

𝑃𝑒 =

𝑈𝐿 𝐷

(6)

𝑆𝑡 =

𝑓𝐷ℎ 𝑈

(7)

𝐿𝐷

(8)

2

𝐷ℎ 𝑈

of

𝐹𝑜 =

(9)

𝜅𝜋 𝑈 2 𝐶𝑠 𝐿

ro

𝐾𝑛 = √

(10)

-p

𝐷ℎ 𝐷𝑒 = 𝑅𝑒√ 𝑅

Jo

ur na

lP

re

where 𝐷ℎ is hydraulic diameter, L is characteristic length scale, f is disturbance frequency, U is average velocity, 𝐶𝑠 is the sound velocity, R is the mean radius of the channel curvature, and 𝜅 is the ratio of specific heats. The Reynolds number determines the flow patterns. In channel flow, critical Reynolds number is about 1500. The fluid flow regime in microchannels is typically laminar due to small dimensions of channels and low fluid flow velocity. Micromixers may reach high mixing index at low, high or optimal Reynolds number depends on their geometries, types of fluids, boundary conditions, and external actuators. Peclet number is employed when there is a competition between convection and diffusion. For the mixing process with a constant diffusion coefficient, the Peclet number indicates the flow rate through the channel. For laminar flow, the Peclet number is proportional to the mixing length [9]. The Strouhal number is used to characterize the operation conditions of active micromixers according to the disturbance frequency. The Fourier number is defined as the ratio of tr to tm, where tr is the residence time and tm is the mixing time [16]. If Fo < 1, tr is sufficient for occurrence of mixing. Hence, when Fo is greater than one, the complete mixing can be achieved by decreasing the flow rate, reducing the characteristic length scale, or increasing the channel length. Knudsen number is used to determine the regimes of fluid rarefaction. As a result, no-slip or slip boundary conditions are employed based on the values of Knudsen number. In gas flow problems, no-slip boundary condition is imposed on the channel walls for Kn < 10-3. When 10-3 < Kn < 10-1, slip boundary condition is employed. The values of 10-1 < Kn < 101 indicate transitional flow regime [17]. Finally, the Dean number is considered for the micromixers with curved channels (for more details, see Sec. 5.1.4). 3. Numerical approaches Numerical simulations of mixing process have been performed using commercial softwares such as ANSYS/CFX, FLUENT and COMSOL Multiphysics or written codes, for instance, lattice Boltzmann technique. Finite volume method (FVM) [18] and finite element method (FEM) [19]

2 − 𝜎𝑣 𝜕𝑢 3 𝜇 𝜕𝑇 | + | 𝜎𝑣 𝜕𝑦 𝑤𝑎𝑙𝑙 4 𝜌𝑇𝑔𝑎𝑠 𝜕𝑥 𝑤𝑎𝑙𝑙

-p

𝑢𝑔𝑎𝑠 − 𝑢𝑤𝑎𝑙𝑙 = 𝜆

ro

of

have been used to solve the velocity field. The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) [20] and Semi-Implicit Method for Pressure Linked Equations-Consistent (SIMPLEC) [18] algorithms have been employed for pressure-velocity coupling. To discretize the velocity fields, upwind Quadratic Upstream Interpolation for Convective Kinematics (QUICK) [18] and second order [21] schemes have been used. QUICK method is usually employed for structured grids along the channel and upwind second order is commonly used for complex flow paths (see Sec. 3.2 for more details). Slip [22] and no-slip [18] boundary conditions have been imposed on the walls of microchannel for hydrophobic and hydrophilic surfaces, respectively. Since most of experimental devices are made of hydrophilic materials, noslip boundary condition is more common in numerical simulations compared to the slip one. Noslip/no-jump boundary conditions are valid for most microscopic fluids. In other words, the velocity and temperature of the fluid are equal to the velocity and temperature of the wall (uwall = uliquid|wall and Twall = Tliquid|wall) [1, 2]. The above governing equations are also valid for gas flows, but their boundary conditions are different. For the case of gases, the slip boundary condition is applied for temperature and velocity depends on the Knudsen number. The velocity slip condition was determined by Maxwell [23]: (11)

2 − 𝜎𝑇 2𝑘 𝜆 𝜕𝑇 | 𝜎𝑇 𝑘 + 1 𝑃𝑟 𝜕𝑦 𝑤𝑎𝑙𝑙

(12)

lP

𝑇𝑔𝑎𝑠 − 𝑇𝑤𝑎𝑙𝑙 =

re

Also, temperature jump condition is defined as follows [24]:

ur na

where 𝜎𝑣 and 𝜎𝑇 are the tangential momentum and temperature accommodation coefficients, respectively. 𝜆 is the mean free space, k is the thermal conductivity, and Pr is the Prandtl number. Slip flow regime using the above boundary conditions have been investigated by some researchers [25-27]. For example, Reyhanian et al. [27] analyzed the micromixing of two gases for 10-2 < Kn < 0.5 using direct simulation Monte Carlo.

Jo

3.1. COMSOL Multiphysics software As mentioned before, commercial softwares are employed to simulate the microfluidic process. Since COMSOL Multiphysics software is widely used in the study of passive and active micromixers, some details are provided on the procedure of numerical simulations using this software. To simulate the mixing process in passive and active micromixers (see Sec. 5), two main modules are “Fluid Flow_ Laminar Flow” and “Chemical Species Transport_ Transport of Diluted”. Simple geometries can be sketched using COMSOL software and complex ones should be created using other softwares such as AutoCAD and SolidWorks and then exported the ECAD or DXF files to COMSOL. For non-Newtonian fluids, the models (Power Law, Carreau Model, and User Defined) are chosen as follows: Laminar Flow_Fluid Properties_Dynamic Viscosity: non-Newtonian. For active micromixers, external actuator is selected as Electric Current, Magnetic Fields, etc. in AC_DC module. As mentioned before, several numerical simulations have been conducted to evaluate the mixing process using COMSOL Multiphysics software.

References [28-34, 93, 103, 105, 107, 127, and 185] are some articles used this software published between 2017 and 2019.

re

-p

ro

of

3.2. Numerical diffusion Numerical diffusion in the numerical solution of mixing at the microscale is one of the critical issues [35-38]. The estimation of mixing index in micromixers is affected by numerical diffusion errors due to the occurrence of oscillations on the interface between the fluids especially when Pe >> 1. Okuducu and Aral [35] investigated three-dimensional swirl-induced micromixers with two and four fluid injections using FVM to evaluate the numerical diffusion effects. They demonstrated that at Re = 240, grid resolution has a significant effect on the estimation of numerical diffusion errors. It was reported that two-inlet configuration leads to higher numerical diffusion than four-inlet one. They concluded that numerical diffusion generated in swirling micromixers depends on the Peclet value and the flow pattern. Also, Okuducu and Aral [36] analyzed the mixing performance of a T-shaped micromixer using FVM and FEM and different types of mesh. They found that at Re = 0.1, similar amount of numerical diffusion is produced for different types of mesh (hexahedral, prism, and tetrahedral). They revealed that FEM can produce higher numerical diffusion error than FVM. The average false diffusivity was computed for connective-diffusive mixing by Liu [37]. The author proposed a method for different numerical schemes and various types of mesh. It was demonstrated that first order upwind scheme produces higher false diffusion than QUICK one. However, the accuracy of second order upwind, QUICK, and Monotone Upstream Scheme for Conservation Laws (MUSCL) schemes in terms of false diffusion is about the same. In addition, it was revealed that tetrahedral cells lead to higher numerical diffusion than hexahedral ones.

Jo

ur na

lP

4. Fabrication techniques In recent years, microtechnology has been developed rapidly. Now, microchannels are integrated with accessories such as sensors, actuators and other electronic devices, and used in laboratories for biological applications [39]. Nano- and micro-scale devices have been studied for many years, however the devices that are now available are much more accurate than previous ones [40]. The application of microdevices depends on their materials. These materials are nonorganic, such as silicon, Plexiglas and glass, or organic such as polydimethylciloxane (PDMS) and polymethyl methacrylate (PMMA) that are rapidly developing with different fluids [41]. The polymers such as PDMS, PMMA, etc. are used for micro and nanodevices due to their low cost and environmental compatibility [39]. One of the main features to fabricate the microfluidic devices is their geometry. Another important factor is the particle size of the materials. Recently, Chaurasia et al. [42] presented a unified microfluidic technique using oil-encapsulated calcium alginate microfibers. They demonstrated that the encapsulate shape can be tuned for different geometries include spherical, ellipsoidal, etc. Nowadays, a variety of techniques have been developed by microfluidic engineers to fabricate microfluidic devices. These approaches can be classified as laminates, polymer molding, threedimensional printing, and nanofabrication. Most of micromixers can be fabricated using polymer laminates [43]. In this approach, two or more layers are bonded together to create the microchannel. Common materials in laminate device fabrication include polycarbonate, PMMA, Cyclic Olefin Copolymer (COC), and glass. Laser cutter (usually CO2 laser) or knife plotter are used to cut each layer [44]. Adhesive and thermal bonding methods are employed for bonding the layers [45]. Second category is polymer molding include soft lithography, injection molding,

of

and hot embossing. Soft lithography uses photolithography such as SU-8 to pour and cure the polymer like PDMS [46]. The cured PDMS is bonded with a glass side to form the microchannel. Micro injection molding uses thermoplastics to form microfluidic devices commercially. In this method, the melted thermoplastic is injected into a mold cavity and then cooled [47]. In hot embossing technique, thermoplastics or polymers such as polycarbonate, PMMA, COC, and polyethylen teraphthalate are shaped as microfluidic devices using a mold, pressure and heat [48]. Third fabrication category is 3D printing, in which three-dimensional model is created by the printer. Acrylonitrile butadiene styrene (ABS), polycarbonate, polyamide, polystyrene, and PDMS are usually employed to create microfluidic devices using different 3D printing techniques [49]. The last method to fabricate microdevices is nanofabrication includes top-down [50] and bottom-up [51] methods. Electron beam lithography and extreme ultraviolet lithography are currently used to fabricate microdevices. Their cost and serial processing are two limitations of these methods.

ur na

lP

re

-p

ro

5. Micromixers Microfluidic devices based on their stimulus can be divided into two categories: passive and active devices. Passive microfluidic devices do not use any external actuator to drive the fluids, guide the particles in the fluid, separate them, etc. Active microfluidic devices use external energy sources for mixing, separation, etc. There are some equations used by the researchers to quantify the mixing quality. Table 1 summarizes these relations, where 𝐶𝑖 , 𝐶𝑜 , 𝐶̅ , 𝐶𝑜̅ and 𝐶∞ indicate the point concentration, the point concentration in the non-mixing cross section, the average concentration, the average concentration in the non-mixing cross section and the concentration of completed mixing, respectively. Also, N and 𝛿 denote the number of nodes in the considered section and the section width, respectively. Eq. (13) computes the mixing index using intensities of pixels across a cross-section of channel. At the inlet MI = 0.5 and when the fluids are mixed completely, MI = 0. Eq. (14) is an improved definition for mixing index. In this equation, mixing index is nondimensionalized by comparing the standard deviation to the average intensity. Some researchers called the ratio as the Absolute Mixing Index (AMI) [52]. The values of 1 and 0 indicate unmixed and fully mixed states, respectively. When the mixing index is non-dimensionalized by comparing the standard deviation to the intensity in non-mixing cross section, Eq. (15) can be used. The difference between Eq. (15) and Eq. (16) is that the last one is expressed based on the integral of the point concentration and intensities of pixels. Table 1. The equations used by the researchers for calculating the mixing index. Equation Reference Equation number 𝑁 (𝐶 − 𝐶̅ )2 1/2 [53] (13) 𝑖

Jo

𝑀𝐼 = [∑

𝑀𝐼 = 1 −

𝑀𝐼 = 1 −

𝑖=1

[∑𝑁 𝑖=1

1/2

(𝐶𝑖 − 𝐶̅ )2 ] 𝑁 𝐶̅

(𝐶𝑖 [∑𝑁 𝑖=1 [∑𝑁 𝑖=1

]

𝑁

(14)

[55]

(15)

1

− 𝐶̅ )2 2 ] 𝑁

(𝐶𝑜 − 𝑁

[54]

1 ̅̅̅ 𝐶𝑜 )2 2

]

𝛿

𝑀𝐼 = 1 −

∫0 |𝐶𝑖 − 𝐶∞ |𝑑𝑦

[56]

(16)

𝛿

∫0 |𝐶𝑜 − 𝐶∞ |𝑑𝑦

There are many researchers who studied the mixing process in active or passive micromixers. Suh and Kang [57] evaluated the advantages and disadvantages of passive micromixers.

-p

ro

of

5.1. Passive micromixers The use of external energy sources leads to an increase in the costs. On the other hand, an enhancement of molecular diffusion and chaotic advection of fluids results in an increase in the mixing quality of passive (static) micromixers. The molecular diffusion and chaotic advection of fluids can be increased by an enhancement in the contact surface between the fluids and a reduction in the mixing path [8]. Passive micromixers are initially divided into two- and threedimensional ones based on their structural dimensions. It should be pointed out that fabrication of two-dimensional passive micromixers using lithography is simpler than three-dimensional ones. Many special structures have been proposed for passive micromixers. Parallel lamination, multi lamination, obstacle (or baffle) based, curved-channel, convergence-divergence based, and unsymmetrical are some features that have been considered in numerical and experimental investigations.

Jo

ur na

lP

re

5.1.1. Lamination based patterns In parallel lamination micromixers, the inlet flows are divided into two (T-type and Y-type mixers) or more sub-streams (multi lamination patterns) [8]. T-type and Y-type micromixers are well known structures in which two streams are injected into two separate channels. The fluid flows are then combined in a straight channel. Since the molecular diffusion causes the fluids to mix in these types of micromixers, two long straight microchannels are required to achieve high mixing efficiency at low Reynolds numbers. Hessel et al. [9] reported that the mixing length Lm = Pe × w for laminar flow, where w is the channel width. To provide fast mixing in this type of micromixers, the researchers generate secondary flow, swirling flow and vortices at highReynolds-number problems. For example, Wong et al. [58] used a diamond step close to the main straight channel of a T-type micromixer fabricated from silicone/glass to disturb the fluid flow for the Reynolds number range of 400-500 (Fig. 2a). Even though the straight microchannel was not roughened, the diamond step caused the flow to be asymmetry due to flow circulation. Gobby et al. [59] evaluated the effect of orientation of two inlets of micro Y-mixers on mixing characteristics and found that the shortest mixing length can be achieved by placing a throttle section in the beginning of the straight channels (Fig. 2b).

ro

of

(a) (b) Fig. 2. (a) Schematic of T-type micromixer fabricated from glass/silicon [58] and (b) methanol mass fraction contours in a venturi-type Y-mixer used for the mixing of oxygen and methanol [59].

Jo

ur na

lP

re

-p

In multi lamination patterns, the fluids enter the mixer with different arrangements compared to Y-type pattern. They include multiple flows [60], hydrodynamic focusing [9, 61], interdigitated mixing [62, 63] and cyclone arrangements [64]. These feed patterns result in a reduction in the mixing distance, leading to an excellent mixing in the millisecond range [8, 9]. Most of multilaminating patterns have three dimensions [65-73], i.e. the streams are joined horizontally and vertically in subsequent stages. Hong et al. [74] introduced a two-dimensional modified Tesla configuration (Fig. 3a) fabricated from cyclic olefin copolymer (COC) using thermal bonding. The increase in the mixing quality of this micromixer is due to chaotic advection due to Coanda effect. Hossain et al. [75] optimized the modified Tesla pattern by considering the ratio of the diffuser gap to the channel width and also the ratio of the curved gap to the channel width for 0.05 < Re < 40. Yang et al. [76] proposed a three-dimensional Tesla structure for realization of the cancer cells (Fig. 3b). Hong et al. [74] and Yang et al. [76] reported that two- and threedimensional Tesla structures work well for Re > 5 and 0.1 < Re < 100, respectively. Other threedimensional designs that have been proposed for multi lamination micromixers include C-shape [77] (Fig. 4a), H-C-shape [78] (Fig. 4b), H-shape [79] (Fig. 4c), L-shape [80] (Fig. 4d) etc. Table 2 compares the lamination based micromixers.

(a)

(b)

(b)

-p

ro

(a)

of

Fig. 3. (a) Schematic of two-dimensional modified Tesla structure [74] and (b) three-dimensional Tesla structure [76].

Table 2. Lamination based micromixers. Re

Focusing / blue dye and pure water Split-join / M chloric acid + methyl orange dissolved in water -

0.1-100

n/r

Mixing efficiency 100%

n/r

91%

Jo

ur na

1-80

Pe

lP

Characteristic/ mixing species Optimized zigzag microchannel / n/r T-shape: simple and serpentine / distilled water and Rhodamine B Hybrid / n/r T-shape / blue dye and a colorless liquid Y-shape / oxygen and methanol Interdigital Interdigital / acetyl chloride and n-butyl amine Interdigital / water blue and pure water Star / dye liquid

re

(c) (d) Fig. 4. Schematic of three-dimensional multi lamination micromixers: (a) C-shape [77], (b) Materials

Year

Reference

Numerical simulation PDMS

2017

[28]

2018

[29]

2018 2004

[30] [58]

2001

[59]

0.001-45 500

n/r 7×105

100% 83%

0.1

150

n/r

PDMS Silicon/Pyrex glass n/r

0.07 n/a

60 n/r

95% n/r

Glass Glass

1999 2004

[60] [61]

2-341

n/r

Glass

2003

[62]

108

6.41×1031.07×106 n/r

n/r

2003

[63]

0.15

200

n/r

Numerical simulation PDMS-Glass

2004

[65]

18

n/r

n/r

Silicon

1996

[66]

oil + air - water + air Split-join / dyed water Split-join / fluorescein dissolved into two different buffers Multi-stream / dyed water Split-join / phenolred and an acid Four-layer / D2O and H2O Three-layer / red and green colored water Crossing manifold / DI water and ethanol

n/r

n/r

Silicon/glass

1999

[67]

0.05

50

97%

Myler

2004

[68]

0.1

14

n/r

Silicon/ PDMS

2004

[69]

0.03-0.66

15-330

n/r

Silicon/glass

1996

[70]

n/r

n/a

90%

Silicon

2011

[71]

< 5.5

n/a

85%

Numerical simulation

2013

[72]

n/r

n/r

90%

Modified 2D Tesla / dyed DI water

n/r

n/r

n/r

Modified 2D Tesla / dyed DI water 3D Tesla / DI water and DI water solution containing fluorescent dye C-shape / water and ethyl alcohol H-C-shape / Blueand yellow-colored food-grade water H-shape / colored water solutions L-shape / deionized water, HCl, and H2O2 Serpentine / dyed water and pure water Serpentine / blue ink and yellow ink T-shape / deionized water

0.05-40

n/r

70.2%

0.1-100

n/r

94%

Numerical simulation Cyclic Olefin Copolymer (COC) Numerical simulation PDMS

n/r

n/r

1-100

n/r

[73]

2004

ro

[74]

2010

[75]

2015

[76]

2000

[77]

93%

Numerical simulation Polycarbonate

2016

[78]

n/r

98%

Plexiglas

2012

[79]

2×103-4×104

n/r

PDMS

2003

[80]

n/r

[81]

> 95%

Numerical simulation PMMA

2018

0.1-100

1×1041.2×106 n/r

2016

[82]

100-500

n/r

~ 65%

PMMA

2019

[83]

1-20

1-120

re 90%

lP

0.08-4.16

-p

2011

ur na

Jo

of

n/r

5.1.2. Obstacle (baffle) based patterns Generation of vortices and chaotic advection by inserting obstacles in the microchannel results in a reduction in the mixing length especially in simple designs such as T- and Y-mixers. Many numerical and experimental investigations have used different configurations of obstacles to evaluate the mixing process. Obstacle on the walls and obstacle in the microchannel are two main classifications. It should be pointed out that these patterns are combined with other configurations such as convergence-divergence and spiral that will be described in sections 5.1.3 and 5.1.4, respectively.

(b)

Jo

(a)

ur na

lP

re

-p

ro

of

First, the micromixers with obstacles in channel are considered. Different layouts for obstacle array were investigated by Wang et al. [84] for a Y-type micromixer (Fig. 5a). They demonstrated that the obstacles can disturb the liquid flows and generate turbulence only for high Reynolds numbers. It was also showed that the most efficient arrangement corresponds to the asymmetric one. Alam et al. [85] used cylindrical obstructions in a curved-channel micromixer for 0.1 < Re < 60 to investigate the mixing index between water and ethanol (Fig. 5b). They compared different shapes of obstruction and demonstrated that mixers with circular and hexagonal cross-section obstacles exhibit the same mixing quality. Lin et al. [86] also used cylindrical obstacles in a microchannel to improve the mixing performance for working at high Reynolds numbers, 200 < Re < 2000. Razavi Bazaz et al. [87] optimized the arrangement of four rectangular obstacles in a T-type micromixer for 0.1 < Re < 60. They used Taguchi method to evaluate the sensitivity of obstacle geometry and revealed that their height is more effective than their width. Bhagat et al. [88] investigated the sensitivity of height and shape of circular, triangular, diamond (smooth) and diamond (stepped) in the mixing process and demonstrated that as the height of obstructions increases, the mixing quality increases. They found that the use of circular obstacles leads to higher mixing efficiency compared to other ones. The obstacle configurations include chevron, check mark, arc, and straight [89], leakage side-channels [90], triangle [91] and staggered grooves [92-96] have been proposed by researchers to obtain short mixing length and high mixing index for various ranges of Reynolds numbers. Sadeghcheri et al. [89] employed round corner rectangular (RCR) and hexagonal (H) chambers and investigated the mixing efficiency using four different obstacles (Fig. 5c) numerically and experimentally. They concluded that the mixing performance of RCR chamber with straight obstacles is higher than that of other geometries. Different staggered grooves have been also evaluated to get higher mixing of fluids in shorter microchannel length. Recently, Hama et al. [93] investigated reversestaggered herringbone micromixer (Fig. 5d) numerically and experimentally for 1 < Re < 100. They demonstrated that mixing efficiency does not depend on the Reynolds number and diffusion coefficient for this range of Reynolds number.

(c) (d) Fig. 5. Schematic of obstacle based micromixers in which they are placed in the channel: (a) cylindrical array [84], (b) cylindrical obstacles in a curved-channel mixer [85], (c) round corner rectangular (RCR) and hexagonal (H) chambers with chevron (CH), check mark (CM), arc (A), and straight (S) obstructions [89] and (d) reverse-staggered herringbone [93].

Jo

(a)

ur na

lP

re

-p

ro

of

It should be mentioned that some of lamination based, obstacle based and divergenceconvergence based micromixers are known as spilt-and-recombine (SAR) or split-joint micromixers [74-76, 89, 97-98]. He et al. [97] experimentally and numerically showed that a Dshaped obstacles lead to the generation of extended vortex and Dean vortices, resulting in the maximum mixing efficiency of 95% for Re = 80. Baheri Islami and Ahmadi [98] combined passive (using rectangular obstacles) and active mixers (using oscillatory inlet velocity) to achieve maximum mixing index of 98% at Re = 0.156. The second category of obstacle based micromixers is those with the obstacles embedded on the walls [17, 99-102]. Karthikeyan et al. [100] used micromixers with triangular and rectangular obstacles on the walls to analyze and optimize the mixing quality of fluids having very low diffusivity (O ~ 10-12 m2/s) (Fig. 6a) using ANOVA approach. Four parameters of height, pitch, width and shape of obstacles were evaluated to find optimum layout for mixing of water and blood. Tsai et al. [101] proposed a planar micromixer with radial obstacles on its wall (Fig. 6b) and demonstrated that Dean vortices, expansion vortices after the obstructions and convergingdiverging flow in the gap between obstacles and mixer wall force the fluids to merge. Milotin et al. [102] analyzed the mixing efficiency of micromixers with bare microtube and quarter and half cross-section obstacles as the orifice for 0.2 < Re < 91 (Fig. 6c). They revealed that the mixing efficiency could reach 100% for the case of quarter cross-section at Re = 91. Recently, the Koch fractal snowflake has been used in obstacle-based micromixers to improve their mixing performance [103-15]. Zhang et al. [103] used staggered Koch fractal-based micromixer to enhance the mixing efficiency (Fig. 6d). The baffles were placed at the top and bottom of a Tmixer, leading to the mixing efficiency of 95% for Re = 0.05 and Re = 100. Chen et al. [105] proposed a Koch fractal mixer with rounding corner pattern (Fig. 6e) and demonstrated that the pressure drop in the micromixer with rounding corners is lower than that with secondary fractal one. Table 3 compares some configurations of obstacles embedded through the channels or on the walls of micromixers.

(c)

(b)

of

Pe

Circular obstacle array in channel Circular and hexagonal obstacles in curved channel Cylindrical obstacle in channel Rectangular obstacle in channel Circular, triangular, diamond (smooth) and diamond (stepped) obstacles in channel Chevron, check mark, arc, and straight obstacles in channel Reverse-staggered herringbone in channel Triangular and rectangular obstacles on the wall Radial obstacles on curved wall Half and quarter cross-section of circular obstacles on the wall

0.13-1333

100-106

0.1-60

n/r

0.2

Materials

Year

Reference

Numerical simulation Numerical simulation

2002

[84]

88%

2014

[85]

200

n/r

Silicon/glass

2003

[86]

n/r

74.5%

2016

[87]

n/r

30%

Numerical simulation PDMS

2007

[88]

0.1-40

n/r

99%

PDMS

2013

[89]

0.01-100

34.4-34400

n/r

PDMS

2018

[93]

n/a

n/r

68%

Numerical simulation

2017

[100]

0.01-100

n/r

93%

PDMS

2011

[101]

0.2-91

n/r

100%

Numerical simulation

2016

[102]

0.1-60 0.02-10

ur na

Jo

Mixing efficiency 55%

lP

Re

re

Table 3. Obstacle based micromixers.

Characteristic

-p

ro

(d) (e) Fig. 6. Schematic of obstacle based micromixers in which they are embedded on the wall: (a) rectangular obstacles [100], (b) radial obstacles on curved wall [101], (c) bare microtube and half and quarter cross-section obstacles [102], (d) staggered Koch fractal [103] and (e) Koch fractal mixer with rounding corner pattern [105].

Koch fractal baffles on the wall Rounded Koch fractal baffles on the wall

0.05-100

n/r

95%

0.1-100

n/r

90%

Numerical simulation Numerical simulation

2019

[103]

2019

[105]

Jo

ur na

lP

re

-p

ro

of

5.1.3. Convergence-divergence patterns These configurations are designed based on the generation of expansion vortices when the crosssectional area increases abruptly. These vortices are created in the horizontal plane, leading to an enhancement in the contact region between the fluids [106-107]. Thus, mixing quality increases. As mentioned in the previous section, convergence-divergence configurations are usually combined with other patterns such as obstacle based, SAR and curved-channel based ones [97, 108-113]. Khosravi Parsa and Hormozi [106] investigated the generation of Dean and expansion vortices in convergent-divergent based micromixers for 0.2 < Re < 75. The convergent-divergent cross section was created by changing the phase shift between the side walls. The maximum mixing efficiency of 90% was obtained for the phase shifts between π/2 and 3π/4. Recently, Mondal et al. [107] compared the mixing performance of micromixers with two configurations, called raccoon and serpentine (Fig. 7a). Their results revealed that the mixing index increases with the wavelength for two types of micromixer, however, the mixing performance of raccoon one is more appropriate than the serpentine one for given Reynolds number and wavelength. Afzal and Kim [108-109] investigated different combinations of SAR and convergencedivergence patterns for 10 < Re < 70 and showed that mixing index is strongly dependent on the ratio of throat-width to the diameter of circular wall of the micromixer (Fig. 7b). Tran-Minh et al. [111] designed a micromixer in which ellipse-like micropillars caused the fluid to converge and diverge and reached the efficiency of 90% for laminar blood mixing (Fig. 7c). Chen and Li [112] employed a topological micromixer to improve the mixing performance by increasing chaotic advection. The mixing efficiency was 95% and 85% for the ranges of (Re < 0.1 and Re > 10) and (0.1 < Re < 10), respectively. Asymmetric structures of the microchannel are another category of divergence-convergence micromixers. Rhombic micromixers proposed by Chung and Shih [113] and Hossain and Kim [114] are two examples of asymmetric passive micromixers. Chung and Shih [113] revealed that combination effects of focusing/diverging, recirculation and Dean vortices lead to very high mixing efficiency. It was observed that Dean vortices and recirculation are strongly depend on the size of the gap between the baffle and channel wall. Their micromixer was modified by Hossain and Kim [114]. They proposed two-split and three-split rhombic configurations and reached the mixing efficiency of 86% for three-split one at Re = 60. Recently, Raza and Kim [115] investigated the mixing performance in unbalanced SAR micromixers for 0.1 < Re < 120 (Fig. 7d). They reported that the mixing efficiency reaches 86% and 95% for Re > 20 and Re > 50, respectively. Table 4 compares some convergence-divergence based micromixers.

(a)

(b)

Re

Pe

Sinusoidal side walls Raccoon and serpentine SAR and convergencedivergence SAR and convergencedivergence Ellipse-like micropillars

0.2-75 0.1-100

n/r n/r

Mixing efficiency 90% ~ 100%

10-70

n/r

95%

10-70

n/r

95%

0.238-2.38

238-2381

90%

Re < 0.1 and Re > 10

n/r

0.1-10 > 20 Re > 20 Re > 50

n/r n/r

ur na

Rhombic Unbalanced SAR

Year

Reference

2014 2019

[106] [107]

2012

[108]

Numerical simulation

2014

[109]

Numerical simulation

2014

[111]

Numerical simulation

2016

[112]

PDMS PDMS

2007 2019

[113] [115]

Plexiglas Numerical simulation Numerical simulation

re 85%

lP

Topological

Materials

-p

Characteristic

ro

Table 4. Convergence-divergence based micromixers.

95% 84% 86% 95%

of

(c) (d) Fig. 7. Schematic of convergence-divergence based micromixers: (a) serpentine [103], (b) SAR and convergence-divergence [109], (c) ellipse-like micropillars [111], and (d) unbalanced SAR [115].

Jo

5.1.4. Curved-channel patterns The main characteristic of curved micromixers is that they perform well at high Reynolds numbers. The Dean number is a dimensionless parameter that describes the fluid flow in this type of micromixer [9]. It was revealed that for De > 150 and De < 150, the secondary flow consists of two and four vortices, respectively [116]. It is obvious that several loops are required to get high mixing efficiency. Hence, creative designs have been proposed to enhance the mixing performance of curved-channel mixers using few numbers of loops. In addition, as pointed out before, this pattern is combined with other configurations such as obstacle-based and convergence-divergence ones [109, 115]. Schönfeld and Hardt [117] proposed a threedimensional micromixer build up from two curved square channel relying on various types of Dean vortices. Jiang et al. [118] found that the mixing process depends on the value of Dean number that is larger or smaller than 140. They proposed a planer meander mixer and stated that chaotic mixing is induced without multistep or three-dimensional structure (Fig. 8a). Spiral microchannels with several mixing sections that are joined by a central S-section were proposed by Sudarsan and Ugaz [119] (Fig. 8b). They considered five spiral configurations for 0.02 < Re <

Jo

(d)

(b)

ur na

(a)

lP

re

-p

ro

of

18.6 and reported that transverse Dean flows lead to the mixing efficiency > 90%. Santana et al. [120] used this design to mix Jatropha curcas oil and ethanol and showed that the mixing performance of spiral micromixer is much higher than that of T-type one. Mehrdel et al. [121] modified this design using expansion and contraction parts (Fig. 8c) and reached the mixing efficiency of 85% and 98.5% for one and three loops with 10% expansion, respectively, at Re = 1. Inspired by spiral configurations, several designs have been proposed to investigate the effect of Dean vortices on mixing performance of micromixers [122-130]. Scherr et al. [123] proposed a logarithmic-spiral based micromixer experimentally using PDMS (Fig. 8d). They achieved mixing efficiency of 86% for Re = 67 and demonstrated that logarithmic curvature leads to the generation of three-dimensional Dean vortices due to variable cross-sectional area. A micromixer composed of staggered three-quarter ring-shaped channels and a semi-circular channel was designed by Sheu et al. [124] (Fig. 8e). The authors concluded that the secondary flows are negligible for Re < 5 and are considerable at Re = 50. Double layers of spiral channel were used by Yang et al. [125] (Fig. 8f), Rafiei et al. [126] (Fig. 8g) and Clark et al. [127] (Fig. 8h) to design three-dimensional micromixers. Yang et al. [125] demonstrated that mixing index increases with the height of channel and using cylindrical geometry instead of cubical one. Rafiei et al. [126] developed a fine-threaded lemniscated-shaped mixer for 1 < Re < 1000 and reached the mixing efficiency of > 90%. Non-rectangular cross-sections were employed by Clark et al. [127] to investigate their effects on the Dean flows in a spiral micromixer. They showed that full mixing is obtained at Re = 20 in their proposed mixers, while it can be achieved at Re = 100 in rectangular cross-section mixer. Table 5 compares curved-channel micromixers.

(c)

(e)

(f) (g) (h) Fig. 8. Schematic of curved-channel micromixers: (a) planer meander mixer [118], (b) double spiral [119], (c) double spiral with expansion and contraction [121], (d) logarithmic spiral [123],

(e) tapered curved [124], (f) two layers of spiral channels overlapped together [125], (g) finethreaded lemniscated-shaped [126], and (h) non-rectangular cross-section [127]. Table 5. Curved-channel micromixers. Characteristic

Re

Pe

3D curved square channel planer curved channel Double spiral Double spiral with expansion and contraction Spiral and concentric circular Logarithmic spiral Tapered curved Two layers of spiral channels overlapped together Fine-threaded lemniscated-shaped Non-rectangular cross-section Spiral, interlockingsemicircle, Ω channel Double helical channel Square, semi-circle, trapezoid cross sections

2-2012

1-900

Mixing efficiency n/r

> 313 < 313 0.02-18.6

n/r

Year

Reference

2004

[117]

n/r

Numerical simulation PMMA

2004

[118]

n/r

> 90%

SEBS

2006

0.1-10

439-1836

98.5%

PDMS

2018

[119] [121]

0.6

n/r

~ 40%

Aluminum

1-70 1-100

n/r n/r

86% 88%

PDMS PDMS

8-40

n/r

90%

Glass

1-1000

n/r

> 90% ~ 100%

0.01-50

n/r

~ 100%

20-277

n/r

99%

lP

0.003-30

n/r

2012 2012

[123] [124]

2012

[125]

PDMS

2017

[126]

Numerical simulation PDMS

2018

[127]

2015

[128]

Numerical simulation

2015

[129]

2017

[130]

ro

[122]

-p

n/r

2012

re

1-100

> 90%

of

Materials

PDMS

ur na

5.2. Active micromixers External energy sources are used to enhance the mixing quality by increasing the contact area between the fluids, disturbing them or inducing the chaotic advection. Pressure filed [131-138], acoustic filed [139-152], magnetic field [153-171], electric field [172-192], thermal field [193205], etc. are types of external energy sources.

Jo

5.2.1. Pressure-driven micromixers The earliest pressure-driven micromixer proposed by Deshmukh et al. [131] was a T-type micromixer. They used an integrated planar micropump to induce alternative fluid perturbation by driving and stopping the flow in the channel. In other words, the step function was used to generate pulsatile flow; hence many pulses were required to mix the fluids. Velocity pulsing has been also used to disturb the fluids and increase their contact area [132-135]. Niu and Lee [132] designed a pressure-driven micromixer according to fluid stretching and folding concepts (Fig. 9a). They used Lyapunov exponent to describe the chaotic behavior and optimize their proposed micromixer. Wu et al. [136] investigated the effect of oscillatory/pulsatile flow on the mixing performance of a micromixer (Fig. 9b). They demonstrated that stretching and folding of the fluids increase due to oscillatory flow and the mixing index reaches 97% after four mixing units for total flow rate of 44 ml/min and fluid viscosity of 8 mPa s. Li and Kim [137] used constant

(b)

lP

re

-p

(a)

ro

of

input of water head pressure to create pulsatile pressure in the mixer unit (Fig. 9c). Their proposed micromixer exhibited the mixing efficiency of about 90% for a range of flow rates up to 20 μl/min and the frequency range of 14-20 Hz. Recently, Zhang et al. [138] investigated the time pulsed mixing for Newtonian and viscoelastic fluids in a T-mixer (Fig. 9d). They demonstrated that as the time pulsing increases, the mixing index of Newtonian fluids decreases and increases for 0.002 < Re < 0.01 and 0.1 < Re < 0.2, respectively. They also revealed that the mixing of viscoelastic fluids is independent of the time pulsing for Weissenberg numbers Wi < 20, however, it reaches a high value for Wi = 50. Table 6 compares some pressure-driven micromixers.

ur na

(c) (d) Fig. 9. Schematic of pressure-driven micromixers: (a) one pair of side channels [132], (b) oscillatory/pulsatile flow in a micromixer [136], (c) Oscillator unit in a mixer [137], and (d) time-pulsed flow in a micromixer [138]. Table 6. Pressure-driven micromixers. Characteristic

Re

Pulsatile flow

Year

Reference

2000

[131]

Multiple side channels Electric circuit methods Planar mixing channel

n/r

n/r

SOI and quartz wafers

Modelling

2003

[132]

0.17

n/r

2012

[133]

83-250

90%

Analytical solution n/r

2013

[135]

n/r

90%

PDMS

2017

[136]

Oscillator and divergent chambers

n/r

97%

PMMA

2018

[137]

Jo

Materials

2.4

Mixing efficiency n/r

Pulsatile micromixer

Time-pulsed flow

0.002-0.1

Newtonian: ~ 53% Viscoelastic: 82%

PDMS

2019

[138]

Jo

ur na

lP

re

-p

ro

of

5.2.2. Acoustic field driven micromixers Acoustically-induced microstreams have been used in micromixers as the air bubbles in a liquid are energized due to an acoustic field [139]. Moroney et al. [140] described the application of an acoustic actuator to stir liquids in a flexible-plate-wave (FPW) system. Liu et al. [139] used a piezoelectric disk to energize the bubbles at a frequency of 5 kHz. The use of higher frequencies (> 50 Hz) leads to an increase in the temperature of fluids that is harmful for biological samples [8, 141]. In bubble-based acoustic micromixers, single [139] or many bubbles [142] can be generated due to different causes. Ahmed et al. [142] generated an air bubble in a horse-shoe pattern in a micromixer using acoustic waves (Fig. 10a). The excited trapped air bubble disturbs the laminar flows in the channel, resulting in their excellent and so fast mixing. They characterized the mixing time as t = dmix/vavg, where dmix and vavg are the distance between unmixed and full mixed regions and the average fluid velocity, respectively. It was concluded that as the number of air bubbles increases, the mixing time decreases considerably [139]. Wang et al. [143] investigated the influence of applied frequency (0.5-10 kHz) on mixing performance of a micromixer (Fig. 10b) and concluded that low (0.5 kHz) and high frequencies (10 kHz) do not affect the mixing index. However, the mixing efficiency is strongly dependent on applied frequencies between 1.0 to 5.0 kHz. This frequency range resulted in the generation of single or multiple bubbles, leading to disturbance in the local flow field. They demonstrated that the mixing efficiency increases significantly by generation of bubbles in the frequency range of 1.0 to 5.0 kHz. Bubbles were not occurred in the microchannel outside this range of actuation frequency. Orbay et al. [144] introduced a bubble-based acoustic micromixer with three inlets in which nitrogen injected into the center inlet to form bubbles in the mixer. Their proposed micromixer worked well for high viscous liquids at low Reynolds numbers. The other types of acoustic micromixers involve ultrasonic transducers [145-146], thin film piezoelectric devices [147-148] and surface acoustic wave ones [149-150]. Yang et al. [146] introduced a micromixer made up of glass to achieve a homogeneous mixture using ultrasonic vibration (Fig. 10c). The ultrasonic vibration was generated by a piezoelectric lead-zirconatetitanate (PZT) ceramic. Luong et al. [151] proposed a surface-acoustic-wave-driven micromixer using parallel and focusing interdigitated electrodes (Fig. 10d). It was showed that the mixing performance depends on applied voltage. It was reported that the focusing type leads to higher mixing index compared to parallel one. Unlike many investigators who used planar piezoelectric transducers with flat surfaces, Lim et al. [152] proposed concave and convex surface structures. They revealed that convex geometry leads to higher mixing quality than flat and concave ones. Table 7 compares the characteristics of some acoustic field driven micromixers.

of

(b)

re

-p

ro

(a)

lP

(c) (d) Fig. 10. Schematic of acoustic filed driven micromixers: (a) bubble-based acoustic micromixer [142], (b) bubble-based acoustic micromixer [143], (c) ultrasonic transducers [146], and (d) parallel interdigitated electrodes design [151].

ur na

Table 7. Acoustic field driven micromixers. Re

Bubble vibration Single-bubbled based Multi-bubbled based Multi-bubbled based Ultrasonic vibration Surface-acousticwave-driven Piezoelectric transducer with curved surface

Jo

Characteristic

Mixing efficiency 91% n/r n/r 93% n/r 88%

Materials

Year

Reference

n/r n/r n/r ~ 0.01 60 3.1-15.4

Frequency (kHz) 5 70-100 1-5 1-5 0-100 1300

PZT PDMS PMMA PDMS Glass PDMS

2002 2009 2012 2016 2001 2010

[139] [142] [143] [144] [146] [151]

<< 1

220-260

45%

n/r

2019

[152]

5.2.3. Magnetic-field driven micromixers Micromixers are magnetically actuated by permanent magnet [153-158], electromagnet [159164], microstirrer [165-168] and integrated electrodes [169-170]. Chen and Zhang [171] gave a review on magnetic field driven micromixers. As a part of present review article, we considered the magnetically driven micromixers include articles published in recent years. Ballard et al. [153] used a permanent magnet rotating over a micromixer with magnetic microbeads orbiting

Jo

ur na

lP

re

-p

ro

of

around NiFe discs placed on the floor (Fig. 11a). Nouri et al. [155] used permanent magnet to investigate the mixing process of deionized water and Fe3O4 ferrofluid in a rectangular crosssectional Y-mixer (Fig. 11b). Hejazian and Nguyen [156] employed a permanent magnet induced non-uniform magnetic field in a straight microchannel to evaluate the mixing of diluted ferrofluid and a non-magnetic flow (Fig. 11c). Kumar et al. [158] developed a numerical model to simulate mass transfer enhancement due to a non-uniform magnetic field. They demonstrated that mass transfer increases with magnetic field strength and size of magnetic particles. Fu et al. [159] studied the mixing of ferrofluid and DI water in a micromixer which used an electromagnet driven by a DC electric field (Fig. 11d) numerically and experimentally. The permanent magnet was placed parallel to the microchannel. Ergin et al. [160] used microPIV technique to analyze transient flow fields during the mixing process. A new magnetic micromixer based on a flexible artificial cilium made up of Fe doped PDMS was presented by Liu et al. [161]. The mixing efficiency of 80% was obtained using the cilia micromixer under a magnetic strength of 200 G. Four electromagnet placed opposite to each other were used in a micromixer to mix Rhodamine dye and DI water by Soraj et al. [162] (Fig. 11e). They determined a critical actuation frequency, where the mixing degree decreases with the actuation frequency for the frequencies greater than critical one. Boroun and Larachi [163] investigated the mixing performance of a T-mixer under static, oscillating and rotating magnetic fields for 10 < Re < 200. It was concluded that the mixing index increases with the magnetic field intensity. They reported that rotating magnetic field leads to better mixing performance compared to static and oscillatory ones. Kang et al. [165] used magnetic particles as magnetic chains to induce the chaotic mixing under a rotating magnetic field. Their results were presented based on Mason number that is the ratio of magnetic to viscous forces. Symmetric and asymmetric motion of artificial cilia was investigated by Chen et al. [166] for enhancing fluid mixing. They demonstrated that the mixing due to the asymmetric motion is 1.34 times faster than that due to the symmetric one. Veldurthi et al. [167] placed a microrotor in a chamber to obtain maximum mixing quality. The magnetic actuator was made of magnetic nanoparticles dispersed PDMS and the micromixer was fabricated with PDMS (Fig. 11f). They achieved the mixing efficiency of 90%. Owen et al. [168] used a regular array of magnetic microbeads to increase the fluid mixing in a channel. They reported that longer array of beads leads to higher mixing efficiency. Kang and Choi [169] designed and fabricated a micropump for mixing at low Reynolds numbers. They revealed that different lengths of electrodes lead to better mixing performance than the electrodes with the same lengths. The micromixer worked based on the Lorentz force and the moving force applied on charged particles. Jeon et al. [170] evaluated the shape and arrangement of electrodes and the applied voltage on the mixing of a reagent and phosphate buffered solution (PBS). Table 8 compares some magnetic field driven micromixers.

(b)

(c)

(d)

ur na

lP

re

-p

ro

of

(a)

(e) (f) Fig. 11. Schematic of magnetic field driven micromixers: (a) rotating permanent magnet [153], (b) Permanent parallel magnet [155], (c) permanent parallel magnet [156], (d) electromagnet driven by a DC electric field [159], (e) four electromagnet placed opposite to each other [162], (f) cylindrical chamber with microrotor [166].

Jo

Table 8. Magnetic field driven micromixers. Characteristic

Permanent magnet rotating over a micromixer with magnetic microbeads Permanent parallel magnet Permanent parallel magnet

Re

<< 1

Magnetic field strength (G) n/r

Mixing efficiency

Materials

Year

Reference

70%

PDMS

2016

[153]

n/r

1280-3000

90%

Plexiglas

2017

[155]

n/r

1750-2500

88%

PDMS

2017

[156]

> 95%

2200

80%

Electromagnet

n/r

4200 and 6000

10-200

0-90 kA/m

Static, oscillating and rotating electromagnet Electromagnet

2010

[159]

2016

[161]

n/r

Fe doped PDMS Polystyrene

2016

[162]

~ 53%

Glass

2017

[163]

2019

[164]

2014

[166]

2015

[167]

2016

[168]

2011 2017

[169] [170]

5-50

n/r

96%

4.64×10-3

n/r

100%

Numerical simulation PDMS

0-40

n/r

90%

PDMS

n/r

n/r

~ 72%

NiFe

n/r

27.8% 100%

PDMS Numerical simulation

n/r n/r

n/r

-p

Asymmetric actuation of artificial cilia Cylindrical chamber with microrotor Array of rotating magnetic microbeads Integrated electrodes Integrated electrodes

n/r

of

200

Electromagnet

0.004 and 0.02 n/r

ro

Electromagnet

Jo

ur na

lP

re

5.2.4. Electric-field driven micromixers Electrohydrodynamic (EHD) disturbance [132, 172-174] and electrokinetic (EKI) instability [175-192] are used in electrical field driven micromixers. Alternating current (AC) and direct current (DC) electric fields are used to charge the fluids in EHD instability-based micromixers. The charged fluids disturb the interface, leading to an enhancement in the mixing performance of micromixers. EI Moctar et al. [172] proposed a T-type micromixer in which an electric field that was perpendicular to the interface was applied to the fluids, leading to the creation of a secondary flow. They used AC and DC electric fields at Re = 0.0174 and observed that a reasonable mixing can be achieved in less than 0.1 s. A Y-mixer with an array of inclined electrodes on the bottom of the main channel was considered by Huang et al. [173] (Fig. 12a). The authors observed that four vortices are generated above each electrode pair so that two strong vortices remain for a long time and two weak ones cancelled out. EKI instability occurs when a liquid or particles move towards a charged surface. EKI mixing methods include electroosmosis [175-186], electrophoresis [187-189] and dielectrophoresis [190-192]. Zhang et al. [175] numerically and analytically studied mixing of electroosmosis flow in microchannles with heterogeneous zeta potential. They demonstrated that symmetrical secondary flows and asymmetrical rolls are generated due to heterogeneous zeta potential, resulting in an improvement in the mixing rate of fluids. Ebrahimi et al. [176] considered a Ttype microchannel to evaluate the effect of non-uniform DC electric field on mixing and heat transfer characteristics for four ribbed channel configurations. They gave interesting results about the mixing rate of fluids: if the Schmidt number is less than a critical one, the mixing index decreases by applying the electric field. Vertical flow enhancement was also observed by Bhattacharyya and Bera [177] for an electroosmosis-pressure driven microchannel with a rectangular block due to the difference between the surface potential of block and the channel wall. Ahmadian Yazdi et al. [179] investigated the effect of ionic size on diffusion in a Ymicromixer at high zeta potentials. They revealed that the mixing length is a decreasing function of ionic concentration for high zeta potentials. The mechanism of chaotic mixing was studied by Shamloo et al. [180] using a charged electrode array with AC electric field. Different

Jo

ur na

lP

re

-p

ro

of

configurations of one-ring, two-ring and diamond types were considered and it was reported that the diamond type has maximum index of 99.8% in comparison one-ring and two-ring ones. Matsubara and Narumi [181] proposed an electroosmotic micromixer with a staggered array of electrodes with AC signal for 0.005 < Re < 1.0. They showed that a core vortex is generated between the electrode pairs and two vortices are formed before and after them for the case of oscillating electroosmotic flow. Kazemi et al. [182] studied the mixing performance of an electroosmotic micromixer by placing an electrical conductive flap at the entrance of the main channel. Asymmetrical planar floating-electrodes were mounted in a T-mixer by Zhang et al. [185] to induce asymmetrical vortices. They obtained the mixing quality of 94.7% for a frequency of 400 Hz with the mixing length of 3.2 mm. Recently, Usefian and Bayareh [186] proposed a novel electroosmotic micromixer (Fig. 12b) in the presence of AC and DC electric fields. Their results revealed that the generated vortices due to DC electric field are stronger than those formed by AC one. It was showed that the mixing index increases with the applied voltage of AC and DC electric fields. Electrophoresis is defined as the motion of conductive or non-conductive particles due to an external electric field that is applied to a solution of an electrolyte. It should be pointed out that the use of conductive particles leads to higher mixing index due to convection. Daghighi and Li [187] proposed a new electrophoresis micromixer including a cylindrical chamber connected to straight channels. A circular conductive particle was placed in the chamber (Fig. 12c). They observed that the external electric field induces vortices around the particle, leading to an enhancement in the mixing rate of the solution. The optimum angle of 45° was found for applying the external electric field relative to the channel direction. Daghighi et al. [188] experimentally observed the vortices generated around conductive and non-conductive particles due to the applied electric field. The generation of vortices and flow circulations around a conductive particle was studied by Kazemi et al. [189] during mixing process in a micromixer which consisted of a rectangular chamber connected to microchannels. They demonstrated that at a specific zeta potential, as the electric field increases, the outlet mass flow rate increases, leading to a reduction in the mixing quality. Dielectrophoresis is defined as the motion of neutrally particles due to AC electric field. It leads to the formation of asymmetric polarization of the particles. A dipole moment is formed on the particles, resulting in a force causes the particles to move away or towards the electrodes. The stretching and folding phenomena occur due to the accumulation of particles in a quasi novelocity region, leading to chaotic motion and an increase in the mixing index. Deval et al. [191] presented a dielectrophoretic micromixer to induce the chaotic motion of particles and showed that the mixing time decreases dramatically. Similar to electrophoretic micromixers, conductive particles can be used in dielectrophoretic ones to improve their mixing performance due to the convection. Kim et al. [192] proposed a new micro/nano mixer based on dielectrophoresis technique (Fig. 12d). It was demonstrated that as the channel depth decreases, the mixing quality increases. However, the channel depth must be greater than about 20 micrometers. Table 9 summarizes the characteristics of some electric-field driven micromixers.

(b)

ro

of

(a)

Table 9. Electric-field driven micromixers. Re

EHD (perpendicular electrode array) EHD (inclined electrode array) Electroosmosispressure driven Electroosmosis mixing at high zeta potentials Electroosmosis mixing in a diamond type mixer Electroosmotic micromixer with a staggered array of electrodes Electroosmotic micromixer with a throat Electroosmotic micromixer with rotating inner obstacle

0.0174

Materials

Year

Reference

0.5-100

Mixing efficiency ~ 81%

Lexan

2003

[172]

1000

94%

n/r

2011

[173]

Numerical simulation Numerical simulation

2014

[178]

2015

[179]

Jo

ur na

n/r

Frequency (Hz)

lP

Characteristic

re

-p

(c) (d) Fig. 12. Schematic of electric-field driven micromixers: (a) EHD based micromixer with an array of inclined electrodes [173], (b) an electroosmotic micromixer with two electrodes [186], (c) electrophoretic micromixer with a conductive particle [187], and (d) dielectrophoretic micro/nano mixer [192].

10

n/r

71%

n/r

n/r

99.5%

n/r

2-16

99.8%

Numerical simulation

2016

[180]

0.005-1.0

0.2-2 (dimensionless frequency)

~ 98%

Numerical simulation

2016

[181]

n/r

n/r

51.5%

2017

[182]

n/r

n/r

~ 98%

2019

[183]

Numerical simulation Numerical simulation

1-10000

n/r

Transparent acrylic

2017

[184]

n/r

400

94.7%

Glass

2018

[185]

n/r

0.5-4

~ 96%

PDMS

2019

[186]

n/r

n/r

100%

Numerical simulation

2013

[187]

n/r

n/r

99.5%

2017

[189]

0.02

n/r

n/r

Numerical simulation Si-SU8-glass

2002

[191]

n/r

n/r

n/r

Silicon

2008

[192]

of

<1

ro

Turbulent-like electroosmotic mixer Planar floatingelectrodes in a Tmixer Electroosmotic micromixer with two electrodes in a chamber Electrophoretic micromixer with cylindrical chamber Electrophoretic micromixer with rectangular chamber Dielectrophoretic micromixer Dielectrophoretic micromixer

Jo

ur na

lP

re

-p

5.2.5. Thermal-field driven micromixers Thermal energy can be used to improve mixing performance of micromixers by increasing the diffusion coefficient [193], utilizing thermal bubbles [194-196] or using electrothermal effects [197-202]. Huang and Tsou [195] used microvalve and micropump to implement a thermal bubble based micromixer (Fig. 13a). It was revealed that larger thermal bubbles lead to higher mixing capacity. Tan [196] simulated the mixing of a dye solution and pure water in a Y-mixer with an embedded microheater (Fig. 13b). Thermal bubbles play the role of a micropump and drive the streams. The author revealed that if the microheater embedded asymmetrically, asymmetric vortex and secondary flow are generated, leading to an enhancement in the mixing rate. Maximum mixing index of 95.6% was obtained when the microheater was placed in the channel inlet. Zhang et al. [199] employed AC electrothermal flow to increase the mixing of two laminar streams. Two asymmetric planar electrodes were mounted along the microchannel and a thin film resistive placed below the electrodes. They showed that the temperature gradient created by external heating leads to stretching and folding of fluid flow, resulting in higher mixing quality. Electrothermal actuated micromixers were also investigated by Kunti et al. [200201]. Kunti et al. [200] used the characteristics of passive micromixers by using grooved floor and the advantages of electrothermal micromixers by mounting pairs of asymmetric electrodes on the walls. They achieved the mixing efficiency of 97.25% for the flow rate of 29.9 μl/s. Meng et al. [202] used AC electrothermal advantages to design a micromixer for biomicrofluidic applications. The micromixer consisted of two straight channels and a cylindrical chamber. The streams were actuated in the chamber due to four arc electrodes (Fig. 13c), leading to the mixing index of 100%. Table 10 summarizes the characteristics of some thermal-field driven micromixers.

of

(b)

-p

ro

(a)

lP

re

(c) Fig. 13. Schematic of thermal-field driven micromixers: (a) thermal-bubble actuated micromixer [195], (b) Y-mixer with an embedded microheater [197], and (c) AC electrothermal micromixer with four arc electrodes [202]. Table 10. Thermal-field driven micromixers. Characteristic

Mixing efficiency n/r

Materials

Year

Reference

SOI

2014

[195]

0.214

95.6%

2019

[196]

n/r

83.6%

2016

[199]

29.9

97.25%

2017

[200]

Inlet velocity 40 μm/s

Numerical simulation Numerical simulation Numerical simulation

~ 100%

PDMS

2018

[202]

Jo

ur na

Thermal-bubble actuated micromixer Electrothermal micromixer Electrothermal micromixer Electrothermal micromixer Electrothermal micromixer

Flow rate (μl/s) 4.5

6. Discussion Characteristic nondimensional numbers such as Reynolds number, Peclet number, Strouhal number, Fourier number and Knudsen number determine the operation conditions of passive and active micromixers. Since viscous effects are dominant in microscale, mixing occurs due to molecular-diffusion mechanism. Hence, passive micromixers need long channel length or complex geometry, leading to high pressure drop along the mixer. Thus, the ratio of mixing index to pressure drop (MI/∆p) should be calculated. It is obvious that a fast flow (high-

ur na

lP

re

-p

ro

of

Reynolds-number flow) has a short residence time (tr), hence higher disturbance frequency (for active micromixers) or longer channel length (or shorter characteristic length) (for passive micromixers) are required. As a result, Strouhal number and Fourier number characterize the mixing process in active and passive micromixers, respectively. Mixing of viscoelastic fluids in microchannels is affected by viscous and elastic effects. It was revealed that sharper and smaller geometries can be used to increase the chaotic flow instability, leading to higher mixing quality [203]. The dimensionless Deborah number that is defined as the ratio of elastic and viscous forces is employed to characterize the mixing of viscoelastic fluid streams. As the Deborah number increases, the flow instability at the interface is suppressed by the elastic force. Therefore, the geometry and external actuators play a crucial role to improve the mixing efficiency of viscoelastic fluids. The constitutive models such as Oldroyd-B, Phan-Thien-Tanner (PTT), Giesekus, etc. can be used to describe the flow of viscoelastic fluids [204]. In numerical simulations, the quantification of the mixing index is strongly depends on the numerical diffusion error. Types of grid and discretization method have significant influences on the generation of false diffusion in the numerical simulations. The presentation of reports about the numerical diffusion error is required to obtain valid mixing index especially for threedimensional micromixers. Time-dependent approach is another important issue in the numerical study of micromixers. Most of numerical simulations have not considered time-dependent scheme to evaluate the mixing performance of the micromixers. Since the mixing time is an essential characteristic parameter of micromixers, it is required to perform time-dependent simulations especially for the case of validation with the experimental results. Many fabrication techniques with different materials have been used to make micromixers. Nowadays, soft lithography using PDMS is widely used in academic microfluidic labs to evaluate the mixing process or particle separation for biomedical devices. The PDMS can be combined with carbon nanotubes or solid nanoparticles to exhibit different thermal and electrical conductivities. In addition, hydrophobic-hydrophilic properties can be controlled by dispersing nanoparticles in the PDMS during the molding process. 3D printing technique is inexpensive for fabricating micromixers in comparison with the molding method. Since the fabrication process is controlled by machine, this technology is cheaper and faster than lithography, thus it can be commercialized. However, the resolutions of PDMS products are higher than those of 3D printing ones [205]. In addition, the fabrication of multi-material chips is still a challenge for 3D printing technology.

Jo

7. Conclusions Passive and active micromixers have been attracted many researchers in recent years due to their applications in many situations such as chemical, medical and biochemical ones. Passive micromixers have been widely used due to their simple fabrication. To enhance their mixing performance, three-dimensional complex designs have been proposed. The researchers combined different configurations of passive micromixers to improve their mixing performance. The use of active micromixers leads to higher mixing index for wider range of Reynolds numbers. Experimentally, electric-field driven and thermal-field driven micromixers have not been considered in comparison with the micromixers use pressure, magnetic and acoustic fields. Conflict of Interest

Jo

ur na

lP

re

-p

ro

of

The authors confirm that: This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue. The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript

Jo

ur na

lP

re

-p

ro

of

References [1] Dietzel A (2016) A brief introduction to microfluidics, Microsystems for Phamatechnology, Springer. [2] Nguyen N-T, Wereley ST (2006) Fundamentals and applications of microfluidics, Artech Print on Demand. [3] Nguyen N-T, Hejazian M, Ooi C, Kashaninejad N (2017) Recent advances and future perspectives on microfluidic liquid handling. Micromachines 8(6): 186. Doi:10.3390/mi8060186 [4] Samiei E, Tabrizian M, Hoorfar M (2016) A review of digital microfluidics as portable platforms for lab-on a-chip applications. Lab Chip 16: 2376-2396. [5] Lion N, Rohner TC, Dayon L, Arnaud IL, Damoc E, Youhnovski N, Wu Z-Y, Roussel C, Josserand J, Jensen H, Rossier JS, Przybylski M, Girault HH (2003) Microfluidic systems in proteomics. Electrophoresis 24(21): 3533–3562. [6] Charmet J, Arosio P, Knowles TPJ (2018) Microfluidics for protein biophysics. J Mol Biol 430: 565–580. [7] Whitesides GM (2006) The origins and the future of microfluidics, Nature 442: 368-373. [8] Nguyen N-T, Wu Z (2005) Micromixers-A review, J. Micromech. Microeng 15: R1-R16. [9] Hessel V, Lowe H, Schonfeld F (2005) Micromixers-A review on passive and active mixing principles. Chem. Eng. Sci. 60: 2479-2501. [10] Mansour EA, Mingxing YE, Yundong WANG, Youyuan DAIA (2008) A state-of-the-art review of mixing in microfluidic mixers. J. Chem. Eng. 16: 503-516. [11] Lee CY, Chang CL, Wang YN, Fu LM (2011) Microfluidic mixing: A review. Int. J. Mol. Sci. 12: 3263-3287. [12] Lee CY, Wang WT, Fu LM (2016) Passive mixers in microfluidic systems: A review. Chem. Eng. Sci. 288: 146-160. [13] Chen X, Zhang L (2017) A review on micromixers actuated with magnetic nanomaterials. Microchim Acta 184: 3639-3649. [14] Cai G, Xue L, Zhang H, Lin J (2017) A review on micromixers, Micromachines, 8. [15] Fox R, McDonald AT (1999) Introduction to fluid mechanics, New York, Wiley. [16] Green J, Holdo AE, Khan A (2007) A reviewe of passive and active mixing systems in microfluidic devices. International Journal of Multiphysics 1(1): 1-32. [17] Hussain M, Poschel T, Muller P (2019) Mixing of rarefied gases in T-shape microscope. Applied Thermal Engineering 146: 39-44. [18] Jiang F, Drese KS, Hardt S, Küpper M, Schönfeld F (2004) Helical flows and chaotic mixing in curved micro channels. AIChE Journal 50(9): 2297–2305. [19] Kamali R, Mansoorifar A, Dehghan Manshadi MK (2014) Effect of baffle geometry on mixing performance in the passive micromixers. IJST: Transactional of Mechanical Engineering 38: 351-360. [20] Yoshimura M, Shimoyama K, Misaka T, Obayashi S (2019) Optimization of passive grooved micromixers based on genetic algorithm and graph theory. Microfluidics and Nanofluidics 23: 30. [21] Naresh V, Bodas D, Sunil C, Tejashree B (2019) Geometrically similar rectangular passive micromixers and the scaling validity on mixing efficiency and pressure drops. Journal of Mechanical Engineering 69: 69-84.

Jo

ur na

lP

re

-p

ro

of

[22] Minakov AV, Rudyak VY, Gavrilov AA, Dekterev AA (2010) On optimization of mixing process of liquids in microchannels. Journal of Serbian Federal University. Mathematics and Physics 3: 146-156. [23] Maxwell JC (1879) On stresses in rarified gases arising from inequalities of temperature. Philosophical Transactions of the Royal Society Part 1, 170: 231–256. [24] Smoluchowski von M (1898) Über Wärmeleitung in verdünnten Gasen. Annalen der Physik und Chemie 64: 101–130. [25] M. Le, I. Hassan, DSMC Simulation of gas mixing in T-shape micromixer, Appl. Therm. Eng. 27 (2007) 2370-2377 [26] Bhagat A, Gijare H, Dongari N (2019) Modeling of Knudsen layer effects in the micro-scale backward-facing step in the slip flow regime. Micromachines 10: 118. [27] Reyhanian M, Croizet C, Gatignol R (2013) Numerical analysis of the mixing of two gases in a microchannel. Mechanics & Industry, EDP Sciences 14(6): 453-460. [28] Chen X, Li T (2017) A novel passive micromixer designed by applying an optimization algorithm to the zigzag microchannel. Chemical Engineering Journal 313(1): 1406-1414. [29] Ansari MA, Kim K-Y, Kim SM (2018) Numerical and experimental study on mixing performances of simple and vortex micro T-mixers. Micromachines 9: 204. [30] Razavi Bazaz R, Abouei Mehrizi A, Ghorbani S, Vasilescu S, Asadnia M, Ebrahimi Warkiani M (2018) A hybrid micromixer with planar mixing units. ASC Advances 8: 3310333120. [31] Gidde RR, Pawar PM, Ronge BP, Shinde AB, Misal AD, Wangikar SS (2019) Flow field analysis of a passive wavy micromixer with CSAR and ESAR elements. Microsystem Technologies 25(3): 1017-1030. [32] Wu Z, Chen X (2019) A novel design for passive micromixer based on cantor fractal structure. Microsystem Technologies 25(3): 985-996. [33] Wu Z, Chen X (2019) Numerical simulation of a novel microfluidic electroosmotic micromixer with cantor fractal structure. Microsystem Technologies 25(3): 3157-3164. [34] Tian Y, Chen X, Zhang S (2019) Numerical study on bilateral Koch fractal baffles micromixer. Microgravity Science and Technology, https://doi.org/10.1007/s12217-019-09713-x [35] Okuducu MB, Aral MM (2019) Computational evaluation of mixing performance in 3-D swirl-generation passive micromixers. Processes 7(3): 121. [36] Okuducu MB, Aral MM (2018) Performance analysis and numerical evaluation of mixing in 3-D T-shape passive micromixers. Micromachines 9(5): 1–28. [37] Liu M (2011) Computational study on convective-diffusive mixing in a microchannel mixer. Chemical Engineering Science 66: 2211-2223. [38] Bailey RT (2017) Managing false diffusion during second-order upwind simulations of liquid micromixing. Internationa Journal of Numerical Methods in Fluids 83(12): 940-959. [39] Reyes DR, Iossifidis D, Auroux PA, Manz A (2002) Micro total analysis systems. 1. Introduction, theory, and technology. Anal. Chem. 74: 2623-2636. [40] Duan C, Wang W, Xie Q (2013) Review article: Fabrication of nanofluidic devices. Biomicrofluidics 7: 026501. [41] Gates BD, Xu Q, Stewart M, Ryan D, Willson CG, Whitesides GM (2005) New approaches to nanofabrication: molding, printing, and other techniques. Chem. Rev. 105: 1171-1196. [42] Chaurasia AS, Jahanzad F, Sajjadi S (2017) Flexible microfluidic fabrication of oilencapsulated alginate microfibers. Chemical Engineering Journal 308: 1090–1097.

Jo

ur na

lP

re

-p

ro

of

[43] Walsh DI, Kong DS, Murthy SK, Carr PA (2017) Enabling microfluidics: from clean rooms to makerspaces. Trends Biotechnol 35: 383–392. [44] Mahmud M, Blondeel E, Kaddoura M, MacDonald B (2018) Features in microfluidic paperbased devices made by laser cutting: How small can they be?. Micromachines 9: 220. [45] Kinahan DJ, Julius LAN, Schoen C, Dreo T, Ducrée J (2018) Automated DNA purification and multiplexed lamp assay preparation on a centrifugal microfluidic “Lab-on-a-Disc” platform. In Proceedings of the 2018 IEEE Micro Electro Mechanical Systems (MEMS) Belfast, UK, pp. 1134–1137. [46] Faustino V, Catarino SO, Lima R, Minas G (2016) Biomedical microfluidic devices by using low-cost fabrication techniques: A review. J. Biomech. 49: 2280–2292. [47] Giboz J, Copponnex T, Mélé P (2007) Microinjection molding of thermoplastic polymers: A review. J. Micromech. Microeng. 17(6): R96-R109. [48] Weerakoon-Ratnayake KM, O'Neil CE, Uba FI, Soper SA (2017) Thermoplastic nanofluidic devices for biomedical applications. Lab Chip 17: 362–381. [49] Waheed S, Cabot JM, Macdonald NP, Lewis T, Guijt RM, Paull B, Breadmore MC (2016) 3D printed microfluidic devices: Enablers and barriers. Lab Chip 16: 1993–2013. [50] Harriott LR (2001) Limits of lithography. Proc. IEEE, 89: 366–374. [51] Zolotoyabko E (2014) Diffraction phenomena in optics. In basics concepts of X-ray diffraction; John Wiley & Sons, Inc.: Hoboken, NJ, USA. [52] Hashmi A, Xu J (2014) On the quantification of mixing in microfluidics. Journal of the Association for Laboratory Automation 19(5): 488-491. [53] Tekin HC, Sivagnanam V, Ciftlik AT, Sayah A, Vandevyver C, Gijs MAM (2010) Chaotic mixing using source-sink microfluidic flows in a PDMS chip. Microfluidics and Nanofluidics 10: 749-759. [54] Liu RH, Stremler MA, Sharp KV, Olsen MG, Santiago JG, Adrian RJ, Aref H, Beebe DJ (2009) Passive mixing in a three-dimensional serpentine microchannel. J. Microelectromech. Syst. 9: 190-197. [55] Phan HV, Coskun MB, Seaen M, Pandraud G, Neild A, Alan T (2015) Vibrating memberane with discontinuities for rapid and efficient microfluidic mixing. Lab Chip 15: 42064216. [56] Du M, Ma Z, Ye X, Zhou Z (2013) On-chip fast mixing by a rotary peristaltic micropump with a single structural layer. Sci. China Technol. Sci 56: 1047-1054. [57] Suh yk, Kang S (2010) A Review on Mixing in Microfluidics. Micromachines 1: 82-111. [58] Wong SH, Ward MCL, Wharton CW (2004) Micro T-mixer as a rapid mixing micromixer. Sensors and Actuators B 100: 359-379. [59] Gobby D, Angeli P, Gavriilidis A (2001) Mixing characteristics of T-type microfluidic mixers. J. Micromech. Microeng. 11: 126-132. [60] Bessoth FG, de Meelo AJ, Manz A (1999) Microstructure for efficient continues flow mixing. Analytical Communications 36: 213-215. [61] Löb P, Drese KS, Hessel V, Hardt S, Hofmann C, Löwe H, Werner B (2004) Steering of liquid mixing speed in interdigital micro mixers– from very fast to deliberately slow mixing. Chemical Engineering & Technology 27(3): 340–345. [62] Hessel V, Hardt S, Löwe H, Schönfeld F (2003) Laminar mixing in different interdigital micromixers: I. Experimental characterization. AIChE Journal 49(3): 566–577. [63] Hardt S, Schönfeld F (2003) Laminar mixing in different interdigital micromixers: II. Numerical simulations. AIChE Journal 49(3): 578–584.

Jo

ur na

lP

re

-p

ro

of

[64] Hardt S, Dietrich T, Freitag A, Hessel V, Löwe H, Hoffman C, Oroskar A, Schönfeld F, VandenBussche K (2002) Sixth International Conference on Microreaction Technology, IMRET 6, ed. I. Rinard, B. Hoch, New Orleans, AIChE Publications 164: 329–344. [65] Walker G M, Ozers M S and Beebe D J (2004) Cell infection within a microfluidic device using virus gradients. Sensors Actuators B 98: 347–55. [66] Schwesinger N, Frank T, Wurmus H (1996) A modular microfluid system with an integrated micromixer. J. Micromech. Microeng. 6: 99–102. [67] Gray B L, Jaeggi D, Mourlas NJ, vAN Drieenhuizen BP, Williams KR, Maluf NI, Kovas GTA (1999) Novel interconnection technologies for integrated microfluidic systems. Sensors Actuators A 77: 57–65. [68] Munson M S, Yager P (2004) Simple quantitative optical method for monitoring the extent of mixing applied to a novel microfluidic mixer. Anal. Chim. Acta 507: 63–71. [69] Melin J, Gimenez G, Roxhed N, van der Wijngaart W, Stemme G (2004) A fast passive and planar liquid sample micromixer. Lab on a Chip 4(3): 214-219. [70] Branebjerg J, Gravesen P, Krog JP, Nielsen CR (1996) Fast mixing by lamination. In Proceedings of the Micro Electro Mechanical Systems, San Diego, CA, USA, 11–15 February 441–446. [71] BucheggerW, Wagner C, Lendl B, Kraft M, Vellekoop MJ (2010) A highly uniform lamination micromixer with wedge shaped inlet channels for time resolved infrared spectroscopy. Microfluid. Nanofluid. 10: 889–897. [72] SadAbadi H, Packirisamy M, Wüthrich R (2013) High performance cascaded PDMS micromixer based on split-and-recombination flows for lab-on-a-chip applications. RSC Adv. 3: 7296. [73] Lim TW, Son Y, Jeong YJ, Yang DY, Kong HJ, Lee KS, Kim DP (2011) Threedimensionally crossing manifold micro-mixer for fast mixing in a short channel length. Lab Chip 11: 100–103. [74] Hong CC, Choi JW and Ahn CH (2004) A novel in-plane microfluidic mixer with modified tesla structures. Lab on a Chip 4: 109–113. [75] Hossain S, Ansari MA, Husain A, Kim K-Y (2010) Analysis and optimization of a micromixer with a modified Tesla structure. Chemical Engineering Journal 158(2): 305–314. [76] Yang A-S, Chuang F-C, Chen C-K, Lee M-H, Chen S-W, Su T-L, Yang Y-C (2015) A high-performance micromixer using three-dimensional tesla structures for bio-applications. Chem. Eng. J. 263: 444–451. [77] Liu RH, Stremler MA, Sharp KV, Olsen MG, Santiago JG, Adrian RJ, Beebe DJ (2000) Passive mixing in a three-dimensional serpentine microchannel. Journal of Microelectromechanical Systems 9(2): 190–197. [78] Viktorov V, Mahmud MR, Visconte C (2016) Numerical study of fluid mixing at different inlet flow-rate ratios in tear-drop and chain micromixers compared to a new h-c passive micromixer. Eng. Appl. Comput. Fluid Mech. 10: 182–192. [79] Nimafar M, Viktorov V, Martinelli M (2012) Experimental comparative mixing performance of passive micromixers with h-shaped sub-channels. Chem. Eng. Sci. 76: 37–44. [80] Vijayendran RA, Motsegood KM, Beebe DJ, Leckband DE (2003) Evaluation of a ThreeDimensional Micromixer in a Surface-Based Biosensor†. Langmuir, 19(5): 1824–1828.

[81] Raza W, Ma S-B, Kim K-Y (2018) Multi-Objective Optimizations of a Serpentine Micromixer with Crossing Channels at Low and High Reynolds Numbers. Micromachines 9(3): 110, 2018.

Jo

ur na

lP

re

-p

ro

of

[82] Chen X, Li T, Zeng H, Hu Z, Fu B (2016) Numerical and experimental investigation on micromixers with serpentine microchannles. International Journal of Heat and Mass Transfer 98: 131-140. [83] Mariotti A, Galletti C, Salvetti MV, Bruenazzi E (2019) Unsteady flow regimes in a Tshaped micromixer: mixing and characteristic frequencies. Industrial and Engineering Chemistry Research 58(29): 13340-13356. [84] Wang H, Iovenitti P, Harvey E, Masood S (2002) Optimizing layout of obstacles for enhanced mixing in microchannels. Smart Materials and Structures 11(5): 662–667. [85] Alam A, Afzal A, Kim K-Y (2014) Mixing performance of a planar micromixer with circular obstructions in a curved microchannel. Chemical Engineering Research and Design 92(3): 423–434. [86] Lin Y, Gerfen GJ, Rousseau DL, Yeh S-R (2003) Ultrafast Microfluidic Mixer and FreezeQuenching Device. Analytical Chemistry 75(20): 5381–5386. [87] Razavi bazaz S, Abouei Mehrizi A, Javid SM, Passandideh Fard M (2016) Increasing the efficiency of microfluidic micromixer with gaps and baffles using design of experiments based on Taguchi method, Canadian Society for Mechanical Engineering (CSME) International Conference 6-26. [88] Bhagat AAS, Peterson ETK, Papautsky I (2007) A passive planar micromixer with obstructions for mixing at low Reynolds numbers. J. Micromech. Microeng. 17: 1017–1024. [89] Sadegh Cheri M, Latifi H, Salehi Moghaddam M, Shahraki H (2013) Simulation and experimental investigation of planar micromixers with short-mixing-length. Chemical Engineering Journal 234: 247–255. [90] Lee CY, Lin C, Hung MF, Ma RH, Tsai CH, Lin CH, Fu LM (2006) Experimental and Numerical Investigation into Mixing Efficiency of Micromixers with Different Geometric Barriers. Materials Science Forum 505-507: 391–396. [91] Wang L, Ma S, Wang X, Bi H, Han X (2014) Mixing enhancement of a passive microfluidic mixer containing triangle baffles. Asia-Pacific Journal of Chemical Engineering 9(6): 877–885. [92] Du Y, Zhang Z, Yim C, Lin M, Cao X (2010) A simplified design of the staggered herringbone micromixer for practical applications. Biomicrofluidics 4(2): 024105. [93] Hama B, Mahajan G, Fodor PS, Kaufman M, Kothapalli CR (2018) Evolution of mixing in a microfluidic reverse-staggered herringbone micromixer. Microfluidics and Nanofluidics 22(5): 22-54. [94] Afzal A, Kim K-Y (2014) Three-objective optimization of a staggered herringbone micromixer. Sensors and Actuators B: Chemical 192; 350–360. [95] Whulanza Y, Utomo MS, Hilman A (2018) Realization of a passive micromixer using herringbone structure, AIP Conference Proceeding, 1933 (1): 040003. [96] Yoshimura M, Shimoyama K, Misaka T, Obayashi S (2019) Optimization of passive grooved micromixers based on genetic algorithm and graph theory. Microfluidics and Nanofluidics 23(3) DOI: 10.1007/s10404-019-2201-6

[97] He X, Xia T, Lingfeng G, Zhidan D, Uzoejinwa B (2019) Simulation and experimental study of asymmetric split and recombine micromixer with D-shaped sub-channels. Micro & Nano Letters 14(3): 293-298. [98] Baheri Islami S, Ahmadi S (2019) The effect of flow parameters on mixing degree of a three dimensional rhombus micromixer with obstacles in the middle of the mixing channel using oscillatory inlet velocities. Transport Phenomena in Nano and Micro Scales 7: 62-71.

Jo

ur na

lP

re

-p

ro

of

[99] Jain M, Nandakumar K (2010) Novel index for micromixing characterization and comparative analysis. Biomicrofluidics 4(3): 031101. [100] Karthikeyan K, Sujatha L, Sudharsan NM (2017) Numerical Modeling and Parametric Optimization of Micromixer for Low Diffusivity Fluids. International Journal of Chemical Reactor Engineering 16(3): 5-12. [101] Tsai RT, Wu CY (2011) An efficient micromixer based on multidirectional vortices due to baffles and channel curvature. Biomicrofluidics 5: 14103. [102] Milotin R., Lelea D (2016) The Passive Mixing Phenomena in Microtubes with Baffle Configuration. Procedia Technology 22: 243–250. [103] Zhang S, Chen X, Wu Z, Zheng Y (2019) Numerical study on stagger Koch fractal baffles micromixer. International Journal of Heat and Mass Transfer 133: 1065–1073. [104] Chen X, Zhang S (2018) 3D micromixers based on Koch fractal principle. Microsyst Technol 24(6): 2627–2636 [105] Chen X, Zhang S, Wu Z, Zheng Y (2019) A novel Koch fractal micromixer with rounding corners structure. Microsystem Technologies 25(7): 2751-2758. [106] Parsa MK, Hormozi F (2014) Experimental and CFD modeling of fluid mixing in sinusoidal microchannels with different phase shift between side walls. Journal of Micromechanics and Microengineering 24(6): 065018. [107] Mondal B, Mehta SK, Patowari PK, Pati S (2018) Numerical study of mixing in wavy micromixers: comparison between raccoon and serpentine mixer. Chemical Engineering and Processing - Process Intensification 136: 44-61. [108] Afzal A, Kim K-Y (2012) Passive split and recombination micromixer with convergent– divergent walls. Chemical Engineering Journal 203: 182–192. [109] Afzal A, Kim K-Y (2014) Performance evaluation of three types of passive micromixer with convergent-divergent sinusoidal walls, Journal of Marine Science and Technology 22(4): 680-686. [110] Afzal A, Kim K-Y (2015) Convergent–divergent micromixer coupled with pulsatile flow. Sens. Actuators B Chem. 211: 198–205. [111] Tran-Minh N, Dong T, Karlsen F (2014) An efficient passive planar micromixer with ellipse-like micropillars for continuous mixing of human blood. Comput. Methods Programs Biomed. 117: 20–29. [112] Chen X, Li T (2016) A novel design for passive misscromixers based on topology optimization method. Biomedical Microdevices 18(4): 57. [113] Chung CK, Shih TR (2007) A rhombic micromixer with asymmetrical flow for enhancing mixing. Journal of Micromechanics and Microengineering 17(12): 2495–2504. [114] Hossain S, Kim,K-Y (2014) Mixing analysis of passive micromixer with unbalanced threesplit rhombic sub-channels. Micromachines 5(4): 913–928.

Jo

ur na

lP

re

-p

ro

of

[115] Raza W, Kim K-Y (2019) An unbalanced split and recombine micromixer with threedimensional steps. Industrial & Engineering Chemistry Research. doi:10.1021/acs.iecr.9b00682 [116] Cheng KC, Lin RC, Ou JW (1976) Fully Developed Laminar Flow in Curved Ducts of Rectangular Channels. Trans. of SME: J. of Fluids Eng. 98: 41-48. [117] Schönfeld F, Hardt S (2004) Simulation of helical flows in microchannels. AIChE Journal 50(4): 771–778. [118] Jiang F, Drese KS, Hardt S, Küpper M, Schönfeld F (2004) Helical flows and chaotic mixing in curved micro channels. AIChE Journal 50(9): 2297–2305. [119] Sudarsan AP, Ugaz VM (2006) Fluid mixing in planar spiral microchannels. Lab Chip 6(1): 74–82. [120] Santana H, Amaral RL, Taranto OP (2015) Numerical study of mixing and reaction for biodiesel production in spiral microchannel, Chemical Engineering Transactions 43: 1663-1668. [121] Mehrdel P, Karimi S, Farré-Lladós J, Casals-Terré J (2018) Novel variable radius spiral– shaped micromixer: from numerical analysis to experimental validation, Micromachines 9: 552. [122] Vanka SP, Winkler CM, Coffman J, Linderman E, Mahjub S, Young B (2003) Novel low Reynolds number mixers for microfluidic applications. ASME Proceeding, 2: 887-892. [123] Scherr T, Quitadamo C, Tesvich P, Park DS-W, Tiersch T, Hayes D, Monroe WT (2012) A planar microfluidic mixer based on logarithmic spirals. Journal of Micromechanics and Microengineering 22(5): 055019. [124] Sheu TS, Chen SJ, Chen JJ (2012) Mixing of a split and recombine micromixer with tapered curved microchannels. Chemical Engineering Science 71: 321–332. [125] Yang J, Qi L, Chen Y, Ma H (2012) Design and Fabrication of a Three Dimensional Spiral Micromixer. Chinese Journal of Chemistry 31(2): 209–214. [126] Rafeie M, Welleweerd M, Hassanzadeh-Barforoushi A, Asadnia M, Olthuis W EbrahimiWarkiani M (2017) An easily fabricated three-dimensional threaded lemniscate-shaped micromixer for a wide range of flow rates. Biomicrofluidics 11: 014108. [127] Clark J, Kaufman M, Fodor PS (2018) Mixing enhancement in serpentine micromixers with a non-rectangular cross-section, Micromachines 9: 107. [128] Al-Halhouli AA, Alshare A, Mohsen M, Matar M, Dietzel A, Büttgenbach S (2015) Passive micromixers with interlocking semi-circle and omega-shaped modules: Experiments and simulations. Micromachines 6: 953–968. [129] Liu K, Yang Q, Chen F, Zhao Y, Meng X, Shan C, Li Y (2015) Design and analysis of the cross-linked dual helical micromixer for rapid mixing at low Reynolds numbers. Microfluid. Nanofluid 19: 169–180. [130] Balasubramaniam L, Arayanarakool R, Marshall SD, Li B, Lee PS, Chen PCY (2017) Impact of cross-sectional geometry on mixing performance of spiral microfluidic channels characterized by swirling strength of Dean-vortices, J. Micromech. Microeng 27: 095016. [131] Deshmukh AA, Liepmann D, Pisano AP (2000) Continuous micromixer with pulsatile micropumps. Technical Digest of the IEEE Solid State Sensor and Actuator Workshop (Hilton Head Island, SC) 73–6 [132] Niu X, Lee Y-K (2003) Efficient spatial-temporal chaotic mixing in microchannels. Journal of Micromechanics and Microengineering 13(3): 454–462. [133] Oh KW, Lee K, Ahn B, Furlani EP (2012) Design of pressure-driven microfluidic networks using electric circuit analogy. Lab Chip 12(3): 515–545. [134] Du M, Ma Z, Ye X, Zhou Z (2013) On-chip fast mixing by a rotary peristaltic micropump with a single structural layer. Science China Technological Sciences 56(4): 1047–1054.

Jo

ur na

lP

re

-p

ro

of

[135] Xia Q, Zhong S (2013) Liquid mixing enhanced by pulse width modulation in a Y-shaped jet configuration. Fluid Dynamics Research 45(2): 025504. [136] Wu JW, Xia HM, Zhang YY, Zhao SF, Zhu P, Wang ZP (2018) An efficient micromixer combining oscillatory flow and divergent circular chambers. Microsystem Technologies 25(7): 2741-2750 . [137] Li Z, Kim S-J (2017) Pulsatile micromixing using water-head-driven microfluidic oscillators. Chemical Engineering Journal 313: 1364–1369. [138] Zhang M, Zhang W, Wu Z, Shen Y, Chen Y, Lan C, Li F, Cai W (2019) Comparison of Micro-Mixing in Time Pulsed Newtonian Fluid and Viscoelastic Fluid. Micromachines 10(4): 262. [139] Liu RH, Yang J, Pindera MZ, Athavale M, Grodzinski P (2002) Bubble-induced acoustic micromixing. Lab on a Chip 2: 151–157. [140] Moroney RM, White RM, Howe RT (1991) Ultrasonically induced microtransport. In Proceedings of the IEEE Micro Electro Mechanical Systems, Nara, Japan, 1–2 January 277–282. [141] Yang Z, Matsumoto S, Goto H, Matsumoto M, Maeda R (2001) Ultrasonic micromixer for microfluidic systems. Sens. Actuators A 93: 266–272. [142] Ahmed D, Mao X, Shi J, Juluri BK, Huang TJ (2009) A millisecond micromixer via single-bubble-based acoustic streaming. Lab on a Chip 9(18): 2738. [143] Wang SS, Jiao ZJ, Huang XY, Yang C, Nguyen NT (2008) Acoustically induced bubbles in a microfluidic channel for mixing enhancement. Microfluidics and Nanofluidics 6(6): 847– 852. [144] Orbay S, Ozcelik A, Lata J, Kaynak M, Wu M, Huang TJ (2016) Mixing high-viscosity fluids via acoustically driven bubbles. Journal of Micromechanics and Microengineering 27(1): 015008. [145] Jang L-S, Chao S-H, Holl MR, Meldrum DR (2005) Microfluidic circulatory flows induced by resonant vibration of diaphragms. Sens. Actuators A Phys. 122: 141–148. [146] Yang Z, Matsumoto S, Goto H, Matsumoto M, Maeda R (2001) Ultrasonic micromixer for microfluidic systems. Sens. Actuator A-Phys. 93(3): 266–272. [147] Yaralioglu GG, Wygant IO, Marentis TC, Khuri-Yakub BT (2004) Ultrasonic mixing in microfluidic channels using integrated transducers. Anal. Chem. 76:3694–3698. [148] Fu Y, Luo J, Nguyen N, Walton A, Flewitt A, Zu X, Li Y, McHale G, Matthews A, Iborra E, Du H, Milne W (2017) Advances in piezoelectric thin films for acoustic biosensors, acoustofluidics and lab-on-chip applications. Prog. Mater. Sci. 89:31–91. [149] Qi A, Yeo LY, Friend JR (2008) Interfacial destabilization and atomization driven by surface acoustic waves. Physics of Fluids, 20(7): 074103. [150] Ang KM, Yeo LY, Hung YM, Tan MK (2016) Amplitude modulation schemes for enhancing acoustically-driven microcentrifugation and micromixing. Biomicrofluidics 10: 054106, 2016. [151] Luong T-D, Phan V-N, Nguyen N-T (2010) High-throughput micromixers based on acoustic streaming induced by surface acoustic wave. Microfluidics and Nanofluidics 10(3): 619–625. [152] Lim E, Lee L, Yeo LY, Hung YM, Tan MK (2019) Acoustically-Driven Micromixing: Effect of Transducer Geometry, IEEE Trans Ultrason Ferroelectr Freq Control. Jun 4. doi: 10.1109/TUFFC.2019.2920683. [153] Ballard M, Owen D, Mills ZG (2016) Orbiting magnetic microbeads enable rapid microfluidic mixing. Microfluid Nanofluid 20(6):1–13

Jo

ur na

lP

re

-p

ro

of

[154] Lee KY, Park S, Lee YR (2016) Magnetic droplet microfluidic system incorporated with acoustic excitation for mixing nhancement. Sensors Actuators A Phys 243:59–65 [155] Nouri D, Hesari AZ, Passandideh-Fard M (2017) Rapid mixing in micromixers using magnetic field. Sensors Actuators A Phys 255: 79–86 [156] Hejazian M, Nguyen NT (2017) A rapid Magnetofluidic micromixer using diluted Ferrofluid. Micromachines 8(2):37. [157] Petkovic K, Metcalfe G, Chen H (2017) Rapid detection of Hendra virus antibodies: an integrated device with nanoparticle assay and chaotic micromixing. Lab Chip 17(1):169–177. [158] Kumar C, Hejazian M, From C, Saha SC, Sauret E, Gu Y, Nguyen N-T (2019) Modeling of mass transfer enhancement in a magnetofluidic micromixer. Physics of Fluids 31(6): 063603. [159] Fu LM, Tsai CH, Leong KP (2010) Rapid micromixer via ferrofluids. Phys Procedia 9:270–273. [160] Ergin FG, Watz BB, Ērglis K (2015) Time-resolved velocity measurements in a magnetic micromixer. Exp Thermal Fluid Sci 67:6–13 [161] Liu F, Zhang J, Alici G (2016) An inverted micro-mixer based on a magnetically-actuated cilium made of Fe doped PDMS. Smart Mater Struct 25(9):095049 [162] Saroj SK, Asfer M, Sunderka A (2016) Two-fluid mixing inside a sessile micro droplet using magnetic beads actuation. Sensors Actuators A Phys 244:112–120 [163] Boroun S, Larachi F (2017) Enhancing liquid micromixing using low-frequency rotating nanoparticles. AICHE J 63(1):337–346 [164] Usefian A, Bayareh M, Ahmadi Nadooshan A (2019) Rapid mixing of Newtonian and non-Newtonian fluids in a three-dimensional micro-mixer using non-uniform magnetic field, Journal of Heat and Mass Transfer Research 6(1):56-61. [165] Kang TG, Hulsen MA, Anderson PD (2007) Chaotic mixing induced by a magnetic chain in a rotating magnetic field. Phys Rev E 76(6):066303 [166] Chen CY, Lin CY, Hu YT (2014) Inducing 3D vortical flow patterns with 2D asymmetric actuation of artificial cilia for high performance active micromixing. Exp Fluids 55(7):1765 [167] Veldurthi N, Chandel S, Bhave T (2015) Computational fluid dynamic analysis of poly (dimethyl siloxane) magnetic actuator based micromixer. Sensors Actuators B Chem 212:419– 424 [168] Owen D, Ballard M, Alexeev A, Hesketh PJ (2016) Rapid microfluidic mixing via rotating magnetic microbeads. Sens. Actuators A: Phys. 251: 84–91. [169] Kang HJ, Choi B (2011) Development of the MHD micropump with mixing function. Sensors Actuators A Phys 165(2):439–445 [170] Jeon H, Massoudi M, Kim J (2017) Magneto-hydrodynamics driven mixing of a reagent and a phosphate-buffered solution: a computational study. Appl Math Comput 298:261–271 [171] Chen X, Zhang L (2017) A review on micromixers actuated with magnetic nanomaterials. Microchimica Acta 184(10): 3639–3649. [172] El Moctar AO, Aubry N, Batton J (2003) Electro–hydrodynamic micro-fluidic mixer Lab on a Chip 3: 273–80 [173] Huang JJ, Lo YJ, Hsieh CM, Lei U (2011) An electro-thermal micro mixer. In Proceedings of the IEEE International Conference on Nano/micro Engineered and Molecular Systems, Kaohsiung, Taiwan, 20–23 February: 919–922. [174] Kim H-S, Kim H-O, Kim Y-J (2018) Effect of Electrode Configurations on the Performance of Electro-Hydrodynamic Micromixer. ASME 16th International Conference on Nanochannels, Microchannels, and Minichannels.

re

-p

ro

of

[175] Zhang J, He G, Liu F (2006) Electro-osmotic flow and mixing in heterogeneous microchannels. Physical Review E, 73(5):056305. [176] Ebrahimi S, Hasanzadeh-Barforoushi A, Nejat A, Kowsary F (2014) Numerical study of mixing and heat transfer in mixed electroosmotic/pressure driven flow through T-shaped microchannels. International Journal of Heat and Mass Transfer 75: 565–580. [177] Bhattacharyya S, Bera S (2015) Combined electroosmosis-pressure driven flow and mixing in a microchannel with surface heterogeneity. Applied Mathematical Modelling 39(15): 4337–4350. [178] Peng R, Li D (2015) Effects of ionic concentration gradient on electroosmotic flow mixing in a microchannel. Journal of Colloid and Interface Science 440: 126–132. [179] Ahmadian Yazdi A, Sadeghi A, Saidi MH (2015) Electrokinetic mixing at high zeta potentials: Ionic size effects on cross stream diffusion. Journal of Colloid and Interface Science 442: 8–14. [180] Shamloo A, Mirzakhanloo M, Dabirzadeh MR (2016) Numerical Simulation for efficient mixing of Newtonian and non-Newtonian fluids in an electro-osmotic micro-mixer. Chemical Engineering and Processing: Process Intensification 107: 11–20. [181] Matsubara K, Narumi T (2016) Microfluidic mixing using unsteady electroosmotic vortices produced by a staggered array of electrodes. Chemical Engineering Journal 288: 638– 647. [182] Kazemi Z, Rashidi S, Esfahani JA (2017) Effect of flap installation on improving the homogeneity of the mixture in an induced-charge electrokinetic micro-mixer. Chemical Engineering and Processing: Process Intensification 121:188–197.

lP

[183] Usefian A, Bayareh M, Shateri A, Taheri N (2019) Numerical study of electro-osmotic micro-mixing of Newtonian and non-Newtonian fluids, J Braz. Soc. Mech. Sci. Eng. 41: 238. https://doi.org/10.1007/s40430-019-1739-2

ur na

[184] Zhao W, Yang F, Wang K, Bai J, Wang G (2017) Rapid mixing by turbulent-like electrokinetic microflow. Chemical Engineering Science 165: 113–121. [185] Zhang K, Ren Y, Hou L, Feng X, Chen X, Jiang H (2018) An efficient micromixer actuated by induced-charge electroosmosis using asymmetrical floating electrodes. Microfluidics and Nanofluidics 22(11):130.

Jo

[186] Usefian A, Bayareh M (2019) Numerical and experimental study on mixing performance of a novel electro-osmotic micro-mixer, Meccanica https://doi.org/10.1007/s11012-019-01018-y [187] Daghighi Y, Li D (2013) Numerical study of a novel induced-charge electrokinetic micromixer. Analytica Chimica Acta 763: 28–37. [188] Daghighi Y, Sinn I, Kopelman R, Li D (2013) Experimental validation of induced-charge electrokinetic motion of electrically conducting particles. Electrochimica Acta 87: 270–276. [189] Kazemi S, Nourian V, Nobari MRH, Movahed S (2017) Two dimensional numerical study on mixing enhancement in micro-channel due to induced charge electrophoresis. Chemical Engineering and Processing: Process Intensification 120: 241–250.

Jo

ur na

lP

re

-p

ro

of

[190] Choi E, Kim B, Park J (2009) High-throughput microparticle separation using gradient traveling wave dielectrophoresis. Journal of Micromechanics and Microengineering 19(12): 125014. [191] Deval J, Tabeling P, Ho CM (2002) A dielectrophoretic chaotic mixer. Technical Digest. MEMS IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.02CH37266). [192] Kim D, Raj A, Zhu L, Masel RI, Shannon MA (2008) Non-equilibrium electrokinetic nanofluidic mixers. IEEE 21st International Conference on Micro Electro Mechanical Systems. [193] Mao H, Yang T, Cremer PS (2002) A microfluidic device with a linear temperature gradient for parallel and combinatorial measurements J. Am. Chem. Soc. 124 4432–5 [194] Tsai JH, Lin L (2002) Active microfluidic mixer and gas bubble filter driven by thermal bubble pump Sensors Actuators A 97–98 665–71 [195] Huang C, Tsou C (2014) The implementation of a thermal bubble actuated microfluidic chip with microvalve, micropump and micromixer. Sens. Actuators A: Phys. 210: 147–156. [196] Tan H (2019) Numerical study of a bubble driven micromixer based on thermal inkjet technology, Physics of Fluids 31: 062006 https://doi.org/10.1063/1.5098449 [197] Huang K-R, Chang J-S, Chao S.D, Wung T-S, Wu K-C (2012) Study of active micromixer driven by electrothermal force. Jpn. J. Appl. Phys. 51: 047002. [198] Sasaki N, Kitamori T, Kim HB (2012) Fluid mixing using ac electrothermal flow on meandering electrodes in a microchannel. Electrophoresis 33: 2668–2673. [199] Zhang F, Chen H, Chen B, Wu J (2016) Alternating current electrothermal micromixer with thin film resistive heaters. Adv. Mech. Eng. 8:168781401664626. [200] Kunti G, Bhattacharya A, Chakraborty S (2017) Rapid mixing with high-throughput in a semi-active semi-passive micromixer. Electrophoresis 38:1310–1317. [201] Kunti G, Bhattacharya A, Chakraborty S (2018). Electrothermally actuated moving contact line dynamics over chemically patterned surfaces with resistive heaters. Physics of Fluids 30(6):062004. [202] Meng J, Li S, Li J, Yu C, Wei C, Dai S (2018) AC electrothermal mixing for high conductive biofluids by arc-electrodes. Journal of Micromechanics and Microengineering 28(6): 065004. [203] Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids. Wiley, New York. [204] Evans JD, Junior ILP, Oishi CM (2017) Stresses of PTT, Giesekus, and Oldroyd-B fluids in a Newtonian velocity field near the stick-slip singularity. Physics of Fluid 29: 121604. [205] Gale BK, Jafek AR, Lambert CJ, Goenner BL, Moghimifam H, Nze UC, Kamarapu SK (2018) A reviewe of current methods in microfluidic device fabrication and future commercialization prospects. Inventions 3: 60. .