Template for Electronic Submission to ACS Journals The Journal of Engineering Research (TJER), Vol. 19, No. 2, (2022) 106-128 0043 Corresponding author's e-mail: afzal19@squ.edu.om DOI:10.53540/tjer.vol19iss2pp106-128 DESIGN AND MIXING PERFORMANCE OF PASSIVE MICROMIXERS: A CRITICAL REVIEW Afzal Husain1*, Asharul Islam Khan1, Wasim Raza2, Nabeel Al-Rawahi1, Nasser Al-Azri1, and Abdus Samad2 1Mechanical and Industrial Engineering Department, Sultan Qaboos University, Muscat, Oman 2Department of Ocean Engineering, Indian Institute of Technology Madras, Tamil Nadu, India. ABSTRACT: This study extracts and reports notable findings on passive micromixers by conducting an exhaustive review of designs, their features, and mixing performance. The study has covered the relevant articles on passive micromixers published from 2010 to 2020. The analysis of filtered and selected articles sums up passive micromixers into four categories: designed inlets, designed mixing-channel, lamination-based, and flow obstacles-based. The prominent mixing channel categories identified in the study are split-and-recombine (SAR), convergent-divergent (C-D), and mixed (SAR, C-D, and others). Moreover, differences in mixing channel designs, number of inlets, and evaluation methods have been used in comparing the mixing performance of passive micromixers. The SAR and the obstacles-based micromixers were found to outperform the others. The designs covered in the present review show significant improvements in the mixing index. However, these studies were conducted in an isolated environment, and most of the time, their fabrication and device integration issues were ignored. The assortment and critical analysis of micromixers based on their design features and flow parameters will be helpful to researchers interested in designing new passive micromixers for microfluidic applications. Keywords: Microfluidics, Passive micromixers; Mixing index; Split-and-recombine; Convergent-divergent; Lamination; Off-set inlets. : مراجعة نقديةغير النشطةالدقيقة للخالطات األداء تصميم وفعالية عبد الصمدوناصر العزري و نبيل الرواحي و وسيم رضاو أشار اإلسالم خانو أفضال حسين تصاميم :الملخص عن شاملة مراجعة بعد السلبية الدقيقة الخالطات عن البيانات أهم ونشر استخالص على الدراسة هذه تقوم م. 0202و 2010الدقيقة السلبية بين العامين الخالطات المنشور عن ومميزات وأداء هذه الخالطات حيث استهدفت هذه الدراسة تصميم المداخل وتصميم أن الخالطات الدقيقة السلبية يمكن تقسيمها بناء على أربعة محاور: نجدوتحليلها دراسات وبعد فرز هذه ال وخلصت هذه الدراسة إلى أن أبرز الفئات المبنية على قناة الخلط هي: الفصل وإعادة .وعوائق الدفققناة الخلط وخاصية التغليف والمتقاربة والمتعددة األنواع. بمتال-الجمع، على اإلضافة إلى ذلك باعدة القطر فإن مقارنة أداء الخلط في هذه الدراسة تم بناؤها وطرق التقييم. تبين االختالف وعدد المداخل على كذلكفي تصميم قنوات الخلط وتلك المبنية الجمع وإعادة أن خالطا الفصل يم التي شملتها هذه المراجعة قد أثبتت تطورات التصامكما أن .الدقيقة السلبية األخرى الخالطات عن أدائها عوائق الدفق تتفوق في إال أن ما يجدر ذكره أن هذه الدراسات قد أجريت في بيئات معزولة كما يغلب عليها إهمال جانب طبيعة .هامة في مؤشرات الخلط الدقي الخالطات وتحليل تصنيف إن األخرى. األجهزة مع المتعلقة بتكامليتها والقضايا الخالطات هذه مزايا تصنيع على بناء قة تصميمها ومعامالت الدفق فيها سيساعد الباحثين المهتمين بتصميم خالطات دقيقة جديدة في تطبيقات الموائع الدقيقة. الخلط ؛الخالطات الدقيقة السلبية ؛الموائع الدقيقة الكلمات المفتاحية: الجمع ؛ مؤشر وإعادة والتباعد ؛الفصل ؛ التغليف ؛التقارب . المداخل المزاحة mailto:afzal19@squ.edu.om Design and Mixing Performance of Passive Micromixers: A Critical Review 107 1. INTRODUCTION A passive micromixer is an important component of lab-on-chip devices. They are one of the most frequently used add-ons in microfluidics for rapid mixing. Micromixers are getting extensive attention in numerous fields of science and engineering disciplines such as biochemical analysis, drug discovery, sensing, microelectromechanical systems (MEMS), micro total analysis systems (μ-TAS), bio-diagnostics, Lab-on-a- Chip (Johnson and Locascio, 2002), and chemical processing. It can be used standalone as well as an integrated mixing unit in microfluidic systems. Micromixers are used to mix two or more fluids rapidly within a short channel length and short time. The advantages associated with the micro-dimension of channels, such as reduced sample volume and reagent requirement along with the lesser amount of waste- product produced, lead to low operating cost, high surface area to volume ratio providing better heat dissipation, faster analysis results, portability, and high-throughput through parallelization. These advantages have enhanced their prospects of usage in a wide range of applications such as DNA purification (Kastania et al., 2016), protein folding (Jang et al., 2019), enzyme catalysis (Zhang et al., 2021), nanoparticle synthesis (Westerhausen et al., 2016), and water quality monitoring. An exhaustive review of the applications of micromixers can be found elsewhere (Jaywant and Arif, 2019; Jeong et al., 2010; Lee and Fu, 2018). The micromixer design, passive structures, and the flow Reynolds number (Re) significantly affect the mixing performance and need further research to meet the contemporary developments in the microsystems. The Reynolds number indicates the degree of dominance of inertial force over viscous force. Turbulent flow, characterized by a high Reynolds number (Re > 2300), has greater inertial force causing flow instabilities in the form of vortices and eddies, which can promote mixing in the channel. However, the flow Reynolds number in a micromixer (Re < 100) is much lower than the limiting Reynolds number for a turbulent flow (Re > 2300). Hence, the adequate mixing of two fluids is difficult to achieve in the absence of flow instability under laminar flow conditions inside the micromixers (Re<<100) as compared to the turbulent flow (Bhopte et al., 2010). Mixing by diffusion is a slow process, which has little relevance to most fluid mixing applications, where fast mixing is a prerequisite. Thus, microfluidic mixing is a challenging problem for low diffusivity fluids under laminar flow conditions and hence requires design improvements to enhance mixing. The micromixers are of the types: active, passive, and hybrid. In addition, each of them has many sub- classifications based on the channel designs and mixing mechanism. The mixing in active micromixers needs external forces like the electric field, acoustic field, magnetic field, and thermal field to disturb the flow. However, mixing in passive micromixers occurs due to molecular diffusion and chaotic advection strengthened through channel structural modifications. Passive micromixers are low-cost, reliable, robust, efficient, and easy to use. Passive micromixers have been used in mixing both miscible and immiscible fluids. The hybrid micromixers use important characteristics of both active and passive micromixers to enhance the mixing capabilities (Bazaz et al., 2018). The passive micromixers are of Y- and T-shape depending on the inlet design. They also differ in terms of mixing-channel configurations, such as obstacles in the main channel or attached to the walls, and designed mixing-channel geometry profiles (e.g., zigzag, Split- and-Recombine (SAR), and a teardrop). There is a proportional relationship between flow path length and mixing performance based on the localized mixing and global mixing principles (Su et al., 2019). The mixing efficiency/performance of the passive micromixer is largely dependent on the geometric layouts and Reynolds number. Thus, there is a striking possibility to achieve different levels of mixing by tweaking and tuning the geometric parameters. For example, in the case of Imitate Cantor structure passive micromixers, reducing space between adjacent fractal obstacles in the mixing channel and increasing the mixing chamber's height improve the mixing performance (with optimum mixing performance at 600 µm height) (Wu and Chen, 2019a). In chaotic advection-type passive micromixers having dual opposing structures on microchannel walls, the alignment of structure strips affects the mixing performance (Chen et al., 2015). The mixing performance is enhanced by interdigital inlets (Cook et al., 2011). Additionally, the geometric-parameters tolerances associated with any fabrication process slightly influence the performance of the passive micromixers. Further, in a study, the authors calculated the cumulative distribution function for three cases to obtain the probability of having mixing efficiency lower than 95% for a Tesla micromixer (Stanciu, 2015). For instance, a small change (up to 5%) in geometric parameters with six and seven elements yields respective probabilities of 11.1% and 2.08% for getting mixing performance lower than 95% (Stanciu, 2015). Although there has been a large array of improvements achieved in the last few years, intense research for more efficient passive micromixers for microfluidic systems is continued to date. Most of the research has focused on the design of new passive micromixers and the estimation of their mixing performance through experiments and numerical simulations. Furthermore, several studies have reviewed the literature on micromixers, such as a comparative review on passive micromixers (Raza et al., 2020), a review on droplets based micromixers (Chen et al., 2019a), a review on active and passive micromixers (Bayareh et al., 2019), a short review on micromixers classification (Mukhopadhyay, 2018), Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 108 and a review on micromixers (Gaozhe et al., 2017). These studies are mainly focused on passive micromixers, their types, and to some extent, fabrication techniques, with some emphasis on micromixers having both passive and active mixing features. There is a significant void in the literature to get a comprehensive spectrum of passive micromixers, their capabilities, applications, and feasibility of integration. Nevertheless, this review investigates the dominant microchannel structures adopted for mixing enhancement in the last decade. Additionally, it sets the base to propose favorable channel structures to be further explored in the future. The study conducts an extensive analysis of the published findings on passive micromixers from the year 2010 to 2020. There are six sections in the article. Section 1 briefly introduces the concept and challenges of passive micromixing, Section 2 illustrates the research method, Section 3 corresponds to the background study, Section 4 aggregates the literature from 2010 to 2020 and classifies passive micromixers, Section 5 presents the analysis and discussion, and the Section 6, the last section, summarizes the findings and discusses future research. The study has followed a systematic literature review approach. Several protocols were set, including the databases to search for articles, inclusion and exclusion criteria for articles, and extraction of relevant information from the filtered articles. This approach helps in getting articles objectively rather than the exploration of databases randomly. The systematic literature review has become a common method of conducting a literature review in different fields of science and engineering. The online databases referred to for collecting the articles include Science Direct, Google Scholar, Springer, and IEEE Xplore. Articles published only in English and published in the years between 2010 and 2020 were considered. 2. BACKGROUND The fluid flow in microchannels is mostly laminar when the channel is of small dimensions, and fluid velocity is low (Bayareh et al., 2019). The efficiency and sensitivity of microfluidic devices are influenced by the passive structures in the micromixers and their designs (Gaozhe et al., 2017). The micromixers found in the literature can be broadly categorized into four principles such as lamination-based, injection-based, droplets-based, and chaotic advection-based (Figure 1). The lamination-based micromixers can be further categorized into parallel and serial lamination-based passive micromixers. In addition, they are sub- classified into; channels with obstacles (or baffles), curved-channel, convergence-divergence, and unsymmetrical (Bayareh et al., 2019). The lamination- based micromixers have a layered structure, and they achieve excellent mixing in a short time (milliseconds) (Gaozhe et al., 2017). The micromixers based on injection have nozzles through which fluid passes in the form of many sub-streams into the mainstream. The droplet-based passive micromixers inject droplets for mixing (Yang et al., 2018) into the main channel. The micromixers based on chaotic advection work on the principle of stretching, folding, and breaking of fluid interfaces for the laminar flow. Mixing in passive micromixers is mainly due to the phenomena of molecular diffusion and chaotic advection. The chaotic advection is favorable when the fluids have large size molecules and small diffusion coefficients. This study classifies passive micromixers based on inlet designs (designed inlets), mixing-channel layout/design, lamination-based, and obstacle-based (Figure 2). 2.1 Designed Inlets The mixing performance of passive micromixers varies with the type of inlets. The designed inlets include (1) an angle between the two inlets (T-, Y-, and configuration with other angles), (2) swirl-induced inlet, and (3) numbers of the inlet (e.g. 2, 3, 4, and 5). The mixing performance of passive micromixers increases with the angle between inlets. The inlet angle has been varied from 60° to 300°; however, the commonly designed inlets are T- and Y-shape (Figure 3). Figure 3 shows the designed inlets and their arrangements at different angles. Figure 1. Working principles of passive micromixers. Figure 2. Classification of micromixers based on geometric features. Figure 3. Micromixers based on inlet channels. micromixer principles Lamination Parallel lamination Serial lamination Injection Droplets Chaotic advection Passive passive micromixers Designed inlets Designed Mixing- channels Lamination- based Flow obstacles Design and Mixing Performance of Passive Micromixers: A Critical Review 109 Figure 4. Micromixer with swirl inlets. It was suggested that the optimal inlet mixing angles are 90°-180° for high mixing and low energy dissipation (Zhang et al., 2016). The maximum and minimum mixing performances were obtained with an intersection of 300° between the inlets at Re values of 60 and 80 (Zadeh and Marahel, 2011), respectively. In addition to various configurations of the inlets, the swirl inlets (Figure 4) have shown a considerable impact on the mixing performance. For example, the T-shape micromixers with swirl inlets showed a mixing enhancement by a factor of more than two compared to a T-mixer at Re = 20–150. Additionally, a T-shaped micromixer with swirl inlets achieved a mixing index of 40 times that of the simple T- micromixer at Re = 100. In the three-dimensional serpentine micromixers, the impact of the antisymmetric inlets was significant at the early stage; mixing index enhancement of 2–10 times was observed at Re = 100 (Matsunaga and Nishino, 2014). The swirl in the inlets improves the mixing performance at intermediate Re values (66 < Re < 180). The reverse orientation swirl (R-O-Swirl) inlets micromixers performed better than the same orientation swirl (S-O-Swirl) inlets micromixers. Dundi et al. (2019) found that the mixing performance of a micromixer with R-O-Swirl inlets increases 300% to 400% at 160 < Re < 180 and with S-O-Swirl inlets increases 30% to 70% at 266 < Re < 372, as compared to a T-shape passive micromixer without swirl. Although the simplest T- and Y-shape passive micromixers have two inlets, there are passive micromixers with more than two inlets. In Y-shape passive micromixers with three inlets, the pressure drop is uniform, and fluid flows with constant velocity, resulting in fast diffusion of fluids (Adam and Hashim, 2012). The four-inlet passive micromixers can have 50% less pressure drop and improved mixing performance of 300% to 500% as compared to the normal passive micromixers (Bhopte et al., 2010). The swirl-induced two-inlets passive micromixers have higher numerical diffusion than the swirl-induced four- inlet passive micromixers at 120 < Re < 240 (Okuducu and Aral, 2019a). In general, swirl inlets and reverse-oriented swirl inlets have shown significant improvement especially advection-driven mixing at higher Reynolds numbers. These inlet designs can be looked at for integrating with other 3D designs of the main channel to achieve higher mixing in a shorter length. 2.2 Mixing-channel layout/design-based The channel layout plays an important role in enhancing the mixing performance. Passive micromixers with hydrophobic microchannels have better performance than hydrophilic microchannels. The spiral microchannels produce higher mixing performance as compared to straight microchannels (Zhang et al., 2016). The prominent two-dimensional (2D) and three-dimensional (3D) microchannel layouts are spiral and wave (e.g., single spiral, double spiral, helical, sinusoidal, rectangular, square, and zigzag), SAR, and convergent-divergent (CD), and mixed (SAR, CD, and others). 2.2.1 Wave/Spiral shaped microchannel This section dealt with the wave and spiral-shaped mixing-channel designs proposed in the last decades. Chen et al. (2016a) reported the shape optimization of a micromixer with six different channel layouts. The authors found that the square wave microchannel produced the highest mixing performance among the tested six layouts. The order of decreasing mixing performance was square wave > multi-wave > zigzag > T > mouth > loop micromixers (Chen et al., 2016a). Scherr et al. (Scherr et al., 2012) proposed a micromixer based on logarithmic spirals and measured the mixing performance at the Reynolds number varying between 1 and 70. They noticed a decline in mixing as the Re values increased from 1.0 to 15 with a transition at Re = 15 (mixing efficiency = 53%); however, mixing increased with a further increase in Re and reached 86% at Re = 67. The new design showed higher mixing as compared to the Archimedes spiral and Meandering-S mixers. Papadopoulos et al. (2014) investigated the effects of inlet velocity in a zigzag microchannel geometry with a T-inlet. It was reported that the number of zigzags affects the mixing at a fixed inlet velocity. A higher velocity requires a larger number of zigzags for efficient mixing. A total of 150 zigzag units were recommended to achieve efficient mixing performance (98%) at a velocity of 2 mm/s and at a diffusion coefficient of 10-10 m2/s. Wang et al. (2018) designed a modified S-shaped microchannel having asymmetric lateral wall structures and conducted numerical simulations for both the modified microchannel and simple S-shaped microchannel at Re values ranging from 0.1 to 100. They found that as Re values increase from 0.1 to 100, modified S-shaped microchannel exhibits high mixing performance than simple S-shaped. It is due to the formation of secondary flow and higher inertial effects. Rafeie et al. (2017) proposed a 3D fine-threaded lemniscate-shaped micromixer to overcome the limitations of other 3D micromixers. They reported a mixing performance of over 90% at Reynolds numbers ranging from 1.0 to 1000, both numerically and experimentally. They observed that the chaotic advection (due to Dean flow) and diffusive mixing (due Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 110 to grooves) are the main cause of high mixing. Zhang et al. (2012) proposed a 3D-twisted compression–expansion microchannel for passive micromixers. They applied simulations to compare the new design with a T-shape having the same cross- sectional perimeters. The new design was reported to have higher mixing efficiency compared to T-mixer. Moreover, clamping angles at 90 degrees, 45−90 degrees, and 45 degrees have different efficiency outputs, with maximum efficiency reported at 45 degrees causing the least pressure drop. Yang et al. (2013) proposed a micromixer with overlapping dual spirals. The micromixer showed enhanced performance due to sustained Dean vortices. There are several studies on mixing-channel design with a helical structure and its variations. The helical structure can be single or double. Liu et al. (2015) studied 3D cross- linked double-helical microchannel for fast mixing at low-Re value. They compared the new channel with a helical and a straight channel of the same dimensions. The numerical Simulation revealed higher mixing of the 3D cross-linked double-helical microchannel with full mixing within three cycles at Re = 0.0015~600. The helical microchannel in 3D micromixers introduces chaotic advection, and the double helix has an agitation effect. Viktorov and Nimafar (2013) analyzed numerical and experimentally mixing performance and pressure drop in two micromixers (chain one and chain 2) consisting of 3D SAR with a special arrangement of microstructures called 'chain mixer'. They found that the chain and teardrop micromixer, due to the SAR mechanism, have higher mixing performance (reached up to 98%) compared to a simple T-shape and O- shaped mixer for Reynolds numbers ranging from 0.083 to 4.166. Furthermore, chain mixers showed lower pressure drop as compared to teardrop mixers. Al-Halhouli et al. (2015) designed ILSC and Ω channels to enhance mixing efficiency by introducing the Dean Vortices and molecular diffusion. They compared the performance of new designs with a spiral design using numerical Simulation and experiment. The ILSC and Ω configurations have complete mixing when the Reynolds number lies between 0.01 and 50, and on the other hand, the complete mixing in the semicircle shapes arranged in a spiral occurred at Re > 50. Afzal and Kim (2015b) numerically carried out multi-objective Optimization of the sigma micromixer using a multi-objective genetic algorithm. The author observed that the geometric parameters could be effectively fixed to maximize the mixer performance. The square-wave channel exhibited significant improvement over other wavy channels and is simpler in fabrication. It is found that in spiral micromixers, repetitive alteration of the flow direction has improved the mixing in a wide range of Reynolds numbers due to changes in Dean vortices' rotational direction. Furthermore, a design with a smaller radius of curvature is better for mixing. 2.2.2 SAR-based microchannel The microchannel based on the SAR principle has higher mixing performance as compared to non–SAR (Ansari and Kim, 2010). The SAR-based microchannel can be with a chamber and without a chamber. The chambered SAR design has several variations as circular, elliptical, and rhombus. The splits in the chambered SAR can be two or more. Moreover, Gidde et al. (2019b) numerically investigated the impact of balanced and unbalanced splits on the mixing performance and pressure drop in the circular split and recombine (CSAR) and elliptical split-and–recombine (ESAR) (Cortes-Quiroz et al.) micromixers at Reynolds numbers ranging from 0.1 to 75. They observed that at 0.1 ≤ Re ≤ 5, mixing is due to diffusion, while for Re ˃ 5, mixing is caused by the secondary flow, separation vortices, and SAR effect. The ESAR micromixer (with balanced and unbalanced split) has higher mixing performance and less pressure drop than the CSAR micromixer over the entire range of Re and showed good mixing performance at Reynolds numbers ranging from 20 to 75. Xia et al. (2011) investigated experimentally and numerically mixing performance in a planar asymmetric split-and-recombine micromixer with a fan-shaped cavity at Re = 1–80. They observed higher mixing due to the combination of expansion vortices (caused by the converging-diverging structure of the fan-shaped cavity) and Dean Vortices, along with unbalanced inertial collisions. The proposed micromixer having a fan-shaped cavity of width equal to three times the width of the major sub-channel, achieved a mixing index of around 75% at Re ≥ 60. Hossain and Kim (2014) designed a passive micromixer with unbalanced three-split rhombic sub- channels and evaluated performance against a two-split micromixer at several Reynolds numbers ranging from 0.1 to 120. They observed that the mixing performance of the three-split rhombic microchannel is 1.49, 1.67, 1.56, and 1.44 times higher than the corresponding two splits at Re = 30, 40, 50, and 60, respectively. Further, Hossain and Kim (2015) investigated the mixing performance of a 3D serpentine split-and-recombine microchannel consisting of a series of "OH"-shaped segments in a Reynolds number range of 0.1–120. They observed that continuous split-and-recombine of the fluid streams due to the O- and H-structures generates chaotic advection and thereby improves the mixing. The inclusion of SAR design with the serpentine structure improved the mixing performance compared to a previously proposed 3D serpentine design in a Reynolds number range of 0.1–70. Gidde et al. (2019a) numerically investigated the flow features, mixing performance, and pressure drop in a proposed eye-shaped split and collision (ES-SAC) passive micromixer for Re ranging from 0.1 to 45. They reported that mixing performance is enhanced due to the unbalanced collision of the two fluid streams in the sub-channels of unequal widths. Among three different ratios of the sub-channel width, i.e., 1, 1.4, Design and Mixing Performance of Passive Micromixers: A Critical Review 111 and 2, the least mixing was observed for the width ratio of 1, while the highest mixing was observed for the width ratio of 2. Furthermore, the pressure drop in the micromixer with a sub-channel width ratio of 2 was the least among the three different width ratios. Nimafar et al. (2012) proposed a microchannel of an H-shape in which the fluid split and repeatedly recombined to maximize the diffusive mixing. The experimental Investigation demonstrated that H-micromixer was more efficient than the other two tested devices, i.e., T- and O-micromixer, in the Reynolds number range of 0.08–4.16. The new H-micromixer indicated a mixing performance of 98% at Re = 0.083. Viktorov et al. (2015) proposed two modified designs of chain mixers, i.e., the Y-Y and the H-C microchannel based on the SAR principle, and investigated mixing and flow numerically and experimentally for Reynolds numbers ranging from 1 to 100. The mixing efficiency of these two passive micromixers showed flat characteristics with a value higher than 90% over the entire range of the Reynolds number investigated, while the mixing efficiency of the teardrop mixer showed a decrease in the mid-range of the Reynolds number. Moreover, the pressure drop was also less in the newly proposed designs as compared to the teardrop micromixer. Ansari et al. (2010) evaluated the mixing performance of a SAR micromixer having sub- channels of unequal widths using numerical simulations and experiments at different Reynolds numbers between 10 and 80. The sub-channels of unequal widths caused unequal mass flux splitting and unbalanced collision on the recombination of mixing species. The combined effect of SAR, unbalanced collisions of the fluid streams, and Dean Vortices in the curved channels caused mixing enhancements. When the major sub-channel was twice as wide as the minor sub-channel, maximum mixing performance was achieved at a Re value greater than 40. Ruijin et al. (2017) proposed a passive micromixer that generates continuous lamination layers using Baker transformation for mixing enhancement. They investigated the mixing performance numerically for Reynolds numbers ranging from 0.01 to 10 and compared its performance against other splitting- merging micromixers such as Helical-mixer and Smale-mixer. They found that the Baker mixer achieved higher mixer efficiency due to a better stratification effect than those in the Helical-mixer and Smale-mixer at low Reynolds numbers. However, due to the convection–dominant mixing at the higher Reynolds numbers, the Baker mixer showed lower mixing compared to the other two mixers. Furthermore, due to the presence of contracting channels in the Baker mixer, the pressure drop through it was higher than that in the other two mixers. Pennella et al. (2012) reported planar SAR micromixers with variable curvature, i.e., clothoid- shaped mixing units. They investigated the mixing performance numerically and experimentally for a Reynolds number range of 1 to 110. Due to the secondary flows in the repetitive mixing units and recirculation effects at the junctions of the unit, the proposed mixer achieved a mixing efficiency of 80% for the Reynolds number greater than 70. Yang et al. (2015) proposed a passive micromixer with 3D Tesla structures and investigated the mixing performance experimentally and numerically for Reynolds numbers ranging from 0.1 to 100. The proposed micromixer showed a maximum mixing efficiency of 94% and a pressure drop of less than 1054 Pa at Re = 100. Le et al. (2014) designed a microchannel that utilizes the impact of stretching-folding in both vertical and horizontal directions through vortices and transverse flow to enhance the performance even for low Re values. They evaluated the mixing performance numerically and reported high efficiency (more than 80%) for Reynolds numbers ranging from 0.5 to 60. The new design indicated 220-240% higher mixing efficiency than a rhombic mixer with branch channels and pure rhombic at a low-Re value. Ta et al. (2015) proposed a trapezoidal channel arranged in a zigzag pattern (TZM) for mixing based on the SAR principle at low Re. The numerical simulation results indicated a mixing efficiency of more than 81% for Re values in the range of 0.1 to 80. For Re ≤ 0.9 and Re ≥ 20, the mixing efficiency was more than 90%. Additionally, the mixing efficiency of the proposed design was 4.07 and 5.58 times as compared to three-split rhombic and T-shape micromixers, respectively, at Re = 20. The high mixing was due to the transverse flows and distortion of fluid streams. Sheu et al. (2012) performed numerical simulations and experiments for the mixing analysis of the proposed micromixers consisting of several staggered three-quarter ring-shaped channels and a semi-circular channel. They found that the staggered curved-channel mixer with a tapered channel achieved 20% higher mixing efficiency with 50% more pressure drop compared to the staggered curved-channel mixer with or without sudden-contracted channels. The Dean vortices formed in the curved channels due to uneven split-and-recombine structures and impingement effects enhanced the mixing in the channel. Tran-Minh et al. (2014) proposed a microchannel based on the SAR principle with ellipse-like micro-pillars and determined the performance using numerical simulations. The proposed design attained a mixing efficiency of 80% for Re values in the range of 1 to 80. Kefala et al. (2014) proposed a SAR mixer design with multiple labyrinthine spirals and conducted numerical simulations to compare its performance with the zigzag, spiral, and linear designs. They observed that the labyrinthine microchannel has higher mixing performance (63%) compared to the spiral (36.5%) and zigzag (35.5%) designs at Re = 0.5. The microchannel with spiral, zigzag, and labyrinthine designs showed higher mixing by 8%, 11%, and 92%, respectively, compared to the T-shape mixer. Chen et al. (2018) modified a previously existing Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 112 F-shaped mixer to propose three designs, namely E- shape, stacking E-shape micromixer (SESM), and folding E-shape micromixer (FESM). They evaluated their performance experimentally for Re values in the range of 0.5 to 100. The new designs work on the chaotic advection and SAR mechanism. The mixing efficiency of the F-mixer and E-mixer started to decrease after reaching a maximum value of 92% and 94%, respectively, at Re = 80. However, the mixing efficiency of FESM and SESM remained close to 100%. For 25 ≤ Re ≤ 80, all three modified designs performed better than the F-shaped mixer. At Re ˃ 80, the mixing performances of two-layer mixers were better than single-layer mixers. The SAR, in general, increases mixing performance due to bifurcation and collision. However, its effects are prominent in the advection regime. The unbalanced SAR shows improved performance over balanced SAR designs. Further, the square and elliptical-shaped mixing channels exhibited higher mixing performance than circular channels. The contraction and expansion of Dean vortices and distortion of flow streams increase fluid chaos resulting in enhanced mixing. 2.2.3 Convergent-divergent microchannels The passive micromixers with microchannel based on the Convergent-Divergent (C-D) principles have mixed first by the convergence of fluids and then by divergence repeatedly. The convergence of the fluid streams reduces the diffusion path length, which enhances the mixing. Furthermore, the fluid layers get stretched on entering the divergent section, which increases the surface area across which diffusion occurs. In addition, due to the sudden expansion of the flow area at high Reynolds numbers, expansion vortices are generated that contribute to mixing. Gidde et al. (2018) compared the mixing performance of passive planar micromixers having circular- and square-shaped mixing chambers numerically, at Reynolds numbers ranging from 0.1−75. At Re = 0.1, 1, and 5, both designs exhibited similar mixing performance; however, the micromixer with square chambers showed higher mixing performance (99% when Re < 1) compared to the circular chambered micromixer. Moreover, both designs with a constriction width of 200 µm attained a mixing index over 95% in a Reynolds number range of 15–75. Afzal and Kim (2015a) designed a C-D channel with sinusoidal channel walls. The C-D channel with sinusoidal walls was found to have 19% higher mixing efficiency as compared to straight, square-wave, zigzag, and sinusoidal microchannels with uniform cross-sections for a fixed mixing length. Further, the new design achieved 92% mixing performance (independent of Re in a range of Reynolds number, 0.25 ≤ Re ≤ 4) when sinusoidal walls have two periods. The design parameters, i.e., the aspect ratio of the cross-section, the ratio of amplitude to wavelength, and the Re values, affect the mixing performance of passive micromixers based on the C-D principle. Parsa et al. (2014) proposed a sinusoidal microchannel with C-D and evaluated the mixing performance by applying numerical simulations and experiments. They observed that the increase in the aspect ratio of the microchannel cross-section improves the mixing performance and reduces the pressure drop due to Dean Vortices formation for Re-value ranging from 0.2 to 50. Khan and Tandon (2017) modified a C-D channel as a wing- shaped and serpentine square wave and evaluated mixing performance via numerical simulations for Re values from 0.01 to 100. They found that a wing- shaped microchannel produced a mixing performance of 87% with a pressure drop of 72 k Pa at Re = 60. Additionally, a wing size of 100-μm gives better mixing efficiency than the 75-μm wings. Rampalli et al. (2020) modified serpentine square wave micromixers by replacing square wave with convergent-divergent portion and evaluated the mixing efficiency for low Reynolds numbers (Re < 100). They found that for Re-value less than ten, diffusion mechanism-controlled mixing in square wave convergent-divergent (SQW-CD) mixer, stretching and folding due to C-D caused mixing when Re value was greater than 10. The SQW-CD mixer performed better than the conventional square wave mixer when Re-value was greater than 10. Hong et al. (2019) designed a gourd-shaped (contract and expand) microchannel and performed a numerical simulation to evaluate the mixing performance (Re values from 1 to 100). The enhancement of mixing was due to vortex generation in the proposed design, and it achieved a mixing efficiency of 83% with a pressure drop of 4860 Pa at Re = 100. The aspect ratio, amplitude, and pitch of the converging-diverging units play a significant role in mixing enhancement along with the contraction and expansion of the fluid streams. Further, a spiral channel with sinusoidal wave-shaped mixing units, which inherently consists of convergent and divergent portions, shows better mixing due to the synergetic effects of Dean vortices, folding, and stretching of fluid interfaces. 2.2.4 Hybrid design based on combined structures of SAR, C-D, and others There is a number of passive micromixers based on SAR, C-D, and other principles combined to achieve higher mixing at different values of Re. Afzal and Kim (2012) introduced a hybrid design using principles of both SAR and C-D. The new design has convergent-divergent channel walls with sinusoidal variations, besides splitting the main channels into two and recombining. They measured the impact of the Reynolds number (between 10 and 70), sinusoidal wall amplitude, and channel aspect ratio on the mixing efficiency. They observed a symmetric double vortex pair at the throat of the convergent- divergent channel and secondary motions in the sub- channels, which enhanced the mixing performance. Design and Mixing Performance of Passive Micromixers: A Critical Review 113 Numerical simulation results revealed that the new design has a higher efficiency compared to the T-mixer and unbalanced split and collision micromixer. Gidde and Pawar (2020) studied numerical flow features and mixing performance of rectangular baffle- based triple split-and-recombine (RB-TSAR) and elliptical baffle-based triple split-and-recombine (EBTSAR) micromixers. Baffles of rectangular and elliptical shapes were placed in diffuser-shaped mixing chambers to generate flow in the transverse direction through the SAR mechanism. Baffles increase the contact area between the layers of mixing species by deflection and folding, thereby contributing to the mixing. The micromixer with elliptical baffles showed better mixing and less pressure drop compared to the micromixer with rectangular baffles due to strengthened secondary flow, separation vortices, and less flow resistance caused by the curved shape. Furthermore, the increase in the divergence angle of the diffuser caused mixing to improve and a reduction in pressure drop. Fan and Hassan (2010) studied experimentally, and numerically a scaled-up micromixer having units called cross and omega at 1 ≤ Re ≤ 50. In addition to the Dean vortices at high Reynolds numbers, split-and- recombine in cross units and focusing/diverging in the omega units were the main mixing mechanisms. The proposed design with five cells achieved a mixing efficiency of 70% at Re = 50, which indicates that this design can be used at high flow rates. Xie et al. (2010) introduced a new design of micromixers with eight semicircles in the microchannel and measured mixing performance both numerically and experimentally for Re values in the range of 0.08 to 40. They observed higher mixing performance (i.e., 90%, for Re < 0.1 and Re > 10) compared to a simple T-shape mixer. Moghimi and Jalali (2020) proposed a micromixer in which mixing occurred through multi-lamination and flow-resistance reduction caused due to combined usage of injection and recombination in a zigzag layout. Experimental and numerical results indicated that the proposed mixer attained a mixing efficiency of 98.02% in a short length of 1858 microns. Cheri et al. (2013) proposed eight planar micromixer designs using four different shapes of obstacles (Straight (S), Arc (A), Chevron (Ch), and Check Mark (CM)) in two different chambers (round corner rectangular (RCR) and hexagon (H)). Using numerical simulations for the mixing analysis in the Reynolds number range of 0.1– 40, it was found that the RCR-S mixer showed optimum performance among the eight mixers with a maximum value of mixing efficiency to pressure drop ratio. The experimental data verified the numerical results that RCR-S micromixer achieved a mixing efficiency of 0.89 and 0.99 in a length of 1.18 mm at Re = 0.1 and 40, respectively. The RCR and H chambers with different obstacles showed minimum pressure drop and maximum efficiency, respectively. The sinusoidal form of sub-channels, which inherently have contraction and expansion passages, exhibited significant mixing improvement. The divergence angle plays a critical role in a diverging mixing chamber. Further, a round-cornered rectangular mixing chamber is preferred over a sharp-cornered rectangle. The baffles in a mixing chamber increase fluid chaos leading to higher mixing. 2.3 Lamination-based designs The lamination-based passive micromixers implement parallel (SadAbadi et al., 2013) and sequential/serial (Lim et al., 2011) lamination techniques to enhance mixing performance. In parallel lamination, each mixing fluid stream is divided into two or more streams which are joined together to form a single stream comprising alternate layers of each mixing fluid side by side. While in sequential/serial lamination mixer designs, the fluid stream (from the inlet) is split and recombined serially (Taheri et al., 2019). Here two or more sub-streams emerge from the inlet stream, and at the recombining point, they are joined again as a single stream. As the number of sub-streams increases, the mixing performances are enhanced. Lim et al. (2011) compared the mixing performance of a 3D (CMM) with a conventional passive micromixer applying numerical simulations and experiments (Lim et al. 2011). They modified CMM by adding six layers of horizontally and vertically crossing manifold micromixer (H/V-CMM) and achieved a mixing efficiency of over 90% in a channel of length (250 mm) less than five times the channel width. The split-and- recombine and the momentum of the fluids were the main mixing mechanisms in theses designs. Moreover, in a lamination based passive micromixers, there can be crossing manifold structure with horizontally crossing manifold micromixer (H-CMM), and vertically crossing manifold micromixer (V-CMM). Buchegger et al. (2011) proposed a horizontal multi-lamination micromixer having wedge-shaped vertical fluid inlets for enhanced mixing performance in a short time. The wedge-shaped inlets produced uniform lamination layers, which were not observed in the micromixer with a straight inlet. Nakahara et al. (2011) proposed a 3D passive lamination micromixer comprised of a multilayered flow generator. By using the proposed technique of the flow generator, multilayer flows were combined in a channel to generate fluid layers with reduced diffusion length. The experimental Investigation showed that the proposed design achieved 1.64 times faster mixing compared to a micromixer with Y-inlet. Generally, the mixing increases with the increase in the number of sub-streams. The wedge-shaped inlets produce uniform diffusion layers hence, improved mixing efficiency. Further, crossing manifolds, although they increased the width of the mixing channel, improved the mixing efficiency significantly. 2.4. Based on flow obstacles The obstacles in the flow streams enhance the mixing performance through the generation of vortices and Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 114 chaotic advection, thereby shortening the diffusion path length. Depending upon the positioning of the obstacles, the passive micromixers can be categorized as micromixers with obstacles furrowed/attached to the sidewalls, micromixers with obstacles inside the channels, i.e., attached to the top/bottom wall, and micromixers with herringbone grooves/ribs as obstacles. 2.4.1. Obstacles furrowed/attached/embedded on the channel sidewalls Under this category, the designs with obstacles of different shapes attached to the sidewalls of the straight/curved microchannels are discussed. Nason et al. (2014) numerically studied flow and mixing in a 3D channel with rectangular- and triangular-shaped obstacles on the walls for Reynolds numbers in the range of 10 to 100. The effect of phase shift of obstacles, channel aspect ratio, and obstacle height on mixing and pressure drop were studied. The greater phase shift of the obstacles produced enhanced mixing because of increased recirculation in the cross-section along with a lower pressure drop compared to a no-phase shift of the obstacles. The design having triangular-shaped obstacles achieved higher mixing performance and lower pressure drop than the design with rectangular- shaped obstacles. The effect of the channel aspect ratio on the mixing was insignificant, but the pressure drop varied significantly and showed the highest pressure drop for the highest aspect ratio. Furthermore, the design with the largest obstruction height showed maximum mixing at higher Reynolds numbers. Sarma and Patowari (2016) numerically investigated the mixing and pressure drop in passive micromixers with rectangular-, triangular- and semicircular-shaped obstructions attached to the wall in a flow of ultra-low Reynolds number of 0.053334. The authors investigated the effects of different parameters, i.e., intersection angle between the inlets (Eθ), obstacle arrangement, obstacle depth, channel aspect ratio (AR), and obstacle packing factor (OPF) on mixing efficiency, and found that the design with rectangular-shaped obstacles achieved the highest mixing with the highest pressure drop, while triangular and semi-circular obstacles had a similar mixing performance. The design with triangular obstacles showed the least pressure drop among these designs. The design with a staggered arrangement showed the highest mixing without significant change in pressure drop. Moreover, the greater obstacle depth and obstacle packing factor increased both mixing and pressure drop, whereas a larger entrance angle enhanced mixing with a negligible effect on the pressure drop. Wang et al. (2015) investigated numerically mixing in a channel with symmetrical cylindrical furrows /grooves for Re = 1–500. They reported that the addition of grooves in the channel increased the mixing performance by 2.22 and 2.18 times compared to conventional Y-micromixer at Re = 10 and 100, respectively. Vijayanandh et al. (2019) studied the effect of different shapes (square, curved, and triangular) of ridges attached to the wall of a meandering channel. They reported that the channel with triangular-shaped ridges has higher mixing performance compared to the geometries with square- and curved-shaped ridges. Tsai and Wu (2011) designed a planar passive micromixer consisting of radial baffles in a curved channel. Multidirectional vortices, i.e., Dean Vortices due to the curved channel and longitudinal vortices due to the radial obstacles, produced significant mixing in this design. Milotin and Lelea (2016) investigated mixing in three passive micromixers ( design with no baffle in microtube, design with four baffles covering the half of the cross-section, and the design with four baffles covering the quarter of the cross-section) for Re = 0.2 – 91. The baffles covering the quarter of the cross-section showed higher mixing for all Re values due to rotational flow, increased interface area and higher residence time caused by 90°– delayed orifice. Lin et al. (2011) designed a chaotic micromixer consisting of a square-wave structure and periodic cubic grooves. The experimental comparison indicated that the overall performance was better than the performances of Accoris, slit interdigital, caterpillar, and T-mixer for Re values from 30 to 220. The higher mixing was due to the combined effect of flow stretching (caused by cubic grooves) and laminar recirculation (caused by square-wave structure). Fractal structures such as Cantor, Minkowski, and Koch have also been used as obstacles by many researchers to enhance mixing. Wu and Chen (2019b) proposed a rectangular fractal-based micromixer named imitate Cantor structure (ICS). The effects of fractal obstacle number, obstacle height, fractal series, and obstacle spacing on mixing were studied using numerical simulations. The better performance of a quadratic fractal series with four obstacles as compared to the primary fractal series with the same number of obstacles indicated that the increase in the number of obstacles and fractal series has a positive impact on the mixing. Furthermore, a staggered arrangement with zero spacing and the largest height showed efficient performance due to vortex generation. Wu and Chen (2019a) introduced a 3D micromixer consisting of a Cantor structure termed as Imitate Cantor Structure Micromixer (ICSM). The Cantor- based obstacle improved mixing with the mechanisms of chaotic advection and folding of fluid interfaces. They investigated the impact of channel height, obstacle height, the spacing between the obstacles, and fractal obstacles arrangement on mixing performance for Reynolds numbers ranging from 0.01 to 100. Different configurations were obtained through variations in the above-mentioned parameters, which showed mixing performance of over 90% for 0.1 > Re > 50. The ICSM with a channel height of 600 μm showed the best performance with a minimum efficiency of 85% over the entire range of Re. The Design and Mixing Performance of Passive Micromixers: A Critical Review 115 increase in the channel height increased an increase in the effective area for fluid folding and, thus, mixing. Chen and Chen (2020) examined the effect of Minkowski fractal obstacles of both primary and secondary types on the mixing and pressure drop at Re = 0.01, 0.1, 1, 10, and 100. The micromixer with secondary Minkowski fractal obstacles showed better mixing than the micromixer with primary type obstacles with a value of more than 98% at Re = 0.01, 0.1, and 100, but with a higher pressure drop. Mixing was enhanced due to vortex formation and chaotic convection with an increase in the obstacle height and a reduction in the obstacle spacing. The vortex due to fractal obstruction was more obvious in the micromixer with minimum obstacle spacing, maximum obstacle height, and the highest Reynolds number. Zhang and Chen (2018) examined the impact of height, spacing, numbers, and configurations of the Koch fractal obstacles attached to the sidewalls on mixing performance. They concluded that greater height, more number, and less spacing of the obstacles have a positive effect on mixing performance. Different configurations formed with four obstacles have a negligible effect on the mixing. The vortex areas produced due to the obstacle helped the mixer to achieve an efficiency of more than 90% at Re = 0.03 and 240. In a similar study with Koch fractal obstacle, X. Chen and Tian (2020) studied the effects of depth, spacing, number, angular inclination, and distribution of baffles on the mixing. The configuration with the bilateral arrangement showed better mixing than the single-sided baffle structure at Re ≥ 10. Furthermore, the design with a lesser spacing, more numbers, and higher inclination of baffles showed better mixing performance. Chen et al. (2019b) studied the effects of rounding the corners of obstacles and examined mixing in the primary fractal micromixer (PFM), secondary fractal micromixer (SFM), and rounding the corners of the secondary fractal micromixer (RCSM). They noticed a higher mixing efficiency of SFM (over 90 % at 0.1, 1, 10, and 100) and RCSM compared to PFM. The rounding of the corner reduced the pressure drop significantly with a slight decrease in mixing compared to SFM. Chen and Chen (2019) proposed several topological micromixers with circular structures (TMCs) with different ratios of an obstacle to channel height using the topological optimization method. The obstacles reversed the flow and promoted mixing through an increased flow path at low-Re and enhanced chaotic advection at high-Re. The mixing was obtained in the configuration TMC0.75 with an efficiency of more than 90% over the entire Re-range. The chaotic advection in the circular mixer was seen at Re = 50, while in the TMC mixer, it was observed at Re = 10. Cortes-Quiroz et al. (2010) performed numerical Simulation and Optimization of a T- micromixer having curved baffles attached to the wall over a Reynolds number range of 1–250. They studied the effects of baffle radius, baffle pitch, and height of the channel on the mixing and pressure drop. The mixing was enhanced due to recirculation and transversal flows caused by the radial baffles. Besides, the curved shape reduces dead volumes and the issue of clogging in the mixer. The proposed design achieved a mixing of over 85% for Re = 1 and ≥ 50. However, due to the larger pressure drop for Re > 100, a Reynolds number range of 50–100 was recommended for efficient operation. Xu and Chen (2019) proposed four passive micromixers, i.e., common micromixer (CM), common micromixer with scaling elements (CMWSE), snake-like micromixer (SM), and snake- like micromixer with scaling elements (SMWSE), and evaluated their mixing performance and pressure drop using numerical simulations. They observed that scaling elements enhance chaotic advection and thus positively affect the mixing performance. The order of mixing performance exhibited was as SMWSE (over 92 %) > SM > SMWSE > CM. However, the pressure drop in the mixers with scaling elements was found to be higher than in the designs without it. The recirculation and transverse flow induced by the baffle, obstacles, and groves on the channel walls, in general, increased flow mixing, which is further increased with the increase in the height of the obstacles/baffles. Further, the packing factor and spread of these obstacles significantly affect the mixing and pressure drop in the channel. The secondary fractals add to the mixing phenomena; moreover, rounding of fractal corners reduces pressure drop significantly with a small decrease in mixing performance. 2.4.2. Obstacles attached to the top/bottom walls Several researchers have performed the mixing enhancement by placing obstacles inside the channel by attaching them to the top/bottom walls. Monaco et al. (2010) studied the effects of different shapes and arrangements of obstacles on the mixing in a T-mixer using the Lattice-Boltzmann method. They reported that the layout of obstacles is a more dominant factor for mixing enhancement than using many obstacles. Furthermore, rectangular-shaped obstacles showed the best mixing. Chen and Zhao (2017) performed the Optimization of obstacles-layout in a T- mixer through an orthogonal experiment and investigated the decreasing order of sensitive parameters, i.e., obstacles height > geometric shape > symmetric layout = a number of obstacles. The optimized multi-unit obstacle micromixer showed more than 90% mixing over a wide range of Peclet numbers. The blockage due to the obstacles changed the velocity field and promoted chaotic advection to enhance the mixing. Alam et al. (2014) studied the impact of cylindrical obstacles in a curved microchannel on the mixing performance, applying numerical simulations for Re values in the range of 0.1 to 60. They noticed higher Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 116 mixing efficiency for the design with cylindrical obstacles in a curved microchannel (88 % at Re =0.1 and Re > 15) compared to the designs with circular obstacles in a T-shape channel and a simple curved channel. The circular and hexagonal obstructions showed similar mixing performances at all Re values; on the other hand, diamond obstructions had less mixing performance except at Re = 50. Wang et al. (2014) proposed a passive mixer with triangular baffles embedded in the main channel and evaluated mixing both experimentally and numerically at different Re values ranging from 0.1 to 500. The proposed design showed higher mixing (2.48, 4.75, and 8.32 times at Re = 1.0, 100, and 500, respectively) than a conventional Y-shape mixer. The mixing increased with the increase in the apical angles of the triangle and the number of triangles. Out of cross, triangle, pentagon, star, hexagon, and I-shape obstacles in the Y-shape passive micromixers, obstacles with sharp edges showed higher mixing performance. The mixing performance of cross, star-, and I-shaped obstacles was 77%, 75%, and 72%, respectively (Pravinraj and Patrikar, 2019). The addition of a screw-shaped propeller blade in a Y- mixer generated additional flow disturbances in the z- direction and, thus, more mixing compared to a flat- shaped blade (Liu et al., 2014). The design, even with a single screw-shaped propeller blade, achieved a mixing of over 80% for a flow rate of 12 µl/min. The introduction of a porous twisted tape (permeability = 10-10 m2) in a T-channel improved the mixing at low to medium Re, while the solid twisted tape improved the mixing at high-Re (Kurnia and Sasmito, 2019). The twisted tape increased the secondary flow and convective mass transfer with an additional pressure drop. Pendharkar and Patrikar (2014) designed a hexagonal passive micromixer and studied the effects of microchannel fabrication on mixing performance for Re values in the range of 0.1 to 0.5. The addition of roughness to the passive mixer geometry resulted in an improvement in mixing (up to 10% at Re = 0.1 to 0.5). Shi et al. (2019) numerically studied mixing in a Koch fractal-based obstructions micromixer and reported that the obstruction pattern present on the top wall (same side) of the channel wall produced more mixing (approx. 98.2%, at Re = 0.1). Cook et al. (2012) designed a planar scaled-up micromixer consisting of an uneven interdigital inlet, staggered teardrop-shaped obstructions, and wall protrusions. The experimental Investigation at Re = 1˗100 showed that the proposed design achieved the maximum efficiency of 68.5% at Re = 1 because of multi-lamination caused by the uneven interdigital inlet. The vortices formed due to the obstructions caused mixing at high Reynolds numbers. The layout of the obstacles is a more significant parameter than the number of obstacles, although mixing efficiency increases with an increase in the number of obstacles, which directly contributes to pressure drop in the channel. The sharp-edged obstacles are more effective for mixing enhancement. Furthermore, the packing of obstacles may have deteriorating effects due to the trapping of fluid on the mixing performance. 2.4.3. Ribs and grooves as obstacles Many researchers have implemented obstacles in the form of ribs and grooves to enhance the chaotic motion of the fluids and mixing. Several findings have revealed that the more the number of internal ribs, the higher the mixing performance of passive micromixers. The height of a channel affects the flow, and the most effective ratio of the height of the main channel to the herringbone structure was found to be 2:1 (Whulanza et al., 2018). The closely spaced blocks in the microchannel can result in the trapping of fluid and can affect the mixing throughput. Kim et al. (2011) studied the effects of four geometric parameters of ribs, such as rib angle, rib height, rib width, and rib spacing numerically, to optimize the mixing performance using the response surface method. The increase in the rib height reduced the area between the wall and rib, which caused the transversal velocity of the vortices to increase and, thus, the mixing. They observed maximum mixing efficiency (over 90 % with channel length 1344 µm) when rib angle, rib height/channel depth, rib width/rib height, and rib spacing/rib height were 35.6°, 0.7, 0.127, and 1.10, respectively. Du et al. (2010) analyzed the mixing performances of slanted groove micromixers (SGMs) numerically and staggered herringbone micromixers (SHMs) (Pendharkar, 2014). Single helical flow in SGM and two helical flows, i.e., large vortex for long arm and small vortex for shorter arm in SHM, were observed. Furthermore, a large peak-to-peak distance in the concentration profile and slow convergence were observed in SGM. Hence, faster and more efficient mixing in SHM, while slower and coarser mixing in SGM was noticed. Guo et al. (2010) studied numerically the impact of rib width, pitch, and channel aspect ratio on mixing performance. The mixing performance of the proposed design decreased with the increase of H/W (channel height/channel width) up to a value of 0.6, and beyond that, the influence was negligible. The ribs caused enlargement of the interfacial area, and thus higher mixing was seen with the addition of more ribs and larger width of rib. In an experiment conducted on a passive scaled-up micromixer with four meandering elements and 36 slanted grooved structures (horizontally stacked), Cook and Hasan (2011) reported higher performance with the increment in the value of Re from 5 to 100 due to the formation of Dean vortices. Additionally, Cook et al. (2013) designed a scaled-up passive micromixer consisting of a main mixing channel of 155.8 mm long, 3 mm wide, and 0.75 mm deep, with nine slanted grooves, and measured the mixing performance experimentally and numerically for Re values ranging from 0.5 to 100. They reported mixing performance Design and Mixing Performance of Passive Micromixers: A Critical Review 117 from 53% at Re = 5 up to 90% at Re = 100. The Dean vortices and helical flows were formed due to the curved channel structure and grooves, respectively. Chen et al. (2015) designed a passive micromixer having dual opposing strips on the top and bottom walls of a microchannel and varying cross-sectional area to enhance mixing performance by increasing contact surface area, two-layer vortices generation, and enhanced diffusion flux. The numerical Simulation revealed mixing performance of 93.97%, 92.53%, and 92.49% at Re = 0.56, 2.8, and 5.6, respectively. However, misalignment between the top and bottom grooves reduced the mixing. Fan and Hassan (2010) proposed a curved micromixer with grooves (CMG) and compared its mixing performance with a slanted grooved micromixer (SGM) and curved micromixer without grooves (CM) for Re values in the range of 1 to 50. CMG showed better performance than SGM and CM. In addition, both CMG and SGM achieved better mixing than CM at Re = 1.0. The new design showed 60% mixing efficiency at Re = 50 with a 1.8 kPa pressure drop. At high Re values, the curved channel created the Dean vortices, while slanted grooves generated helical flow at low-Re values. The elements optimized for the new design included the slanted angle (θ), the width of the grooves angle (ω), and the height ratio of grooves to channel height (Hg/H). Okuducu and Aral (2019b) proposed a passive micromixer with semi-circular ridges in the microchannel. The new design with the convex alignment of semi-circular elements was found to have a mixing index and mixing performance more than the classical T-shape mixer by the factors of 8.7 (at Re = 1 to 10) and 3.3 (at Re = 20), respectively. They reported the enhanced mixing (over 80 %) due to the helicoidal- shaped fluid stream generated by the convex alignment of semi-circular elements for Re values from 0.1 and 40. The staggered herringbone design has V-shaped ridges attached to the channel walls, and these arrangements enhance mixing at low Re values by creating transverse flow patterns. Hama et al. (2018) proposed a micromixer (reverse-staggered herringbone) based on staggered herringbone design geometry and evaluated the mixing performance both numerically and experimentally. They found that the flow rate ratio of fluids positively affects the mixing; however, the Re values impact was not significant in the first three and six cycles. The number of ribs creates more chaos. Hence more mixing of fluid in the channel, the rib height to channel height ratio is a critical parameter in micromixer design; the larger the ratio greater the mixing. A staggered herringbone groove micromixer, which induces dual helical flows, performs better than a mixer with inline helical grooves. 3. ANALYSIS AND DISCUSSION The Reynolds number and Peclet number are the two significant parameters for the design of passive micromixers. Hence, for an accurate comparison of the performance of different micromixer designs and configurations, it is essential to define these numbers in a similar manner and at the same location. However, after a thorough literature review, it was noticed that most of the studies had defined these numbers either at the inlets or at the main channel. Therefore, carrying out performance comparisons between different designs based on these numbers is highly cumbersome. Furthermore, the review of studies reveals that most of the studies performed have reported only mixing index without attributing proper significance to the pressure drop encountered, device fabrication methods, design complexity, wettability effects, and surface roughness. Hence, for proper advancement of the micromixer designs and their adoption to real applications, the issues mentioned above should be addressed through a proper design criterion prepared by the research community for future studies. The research studies on micromixers have highlighted that many variables, such as geometric parameters, mixing-channel designs, and flow Reynolds numbers, affect the mixing performance. The high Reynolds number value reduces the contact time between the two fluids and decreases mass diffusion leading to lower efficiency in diffusive mixing-based designs. The fluid mixing at a very low Re value is dominated by the residence time and the total path of the flow (Nason et al., 2014). This study presents a classification of micromixers into several categories, such as designed inlets, designed mixing channels, lamination phenomenon, and flow obstacles. Additionally, charts and graphs present the study outcomes. Analysis of the research studies has shown important outcomes, which will assist in understanding various aspects of micromixers. Figure 5 shows the published articles and evaluation methods used in the studies. The year 2019 reported the highest number of studies, followed by 2014, 2015, 2011, and 2018. The performance evaluation methods used in these studies are mainly numerical simulations or both numerical simulations and experiments, while very few have carried out the only experimental study. The maximum number of studies correspond to experiments and numerical simulations together, followed by numerical simulations alone. Most of the studies revealed that numerical simulations show relatively higher mixing than the actual value achieved through experiments. But a great deal of work has been done on mixing performance via numerical simulations. However, the reliability of the results is always doubtful due to external factors of the real environment unless they are substantiated with experiments. Hence, there is a need to conduct more studies with experiments for measuring the micromixer performance rather than doing only numerical simulations. Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 118 Figure 5. (a) The number of published articles on passive micromixers, and (b) Evaluation methods used in passive micromixers. Figure 6. (a) Design type as reported in different studies, and (b) Mixing-channel designs as reported in different studies. (a) (b) (a) (b) Design and Mixing Performance of Passive Micromixers: A Critical Review 119 (a) (b) Figure 7. (a) Number of articles with different inlet shape, and (b) Number of inlets as reported in the existing studies. (a) (b) Figure 8. (a) The mixing performance of passive micromixers, and (b) Re values considered in the existing studies. Figure 6 shows the distribution of the studies carried out under different microchannel categories and mixing-channel designs. It shows that the maximum number of obstacle-based designs have been proposed, followed by SAR, mixed category, designed inlet, C-D, and wave. The microchannel has various designs as sinusoidal, square, trapezoidal, etc. The passive micromixers have inlet shapes as Y-, T-, F-, E-, H-C, Tapered, and hybrid. The number of studies on micromixers is plotted against inlet shape. The maximum number of passive micromixers reported have inlet shape as T-, followed by Y-, and hybrid. Moreover, the most reported number of inlets is two, followed by three. Most of the researchers who reported high performance have used two inlets. Figure 7 shows the distribution of studies reported under different inlet shapes and their numbers. Most of the studies have reported achieving maximum mixing performance between 80 and 100%. Very few of them have shown mixing performance between 60 to 75 %. Figure 8 shows the mixing performance of passive micromixers and the range of Re values reported in the existing studies. Although the results of the analysis cannot firmly establish the superiority of one method over the others, it can qualify for demonstrating the trends of passive micromixer performance concerning different factors. Appendix A presents the reported studies with above 90% mixing performance, including Re values, designs, and other details. 4. CONCLUSION The number of articles on passive micromixers has increased significantly due to proposed wider applications; however, the research on the mixing performance and micromixer designs is highly fragmented. This review of designs and mixing performance of micromixers have classified passive micromixers based on the designed inlets, mixing- channel design, fluid lamination, and obstacles in the channel. Based on this review study, the following points can be concluded: 1. Most of the researchers have used numerical simulations for evaluating micromixer designs, although the simulation results are not always comparable to physical experiments. 2. Micromixers with T-shape inlets and two inlets are the most preferred choice of micromixers researchers. The obstacles and SAR-based micromixer designs have the edge over other types. Moreover, new mixing-channel designs, such as the Koch fractal and Minkowski fractal, are under Investigation for higher mixing performance. 3. Although several designs have demonstrated higher mixing performance using water-dye experimental and numerical studies, there is a scarcity of work that can demonstrate their capabilities in real applications. Furthermore, in most of these works, little consideration has been Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 120 given to the required device material and fabrication process. 4. The open literature lacks micromixer classification based on microfluidic applications. 5. The adoption of micromixers to the real application is highly dependent upon the ease of fabrication and device integration. Hence, future research should consider the factors like material, fabrication method, and design integration along with capabilities in proposed applications. 6. The micromixer designs demonstrating good merit in these aspects, in addition to better mixing, will help integrate them into microsystems for actual applications and accelerate the market growth of microfluidic systems. CONFLICT OF INTEREST The authors have no conflict of interest. FUNDING Deanship of Research Fund, Grant No. RF/ENG/MEID/19/01. ACKNOWLEDGMENT The authors acknowledge the support of Sultan Qaboos University, Oman, for conducting this research. REFERENCES Adam T, Hashim U (2012), Simulation of passive fluid driven micromixer for fast reaction assays in nano lab-on-chip domain. 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Design and Mixing Performance of Passive Micromixers: A Critical Review 125 Appendix A: Reference Year Inlet shape Inlet no Design type Mixing-channel design Mixing performance (max %) Re value Evaluation method (Moghimi and Jalali, 2020) 2020 Y-Shape 2 Mixed Injection, SAR, and zigzag 98.02 100 Both Numerical and Experimental (Chen and Chen, 2020) 2020 T-Shape 2 Obstacle Furrowed- Secondary Minkowski fractal 98 0.01 Numerical Simulation 98 1 98 100 (Chen and Tian, 2020) 2020 T-Shape 2 Obstacle Furrowed-Koch fractal (30 angle) 99.48 100 Numerical Simulation (Rampalli et al., 2020) 2020 T-Shape 2 C-D Serpentine square 100 160 < Or <180 Numerical Simulation (Wu and Chen, 2019a) 2019 T-Shape 2 Obstacle Furrowed- Imitate Cantor structure 90 >=50 Or <=0. 1 Numerical Simulation (Shi et al., 2019) 2019 T-Shape 2 Obstacle Inside-Koch fractal 98 0.1 Numerical Simulation (Chen and Chen, 2019) 2019 T-Shape 2 Obstacle Furrowed- Minkowski fractal 95 >=5 Numerical Simulation (Chen et al., 2019b) 2019 T-Shape 2 Obstacle Furrowed- Secondary Koch fractal 95 0.05- 100 Numerical Simulation 90 0.1- 100 (Mondal et al., 2019) 2019 T-Shape 2 C-D Raccoon 100 0.1- 100 Numerical Simulation Serpentine 100 0.1- 100 (Dundi et al., 2019) 2019 T-Shape 2 Designed inlet Swirl induced 95 106 Numerical Simulation (Gidde et al., 2019b) 2019 T-Shape 2 SAR Elliptic 99 20- 75 Numerical Simulation (Xu and Chen, 2019) 2019 Y-Shape 2 Obstacle Furrowed- SMWSE 92 22 Both Numerical and Experimental (Shi et al., 2019) 2019 T-Shape 2 Obstacle Inside- Koch obstacle 98.2 0.1 Numerical Simulation (Gidde et al., 2018) 2018 T-Shape 2 SAR Circular and square chamber 99 <1.0 Numerical Simulation (Zhang and Chen, 2018) 2018 T-Shape 2 Obstacle Furrowed-Koch fractal 99 0.03 Numerical Simulation 90 240 (Chen et al., 2018) 2018 F-Shape 2 SAR Stacked 92 80 Both Numerical and Experimental E-Shape 94 80 (Ansari et al., 2018) 2018 T-Shape 2 C-D Serpentine 91 2922 1 Both Numerical and Experimental (Mehrdel et al., 2018) 2018 T-Shape 3 Mixed Double spiral 98.5 0.1- 10 Both Numerical and Experimental Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 126 (Hama et al., 2018) 2018 T-Shape 2 Obstacle Ribs-Reverse staggered herringbone 98.5 100 Both Numerical and Experimental (Hossain et al., 2017) 2017 Y-Shape 2 SAR Serpentine 99 0.2- 10 Both Numerical and Experimental (Rafeie et al., 2017) 2017 Y-Shape 2 Wave Spiral 90 1- 1000 Numerical Simulation (Chen and Li, 2017) 2017 T-Shape 2 Obstacle Furrowed- Trapezoidal zigzag 95 <=0. 5 Or >=5 Both Numerical and Experimental (Chen et al., 2016a) 2016 T-Shape 2 Obstacle Furrowed- Trapezoidal zigzag 93 <=0. 5 or >=5 Numerical Simulation (Viktorov et al., 2016) 2016 H-C Shape 2 SAR H-C 90 >=1 Or <=10 0 Both Numerical and Experimental (Chen et al., 2016b) 2016 T-Shape 2 C-D Serpentine 95 0.1- 100 Both Numerical and Experimental (Milotin and Lelea, 2016) 2016 T-Shape 2 Obstacle Furrowed- Circular 100 0.2- 91 Numerical Simulation (Afzal and Kim, 2015a) 2015 T-Shape 2 C-D Sinusoidal 92 0.5 Numerical Simulation (Chen et al., 2015) 2015 Y-Shape 2 Obstacle Ribs-Two strips 93.97 0.56 Both Numerical and Experimental (Le The et al., 2015) 2015 Hybrid 3 SAR Trapezoidal 90 >= 20, Or <=0. 9 Both Numerical and Experimental (Liu et al., 2015) 2015 Y-Shape 2 Wave Double helical 99 0.003 -30 Both Numerical and Experimental (Al-Halhouli et al., 2015) 2015 T-Shape 2 Wave ILSC 100 0.01 - 50 Both Numerical and Experimental Omega 100 0.01 - 50 Semi-circular 100 > 50 (Viktorov et al., 2015) 2015 Y-Shape 2 SAR Chain (Y-Y and H-C) 90 1- 100 Both Numerical and Experimental (Ta et al., 2015) 2015 Hybrid 3 SAR Trapezoidal zigzag 94 >=20 Both Numerical and Experimental 90 <=0. 9 (Li et al., 2015) 2015 T-Shape 2 SAR Overbridge 90 0.01- 50 Both Numerical and Experimental (Yang et al., 2015) 2015 T-Shape 2 SAR Tesla 90 0.1- 100 Both Numerical and Experimental (Le The et al., 2014) 2014 Hybrid 3 SAR Trapezoidal 95 40 Both Numerical and Design and Mixing Performance of Passive Micromixers: A Critical Review 127 Experimental (Parsa et al., 2014) 2014 T-Shape 2 C-D Sinusoidal 99 0.2 Both Numerical and Experimental 99 >30 (Li et al., 2014) 2014 Y-Shape 2 SAR Triangular 90 0.01 Numerical Simulation (Nason et al., 2014) 2014 Y-Shape 2 Obstacle Furrowed- Triangular 90 50 Numerical Simulation (Wang et al., 2014) 2014 Y-Shape 2 Obstacle Inside-Triangular 91.2 0.1 Both Numerical and Experimental (Cheri et al., 2013) 2013 Hybrid 3 Mixed Hexagonal chamber 99 40 Both Numerical and Experimental (Hsieh et al., 2013) 2013 Hybrid 2 Designed inlet At -60° 99 0.027 Experiment (Cook et al., 2013) 2013 Y-Shape 2 Obstacle Ribs 90 100 Both Numerical and Experimental (Yang et al., 2013) 2013 Y-Shape 2 Wave Double Spiral 90 40 Both Numerical and Experimental (Viktorov and Nimafar, 2013) 2013 T-Shape 2 SAR Chain 98 0.416 Both Numerical and Experimental (Afzal and Kim, 2012) 2012 T-Shape 2 Mixed Sinusoidal wall 90 70 Numerical Simulation (Nimafar et al., 2012) 2012 H-Shape 2 SAR H-shape 98 0.083 Both Numerical and Experimental (Sheu et al., 2012) 2012 Tapered 2 SAR Staggered curve 90 50 Both Numerical and Experimental (Tsai and Wu, 2011) 2011 Y-Shape 2 Obstacle Furrowed-Radial 93 81 Both Numerical and Experimental (Lim et al., 2011) 2011 Multi- laminati on Mul tiple Laminatio n 3D-CMM 90 1 Experiment (Lin et al., 2011) 2011 Y-Shape 2 Obstacle Square Wave 90 >=40 Both Numerical and Experimental (Kim et al., 2011) 2011 T-Shape 2 Obstacle Rib 95 1.69 Both Numerical and Experimental (Tseng et al., 2011) 2011 Y-Shape 2 Obstacle Diamond 96 >10 Or <0.1 Numerical Simulation (Zadeh and Marahel, 2011) 2011 Hybrid 4 Designed inlet 300° 100 60 Numerical Simulation (Chung et al., 2010) 2010 Hybrid 3 SAR Rhombic 95 >180 Both Numerical and Experimental Afzal Husain, Asharul Islam Khan, Wasim Raza, Nabeel Al-Rawahi, Nasser Al-Azri, and Abdus Samad 128 (Du et al., 2010) 2010 T-Shape 2 Obstacle Staggered herringbone 95 0.3 Numerical Simulation (Xie et al., 2010) 2010 T-Shape 2 Mixed Semi-circular 90 <0.1 Or >10 Both Numerical and Experimental (Ansari et al., 2010) 2010 T-Shape 2 Mixed Unbalanced circles 90 >40 Both Numerical and Experimental (Cortes-Quiroz et al., 2010) 2010 T-Shape 2 Obstacle Furrowed- Curved 95 50- 100 Both Numerical and Experimental (Bhopte et al., 2010) 2010 Hybrid 4 Designed inlet Split 92 1 Numerical Simulation