A Review on Mixing in Microfluidics
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paper_title: Current methods for characterising mixing and flow in microchannels

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This article reviews existing methods for the characterisation of mixing and flow in microchannels, micromixers and microreactors. In particular, it analyses the current experimental techniques and methods available for characterising mixing and the associated phenomena in single and multiphase flow. The review shows that the majority of the experimental techniques used for characterising mixing and two-phase flow in microchannels employ optical methods, which require optical access to the flow, or off-line measurements. Indeed visual measurements are very important for the fundamental understanding of the physics of these flows and the rapid advances in optical measurement techniques, like confocal scanning laser microscopy and high resolution stereo micro particle image velocimetry, are now making full field data retrieval possible. However, integration of microchannel devices in industrial processes will require on-line measurements for process control that do not necessarily rely on optical techniques. Developments are being made in the areas of non-intrusive sensors, magnetic resonance techniques, ultrasonic spectroscopy and on-line flow through measurement cells. The advances made in these areas will certainly be of increasing interest in the future as microchannels are more frequently employed in continuous flow equipment for industrial applications.
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paper_title: Performance comparison of micromixers

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The present paper proposes a detailed comparison of mixing efficiency of different mixers that have been characterized by the Villermaux/Dushman test reaction. Considering simple relations of mixing in laminar flow, it is shown how to obtain the theoretical mixing time and how to relate it with operating parameters as the Reynolds number of the flow and the specific power dissipation per mass unit of fluid. The comparison of the experimental and of the theoretical mixing times indicates that only a few percents of the total mechanical power transmitted to the fluid is effective for mixing.
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paper_title: Micromixers—a review on passive and active mixing principles

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A review on microstructured mixer devices and their mixing principles concerning miscible liquids (and gases) is given. This is supplemented by the description of typical mixing element designs, methods for mixing characterisation, and application fields. The mixing principles applied can be divided in two classes relying either on the pumping energy or provision of other external energy to achieve mixing, termed passive and active mixing, respectively. As far as passive mixing is concerned, devices and techniques such as Y- and T-type flow-, multi-laminating-, split-and-recombine-, chaotic-, jet colliding-, recirculation flow-mixers and others are discussed. Active mixing can be accomplished by time-pulsing flow owing to a periodical change of pumping energy or electrical fields, acoustic fluid shaking, ultrasound, electrowetting-based droplet shaking, microstirrers, and others.
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paper_title: A review on the analysis and experiment of fluid flow and mixing in micro-channels

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The studies with respect to micro-channels and micro-mixers are expanding in many dimensions. Most significant area of micro-mixer study is the flow analysis in various micro-channel configurations. The flow phenomena in microchannel devices are quite different from that of the macro-scale devices. An attempt is made here to review the important recent literature available in the area of micro-channel flow analysis and mixing. The topics covered include the physics of flow in micro-channels and integrated simulation of the micro-channel flow. Also, the flow control models and electro-kinetically driven micro-channel flows are dealt in detail. A survey of important numerical methods, which are currently popular for micro-channel flow analysis, is carried out. Different options for mixing in microchannels are provided, in sufficient detail.
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paper_title: Micromixers—a review

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This review reports the progress on the recent development of micromixers. The review first presents the different micromixer types and designs. Micromixers in this review are categorized as passive micromixers and active micromixers. Due to the simple fabrication technology and the easy implementation in a complex microfluidic system, passive micromixers will be the focus of this review. Next, the review discusses the operation points of the micromixers based on characteristic dimensionless numbers such as Reynolds number Re, Peclet number Pe, and in dynamic cases the Strouhal number St. The fabrication technologies for different mixer types are also analysed. Quantification techniques for evaluation of the performance of micromixers are discussed. Finally, the review addresses typical applications of micromixers.
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paper_title: Stirring by chaotic advection

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In the Lagrangian representation, the problem of advection of a passive marker particle by a prescribed flow defines a dynamical system. For two-dimensional incompressible flow this system is Hamiltonian and has just one degree of freedom. For unsteady flow the system is non-autonomous and one must in general expect to observe chaotic particle motion. These ideas are developed and subsequently corroborated through the study of a very simple model which provides an idealization of a stirred tank. In the model the fluid is assumed incompressible and inviscid and its motion wholly two-dimensional. The agitator is modelled as a point vortex, which, together with its image(s) in the bounding contour, provides a source of unsteady potential flow. The motion of a particle in this model device is computed numerically. It is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator. With the agitator held at a fixed position, integrable marker motion ensues, and the model device does not stir very efficiently. If, on the other hand, the agitator is moved in such a way that the potential flow is unsteady, chaotic marker motion can be produced. This leads to efficient stirring. A certain case of the general model, for which the differential equations can be integrated for a finite time to produce an explicitly given, invertible, area-preserving mapping, is used for the calculations. The paper contains discussion of several issues that put this regime of chaotic advection in perspective relative to both the subject of turbulent advection and to recent work on critical points in the advection patterns of steady laminar flows. Extensions of the model, and the notion of chaotic advection, to more realistic flow situations are commented upon.
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paper_title: Micromixers—a review

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This review reports the progress on the recent development of micromixers. The review first presents the different micromixer types and designs. Micromixers in this review are categorized as passive micromixers and active micromixers. Due to the simple fabrication technology and the easy implementation in a complex microfluidic system, passive micromixers will be the focus of this review. Next, the review discusses the operation points of the micromixers based on characteristic dimensionless numbers such as Reynolds number Re, Peclet number Pe, and in dynamic cases the Strouhal number St. The fabrication technologies for different mixer types are also analysed. Quantification techniques for evaluation of the performance of micromixers are discussed. Finally, the review addresses typical applications of micromixers.
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paper_title: The Kinematics of Mixing: Stretching, Chaos, and Transport

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Preface Acknowledgments 1. Introduction 2. Flow, trajectories and deformation 3. Conservation equations, change of frame, and vorticity 4. Computation of stretching and efficiency 5. Chaos in dynamical systems 6. Chaos in Hamiltonian systems 7. Mixing and chaos in two-dimensional time-periodic flows 8. Mixing and chaos in three-dimensional and open flows 9. Epilogue: diffusion and reaction in lamellar structures and microstructures in chaotic flows Appendix List of frequently used symbols References Author index Subject index.
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paper_title: Silicon Micromixers with Infrared Detection for Studies of Liquid-Phase Reactions

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We present an integrated microchemical system that combines micromixing, a reaction channel, an IR detection region, and temperature control for monitoring and kinetic studies of liquid-phase reactions. The microdevices exploit the transparency of silicon to infrared radiation in most of the wavelength region of interest (4000−800 cm-1), the precise definition of microfluidic channels by deep reactive ion-etching, the high thermal conductivity of silicon, and the fusion bonding of silicon for fixed-path-length transmission cells. Two devices are considered, a simple T-shaped mixer and an efficient mixer with interleaving channels for rapid mixing. The first device is used to characterize IR transmission characteristics in silicon-based microreactors and to demonstrate the feasibility of monitoring exothermic reactions, the hydrolysis of propionyl chloride under isothermal conditions. The mixing characteristics of the second microreactor are evaluated experimentally by an acid−base reaction and predicted b...
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paper_title: Mixing in microchannels based on hydrodynamic focusing and time-interleaved segmentation: modeling and experiment

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This paper reports a new mixing concept in microscale using hydrodynamic focusing and sequential segmentation. Both focusing and segmentation were used in the present study to reduce mixing path, to shorten mixing time, and to enhance mixing quality. Transversal mixing path is reduced by hydrodynamic focusing, while sequential segmentation shortens the axial mixing path. Assuming the same viscosity in the different streams, the focused width can be adjusted by the flow rate ratio. The axial mixing path can be controlled by the switching frequency of the inlet valves and the mean velocity of the flow. Both flow rate ratio and pulse width modulation of the switching signal can adjust the desired mixing ratio. This paper first presents a time-dependent two-dimensional analytical model for the mixing concept. This model considers an arbitrary mixing ratio between solute and solvent as well as the axial Taylor-Aris dispersion. A polymeric micromixer was designed and fabricated by CO 2 laser micromachining and hot lamination. Sequential segmentation was realized by two piezoelectric valves. The sheath streams for hydrodynamic focusing are introduced through other two inlets. We also designed a measurement system that can synchronize of the mixer's switching signal with the camera's trigger signal. The system allows our relatively slow and low-resolution CCD camera to freeze and to capture a large transient concentration field. The concentration profile along the mixing channel agrees qualitatively well with the analytical model.
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paper_title: Achieving uniform mixing in a microfluidic device: hydrodynamic focusing prior to mixing.

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We describe a microfluidic mixer that is well-suited for kinetic studies of macromolecular conformational change under a broad range of experimental conditions. The mixer exploits hydrodynamic focusing to create a thin jet containing the macromolecules of interest. Kinetic reactions are triggered by molecular diffusion into the jet from adjacent flow layers. The ultimate time resolution of these devices can be restricted by premature contact between co-flowing solutions during the focusing process. Here, we describe the design and characterization of a mixer in which hydrodynamic focusing is decoupled from the diffusion of reactants, so that the focusing region is free from undesirable contact between the reactants. Uniform mixing on the microsecond time scale is demonstrated using a device fabricated by imprinting optical-grade plastic. Device characterization is carried out using fluorescence correlation spectroscopy (FCS) and two-photon microscopy to measure flow speeds and to quantify diffusive mixing...
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paper_title: A highly efficient 3D micromixer using soft PDMS bonding

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This paper presents a novel highly efficient passive micromixer that employs diffusion for micromixing. Since conventional fabrication methods cannot form precise aligned microchannels, the realization of a complex 3D micromixer has been difficult. Here, we report a novel micromixer, named a chessboard mixer. In addition, a new polydimethylsiloxane (PDMS) bonding method was developed to produce the proposed mixer. The new PDMS bonding technique requires PDMS-to-PDMS bonding and the moldable flexibility of partially cured PDMS to form the structure. Accordingly, a two-step curing process was used to solve these problems. Adhesion control was also considered when forming the PDMS membranes. Complex 3D microchannels in the micromixer were aligned within 1 m using the proposed new bonding method. The presented micromixer could increase the mixing effect by expanding interfaces between mixing fluids. Thus, this mixer makes it possible to mix within a shorter distance than other pre-existing micromixers do. A simulation using computational fluid dynamics (CFD)-ACE software showed a highly efficient performance, and an experiment involving the mixing of NaOH and phenolphthalein confirmed the rapid mixing performance (<1400 µm).Corrections were made to the authors' affiliations on 27 July 2006. The corrected electronic version is identical to the print version.
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paper_title: Mass transfer enhancement in microchannel reactors by reorientation of fluid interfaces and stretching

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Abstract The poor mixing in microchannel reactors, most especially in liquid-phase reactions, primarily due to the inherently diffusion-dominated laminar flow characteristic of microreactors has attracted the attention of many researchers. The aim of this research study is to investigate mass transfer enhancement in microchannel reactors, through a theoretical mixing study of the currently utilized standard, single-channel T-junction configuration as well as four proposed multi-channel, microreactor configurations. The mass transfer enhancement in the proposed configurations is achieved via ‘reorientation and stretching of fluid interfaces’ by imposing some geometric constraints on these microreactor configurations. These configurations are studied for their mixing performance by performing computational fluid dynamics (CFD) simulations of pulse tracer and flow visualization experiments, and using residence time distribution (RTD) and species mass fraction distribution (SMFD) as mixing characterization measures, respectively. Based on the criteria of low pressure drop as well as high mixing performance, the best enhanced-mixing configuration is identified and subsequently optimized. This theoretical study on laminar mixing problem in micromixers/reactors shows CFD simulations as a very useful tool for the design and optimization of micromixing/reaction configurations.
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paper_title: Investigations of mixing process in microfluidic manifold designed according to biomimetic rule.

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The paper is focused on the mechanism of mixing process in a manifold which mimics the geometrical properties of vascular systems. The relationship governing the optimum ratio between the diameters of the parent and daughter branches in vascular systems was first discovered by Murray using the principle of minimum work. However, in contrast to biological vascular networks, which are composed of circular pipes, microfluidic manifolds are fabricated using a range of processes (photolithography, wet or dry etching, surface micromachining), which result in channels of rectangular or trapezoidal sections and constant depth throughout the device. The paper focuses on constant-depth rectangular channels often employed in lab-on-a-chip systems and provides comprehensive numerical studies of mixing in such geometry. It also presents simplified analytical estimation on how the coefficient of mixing depends on the number of generations and Reynolds number. The main goal of the paper is to describe the concept of a mixer which provides almost perfect mixing at the outlet regardless of the value of Re and for a minimal number of manifold's generations.
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paper_title: Residence-time distribution as a measure of mixing in T-junction and multilaminated/elongational flow micromixers

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Abstract The ineffective mixing in microchannel mixers or reactors, primarily due to the laminar flow behavior in such microfluidic devices, has become an issue of significant interest to many researchers working in the field of microreaction engineering and related disciplines. The present study describes the numerical and experimental investigation of mixing performance in a proposed multilaminated/elongational flow micromixer (herein referred to as MEFM-4) and a standard T-junction micromixer (TjM). These two micromixers that employ different mixing enhancement strategies were fabricated from silicon using micro-electromechanical systems (MEMS) technology. Computational fluid dynamics (CFD) approach was first used to establish the experimental platform for the mixing study. Tracer experiment utilizing UV–vis absorption spectroscopy detection technique was used to obtain the required concentration data for residence-time distribution (RTD) analysis. The RTD and its coefficient of variation (CoV) were used for indirect characterization of flow and mixing behavior in the micromixers. Using this measure, the proposed MEFM-4, as expected, exhibits a better mixing performance (with its narrower RTD and lower CoV values) than the standard TjM. The comparison of results from the CFD simulation and the experiment shows very good agreement, especially in the low Reynolds number flow regime (Re
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paper_title: Experimental study and nonlinear dynamic analysis of time-periodic micro chaotic mixers

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The efficiency of MEMS-based time-periodic micro chaotic mixers is experimentally and theoretically investigated in this study. A time-periodic flow perturbation was realized using digitally controlled solenoid valves to activate a source and sink alternately, acting together as a pair, with different driving frequencies. Working fluids with and without fluorescent dye were used in the micromixing experiments. The spatio-temporal variation of the mixing concentration during the mixing process was characterized at different Strouhal numbers, ranging from 0.03 to 0.74, using fluorescence microscopy. A simple kinematical model for the micromixer was used to demonstrate the presence of chaotic mixing. Specific stretching rate, Lyapunov exponent, and local bifurcation and Poincar´ e section analyses were used to identify the emergence of chaos. Two different numerical methods were employed to verify that the maximum Lyapunov exponent was positive in the proposed micromixer model. A simplified analytical analysis of the effect of Strouhal number is presented. Kolmogorov–Arnold–Mose (KAM) curves, which are mixing barriers, were also found in Poincar´ e sections. From a comparative study of the experimental results and theoretical analysis, a finite-time Lyapunov exponent (FTLE) was shown to be a more practical mixing index than the classical Lyapunov exponent because the time spent in mixing is the main concern in practical applications, such as bio-medical diagnosis. In addition, the FTLE takes into account both fluid stretching in terms of the stretching rate and fluid folding in terms of curvature.
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paper_title: Investigation of alternating-flow mixing in microchannels

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Abstract A number of different approaches to mixing liquids in microscale systems can be found in the literature. In the case of miscible liquids it is desirable to produce mixtures with residual non-uniformity in composition that is below some specified level. Yet very little quantitative information is available concerning the conditions required to produce a given level of mixture uniformity. A theoretical approach to this problem is described. Computational fluid dynamics and simple scaling are used to develop a quantitative understanding of the alternating flow method of mixing using pressure driven flow. In this approach, external flow control is used to produce alternating injection into a single microchannel of two or more solutions to be mixed. The resulting streamwise slugs of solution then mix by the stretching of the slugs into thin striations resulting from shear strain. The most challenging condition for mixing is where the Reynolds number is approaching zero and inertia effects are negligible, a common situation in microchannel flows, particularly where relatively high-viscosity liquids, for example ionic liquids, are involved. The scaling theory demonstrates that an initial time period of rapid mixing of fluid outside the core of the flow, scaling as Pe - 2 / 3 , is followed by a far slower process of mixing in the core region, scaling as Pe - 1 / 2 . An approximate correlation for the deviation from the perfectly mixed state as a function of time is found. This correlation applies over the range of Peclet number, slug length and solution mixture ratio that are of interest. The mixture uniformity produced is shown to be limited by the initial uniformity of each solution over the channel section resulting from the injection process.
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paper_title: High-efficiency electrokinetic micromixing through symmetric sequential injection and expansion.

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Rapid electric field switching is an established microfluidic mixing strategy for electrokinetic flows. Many such microfluidic mixers are variations on the T- or Y-form channel geometry. In these configurations, rapid switching of the electric field can greatly improve initial mixing over that achieved with static-field mixing. Due to a fundamental lack of symmetry, however, these strategies produce lingering cross-channel concentration gradients which delay complete mixing of the fluid stream. In this paper, a field switching microfluidic mixing strategy which utilizes a symmetric sequential injection geometry with an expansion chamber to achieve high efficiency microfluidic mixing is demonstrated experimentally. A three-inlet injector sequentially interlaces two dissimilar incoming solutions. Downstream of the injector, the sequence enters an expansion chamber resulting in a dramatic (two orders of magnitude) decrease in Peclet number and rapid axial diffusive mixing. The outlet concentration may be accurately varied over the full spectrum by tuning the duty cycle of the field switching waveform. The chips are designed with input from a previous numerical study, manufactured in poly(dimethylsiloxane) using soft-lithography based microfabrication, and tested using fluorescence microscopy. In the context of on-chip chemical processing for analytical operations, the demonstrated mixing strategy has several features: high mixing efficiency (99%), compact axial length (2.3 mm), steady outflow velocity, and readily variable outlet concentration (0.15 < c* < 0.95).
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paper_title: Rapid Microfluidic Mixers Utilizing Dispersion Effect and Interactively Time-Pulsed Injection

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In this paper, we present a novel active microfluidic mixer utilizing a dispersion effect in an expansion chamber and applying interactively time-pulsed driving voltages to the respective inlet fluid flows to induce electroosmotic flow velocity variations for developing a rapid mixing effect in a microchannel. Without using any additional equipment to induce flow perturbations, only a single high-voltage power source is required for simultaneously driving and mixing sample fluids, which results in a simple and low-cost system for mixing. The effects of the applied main electrical field, interactive frequency, and expansion ratio on the mixing performance are thoroughly examined experimentally and numerically. The mixing ratio can be as high as 95% within a mixing length of 3000 µm downstream from the secondary T-form when a driving electric field strength of 250 V/cm, a periodic switching frequency of 5 Hz, and the expansion ratio M=1:10 are applied. In addition, the optimization of the driving electric field, switching frequency, expansion ratio, expansion entry length, and expansion chamber length for achieving a maximum mixing ratio is also discussed in this study. The novel method proposed in this study can be used for solving the mixing problem in the field of micro-total-analysis systems in a simple manner.
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paper_title: Design of Interactively Time-Pulsed Microfluidic Mixers in Microchips using Numerical Simulation

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In this paper, we propose a novel technique in which driving voltages are applied interactively to the respective inlet fluid flows of three configurations of a microfluidic device, namely T-shaped, double-T-shaped, and double-cross-shaped configurations, to induce electroosmotic flow (EOF) velocity variations in such a way as to develop a rapid mixing effect in the microchannel. In these configurations a microfluidic mixer apply only one electrokinetic driving force, which drives the sample fluids and simultaneously produces a periodic switching frequency. It requires no other external driving force to induce perturbations to the flow field. The effects of the main applied electric field, the interactive frequency, and the pullback electric field on the mixing performance are thoroughly examined numerically. The optimal interactive frequency range for a given set of micromixer parameters is identified for each type of control mode. The numerical results confirm that micromixers operating at an optimal interactive frequency are capable of delivering a significantly enhanced mixing performance. Furthermore, it is shown that the optimal interactive frequency depends upon the magnitude of the main applied electric field. The interactively pulsed mixers developed in this study have a strong potential for use in lab-on-a-chip systems. They involve a simpler fabrication process than either passive or active on-chip mixers and require less human intervention in operation than their bulky external counterparts.
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paper_title: Effects of microchannel geometry on pulsed flow mixing

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Abstract Although the mixing of reagents is often crucial in many microfluidic devices, good mixing in these laminar, low Reynolds number, flows remains a challenge. It was shown in Refs. [Glasgow, I., Aubry, N., 2003. Lab on a Chip 3, p. 114; Glasgow, I., Batton, J., Aubry, N., 2004. Lab on a Chip 4, p. 558] that pulsing can induce mixing at the confluence of two inlet microchannels in an efficient manner. In this paper, we show that this mixing is affected by both the geometry of the confluence and the inclusion of features in the channels, which induce secondary flow. More specifically, we study mixing in 200 μm wide by 120 μm deep channels, at flow rates from 48 nl s−1 to 4.8 μl s−1, corresponding to Reynolds numbers of 0.3–30. For the parameter values studied, the pulsed flow technique is more effective at mixing than the secondary flow induced by the channel geometry features, and combining both methods leads to even better mixing. In addition, pulsing the reagents such that they pass multiple times through the spatial features, which induce secondary flow leads to mixing over shorter distances.
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paper_title: A combined active/passive scheme for enhancing the mixing efficiency of microfluidic devices

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Abstract The straight microchannels used in conventional microfluidic devices yield a poor mixing performance because the fluid flow is restricted to the low Reynolds number regime, and hence mixing takes place primarily as a result of diffusion. In an attempt to improve the mixing efficiency of pressure-driven microfluidic flows, the current study applies periodic velocity perturbations to the species flows at the microchannel inlet and incorporates a wavy-wall section within the mixing channel. Numerical simulations are performed to analyze the respective effects on the mixing efficiency of the geometric amplitude of the wavy surface, the length of the wavy-wall section, and the Strouhal number of the periodic velocity perturbations. Overall, the results reveal that the mixing performance is improved by increasing the geometric wave amplitude or length of the wavy-wall section and by applying a Strouhal number in the range 0.33–0.67.
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paper_title: Theoretical investigation of electro-osmotic flows and chaotic stirring in rectangular cavities

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Abstract Two-dimensional, time-independent and time-dependent electro-osmotic flows driven by a uniform electric field in a closed rectangular cavity with uniform and non-uniform zeta potential distributions along the cavity’s walls are investigated theoretically. First, we derive an expression for the one-dimensional velocity and pressure profiles for a flow in a slender cavity with uniform (albeit possibly different) zeta potentials at its top and bottom walls. Subsequently, using the method of superposition, we compute the flow in a finite length cavity whose upper and lower walls are subjected to non-uniform zeta potentials. Although the solutions are in the form of infinite series, with appropriate modifications, the series converge rapidly, allowing one to compute the flow fields accurately while maintaining only a few terms in the series. Finally, we demonstrate that by time-wise periodic modulation of the zeta potential, one can induce chaotic advection in the cavity. Such chaotic flows can be used to stir and mix fluids. Since devices operating on this principle do not require any moving parts, they may be particularly suitable for microfluidic devices.
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paper_title: Micromixing using induced-charge electrokinetic flow

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Abstract The mixing effect of induced-charge electrokinetic flow (ICEKF) in a rectangular microchannel with embedded conducting hurdles is investigated in this paper. A correction method is suggested to estimate numerically the induced zeta potential on the conducting surface. Two-dimensional pressure-linked Navier–Stokes equation is used to model the flow field in the channel. The numerical results show flow circulations generated from the induced non-uniform zeta potential distribution along the conducting hurdle surfaces. It is demonstrated that the local flow circulations provide effective means to enhance the flow mixing between different solutions. The mixing enhancement effect is experimentally validated using PDMS based microchannels with embedded platinum hurdles. The dependence of the degree of mixing enhancement on the hurdle geometries and hurdle numbers is also predicted. The mixing using ICEKF described in this paper can be used in various microfluidics and lab-on-a-chip applications.
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paper_title: Chaotic Mixing in a Steady Flow in a Microchannel

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We report experiments on mixing of a passively advected fluorescent dye in a low Reynolds number flow in a microscopic channel. The channel is a chain of repeating segments with a custom designed profile that generates a steady three-dimensional flow with stretching and folding, and chaotic mixing. A few statistical characteristics of mixing in the flow are studied and are all found to agree with theoretical and experimental results for the flows in the Batchelor regime of mixing that are chaotic in time. The proposed microchannel provides fast and efficient mixing and is simple to fabricate.
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paper_title: Ultrafast active mixer using polyelectrolytic ion extractor.

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We report on a low voltage, straight/smooth surface, and efficient active micromixer. The mixing principle is based on alternative ion depletion-enrichment using a pair of positively charged polyelectrolytic gel electrodes (pPGEs), which face each other joined by a microchannel. This system has an external AC signal source electrically connected to the pPGEs via the respective 1 M KCl solutions and Ag/AgCl electrodes. When an electric bias is applied between the two pPGEs, anions are extracted through one of the pPGEs to create a local ion-deficient region. Simultaneously, an ion-rich area appears near the other pPGE due to an inward anionic flux. As the direction of the charge flow is periodically reversed by the AC signal source, the ion depletion-enrichment regions are alternately swapped with each other on the 'push-pull' basis. The turmoil between the pPGEs quickly mixes the solutions in the microchannel without any mechanical moving part or specially machined structures. In the proposed system, both AC frequency and current density can be easily and finely controlled so that one can quickly find the optimal conditions for a given sample. The micromixer as made showed a mixing efficiency higher than 90% for sample solutions of 1 mM Rhodamine 6G and PBS at pH 7.4 when the flow rate was under 6 mm s(-1). In addition to the solution-solution mixing, the micromixer can effectively mix suspended microparticles with solution. As a representative example, rapid and efficient lysis of human red blood cells was demonstrated allowing minimal damage of the white blood cells.
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paper_title: Mixing enhancement by using electrokinetic instability under time-periodic electric field

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Experimental studies have been performed to apply electrokinetic instability as a means of fluid mixing. A time-periodic electric field is introduced to excite the instability in a cross channel. It is generated by the sum of a static field and an alternating field. The characteristics of instability have been considered with the frequency of applied electric field as a key parameter. Through the frequency sweeping from 0.1 Hz to 50 Hz, it has been found that the instability is most enhanced when the period of the applied electric field is close to half of the period of instability in the form of a sinusoidal wave generated under a the static electric field. This fact may be explained based on the concept of hydrodynamic resonance. The degree of mixing is evaluated quantitatively by analyzing the distribution of fluorescent dye and it is confirmed that there exists an optimal frequency for enhancement of fluid mixing. The existence of the optimal frequency is expected to provide a valuable guideline for the design of an efficient micro-mixer.
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paper_title: Passive mixing in a three-dimensional serpentine microchannel

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A three-dimensional serpentine microchannel design with a "C shaped" repeating unit is presented in this paper as a means of implementing chaotic advection to passively enhance fluid mixing. The device is fabricated in a silicon wafer using a double-sided KOH wet-etching technique to realize a three-dimensional channel geometry. Experiments using phenolphthalein and sodium hydroxide solutions demonstrate the ability of flow in this channel to mix faster and more uniformly than either pure molecular diffusion or flow in a "square-wave" channel for Reynolds numbers from 6 to 70. The mixing capability of the channel increases with increasing Reynolds number. At least 98% of the maximum intensity of reacted phenolphthalein is observed in the channel after five mixing segments for Reynolds numbers greater than 25. At a Reynolds number of 70, the serpentine channel produces 16 times more reacted phenolphthalein than a straight channel and 1.6 times more than the square-wave channel. Mixing rates in the serpentine channel at the higher Reynolds numbers are consistent with the occurrence of chaotic advection. Visualization of the interface formed in the channel between streams of water and ethyl alcohol indicates that the mixing is due to both diffusion and fluid stirring.
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paper_title: AC electroosmotic micromixer for chemical processing in a microchannel

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A rapid micromixer of fluids in a microchannel is presented. The mixer uses AC electroosmotic flow, which is induced by applying an AC voltage to a pair of coplanar meandering electrodes configured in parallel to the channel. To demonstrate performance of the mixer, dilution experiments were conducted using a dye solution in a channel of 120 µm width. Rapid mixing was observed for flow velocity up to 12 mm s−1. The mixing time was 0.18 s, which was 20-fold faster than that of diffusional mixing without an additional mixing mechanism. Compared with the performance of reported micromixers, the present mixer worked with a shorter mixing length, particularly at low Peclet numbers (Pe < 2 × 103).
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paper_title: A chaotic micromixer modulated by constructive vortex agitation

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A novel design for vortex modulation of a passive micromixer, named as the circulation–disturbance micromixer (CDM), has been achieved and analyzed experimentally and numerically. The micromixer consists of slanted grooves on the bottom and a zigzag barrier on the top. In this micromixer, the fluid produces a transverse motion perpendicular to the main field, and two modulated and hyperbolic vortices of disparate size are induced. The active-like agitation produced by the constructive interference of these two vortices induces increased flow through the grooves and the mixing efficiency is hence improved significantly. The 3D flow structure in CDM has been analyzed through both numerical simulation (CFD-ACE+) and two methods of visualization—using dyes and using micro laser-induced fluorescence (μ-LIF, B-phycoerythrin (BPE) and Allophycocyanin alpha subunit (ApcA)) with a confocal microscope. Our results contribute to an understanding of the resulting enhanced hyperbolic flow mixing and provide also a superior microfluidic element for a 'lab on a chip'. Compared with a slanted groove micromixer, the mixing index of the designed CDM-2T increases 132%, whereas CDM-4T and CDM-8T respectively increase 183% and 280% at Reynolds number 10.
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paper_title: AC Electroosmotic Generated In-Plane Microvortices for Stationary or Continuous Fluid Mixing

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This paper proposes a novel design of the patterned AC electroosmotic flows (AC-EOF) by various electrode configurations to locally and simultaneously generate in-plane microvortices of clockwise, counter-clockwise, or pair rotation in a microchannel for micro mixing applications. Microparticle image velocimetry (muPIV) was used to characterize the flow fields of the generated in-plane microvortices. The sizes of the active regions and the magnitudes of the rotational strength of microvortices were found to increase with the increase of the applied voltages and an optimal value was achieved at an appropriately applied frequency. By employing the microvortices, AC-EOF micromixers were successfully carried out for either rapid local mixing of two stationary fluids with high viscosity ratio or continuous mixing of two flowing fluids introduced into a Y-shaped microchannel. The mixing times for the stationary fluids with viscosity ratio of 450 and the continuously flowing fluids were 2 minutes and 0.86 s, respectively, which are 15-fold and 30-fold faster than that of mixing directly by diffusion. The AC-EOF micromixer provides a great mixing enhancement with a shorter mixing length for the application of flows in low Peclet numbers (Pe<3 X 105).
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paper_title: Parametric study on mixing of two fluids in a three-dimensional serpentine microchannel

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Abstract A flow analysis method using Navier–Stokes equations has been applied to a parametric investigation of mixing two fluids in a three-dimensional serpentine microchannel, which has not been reported so far. The serpentine microchannel with “L-shaped” repeating units is found to be effective in mixing fluids at Reynolds numbers, 1, 10, 35 and 70. Mixing performance and pressure drop characteristics with two geometrical parameters, i.e., the ratio of channel height to channel width and the ratio of the length of a straight channel in an “L-shaped” unit to the channel width, have been analyzed at four different Reynolds numbers. A mixing index has been used to quantify and elucidate mixing behavior in the microchannel. The vortical structure of the flow in the channel is also analyzed to identify the relationship with mixing performance. The results reveal that mixing and pressure drop characteristics in a serpentine channel are very sensitive to the geometric parameters, showing different behavior at various Reynolds numbers.
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paper_title: Chaotic mixer for microchannels.

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It is difficult to mix solutions in microchannels. Under typical operating conditions, flows in these channels are laminar—the spontaneous fluctuations of velocity that tend to homogenize fluids in turbulent flows are absent, and molecular diffusion across the channels is slow. We present a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number. Using this method, the length of the channel required for mixing grows only logarithmically with the Pe «clet number, and hydrodynamic dispersion along the channel is reduced relative to that in a simple, smooth channel. This method uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.
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paper_title: A serpentine laminating micromixer combining splitting/recombination and advection

paper_content:

Mixing enhancement has drawn great attention from designers of micromixers, since the flow in a microchannel is usually characterized by a low Reynolds number (Re) which makes the mixing quite a difficult task to accomplish. In this paper, a novel integrated efficient micromixer named serpentine laminating micromixer (SLM) has been designed, simulated, fabricated and fully characterized. In the SLM, a high level of efficient mixing can be achieved by combining two general chaotic mixing mechanisms: splitting/recombination and chaotic advection. The splitting and recombination (in other terms, lamination) mechanism is obtained by the successive arrangement of “F”-shape mixing units in two layers. The advection is induced by the overall three-dimensional serpentine path of the microchannel. The SLM was realized by SU-8 photolithography, nickel electroplating, injection molding and thermal bonding. Mixing performance of the SLM was fully characterized numerically and experimentally. The numerical mixing simulations show that the advection acts favorably to realize the ideal vertical lamination of fluid flow. The mixing experiments based on an average mixing color intensity change of phenolphthalein show a high level of mixing performance was obtained with the SLM. Numerical and experimental results confirm that efficient mixing is successfully achieved from the SLM over the wide range of Re. Due to the simple and mass producible geometry of the efficient micromixer, SLM proposed in this study, the SLM can be easily applied to integrated microfluidic systems, such as micro-total-analysis-systems or lab-on-a-chip systems.
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paper_title: Enhancement of stirring in a straight channel at Low Reynolds-numbers with various block-arrangement

paper_content:

In this study a newly designed microchannel as an efficient fluid-mixer is proposed. This design is comprised of a channel and a series of blocks periodically attached on the bottom surface of the channel. In this configuration, the stirring is greatly enhanced at a certain range of parametric values. To characterize the flow field and the stirring effect, both numerical and experimental methods were employed. To obtain the velocity field, three-dimensional numerical computation to the Navier Stokes equations was performed by using a commercial code, FLUENT 6.0. The fluid-flow solutions were then cast into studying the characteristics of stirring with the aid of Lyapunov exponent. In this study, the Lyapunov exponents were computed manually because the commercial code does not provide the corresponding tool. In the experiment, flow visualization was performed by using pure glycerin in a tank and glycerin mixed with small amount of a fluorescent dye in the other tank. The numerical results show that the pattern of the particles’ trajectories in the microchannel heavily depends on the block arrangement. It was shown that the stirring is significantly enhanced by a larger block-height and reaches maximum when the height is 0.8 times the channel width. We also studied the effect of the block stagger angle. It was found that stirring performance is the best at the block stagger angle of 45°.
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paper_title: Microfluidic chaotic stirrer utilizing induced-charge electro-osmosis

paper_content:

Recently, there has been a growing interest in using induced electro-osmosis to pump fluids in microfluidic devices. We show that induced electroosmosis can also be used to promote stirring and chaotic advection. To this end, we study theoretically a stirrer in which the flow patterns are alternated in time. We first analyze an idealized embodiment of the stirrer that admits a simple analytical solution for the flow patterns. The stirrer consists of a concentric annulus whose outer surface is defined by an array of electrodes that provide a spatially varying potential distribution. The resulting electric field induces quadruple electro-osmotic flow around the inner cylinder. By timewise alternating the potential distribution around the outer cylinder, we induce chaotic advection in the cavity. Subsequently, we carry out numerical simulations for a more realistic design that can be readily constructed, and demonstrate that it is possible to induce chaotic advection also in this case.
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paper_title: A microfluidic mixer with grooves placed on the top and bottom of the channel

paper_content:

A new microfluidic mixer is presented consisting of a rectangular channel with grooves placed in the top and bottom. This not only increases the driving force behind the lateral flow, but allows for the formation of advection patterns that cannot be created with structures on the bottom alone. Chevrons, pointing in opposite directions on the top and bottom, are used to create a pair of vortices positioned side by side. Stripes running the width of the channel generate a pair of vertically stacked vortices. Computational fluid dynamics (CFD) simulations are used to model the behavior of the systems and provide velocity maps at cross-sections within the mixer. Experiments demonstrate the mixing that results when two segregated species enter the mixer side-by-side and pass through two cycles of the mixer (i.e., two alternating sets of four stripes and four chevrons).
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paper_title: A split and recombination micromixer fabricated in a PDMS three-dimensional structure

paper_content:

In this paper we propose a new split and recombination (SAR) micromixer that is compatible with the microfabrication process of polydimethylsiloxane (PDMS). We evaluate the mixing efficiency of the fabricated SAR micromixer and find that it increases interfaces exponentially. Simulation using CFD-ACE+ shows a cross-sectional view of the flow and estimates the mixing efficiency of the SAR micromixer and the pressure drop for a unit of the SAR micromixer. A mixing experiment involving phenolphthalein and NaOH solutions shows that interfaces, represented as red lines, are increased by SAR mixing. The result of our mixing experiment involving blue dye and water is evaluated to determine the mixing efficiency by calculating the standard deviation (stdev) of the pixel intensity of the observed image. After the seventh unit of the SAR micromixer, solutions are mixed to 90% at Re 0.6. The number of units needed to reach a mixed state in which the stdev is lower than 0.05, a 90% mixed state, increases from 5 to 10 for a flow rate ranging from 0.1 µl min−1 (Re 0.012) to 1000 µl min−1 (Re 120) including numerical analysis results. The pressure drop increases proportionally from 2.8 Pa to 35 000 Pa when the flow rate increases from 0.1 µl min−1 (Re 0.012) to 1000 µl min−1 (Re 120) in the numerical analysis results.
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paper_title: Chaotic micromixers using two-layer crossing channels to exhibit fast mixing at low Reynolds numbers

paper_content:

We report two chaotic micromixers that exhibit fast mixing at low Reynolds numbers in this paper. Passive mixers usually use the channel geometry to stir the fluids, and many previously reported designs rely on inertial effects which are only available at moderate Re. In this paper, we propose two chaotic micromixers using two-layer crossing channels. Both numerical and experimental studies show that the mixers are very efficient for fluid manipulation at low Reynolds numbers, such as stretching and splitting, folding and recombination, through which chaotic advection can be generated and the mixing is significantly promoted. More importantly, the generation of chaotic advection does not rely on the fluid inertial forces, so the mixers work well at very low Re. The mixers are benchmarked against a three-dimensional serpentine mixer. Results show that the latter is inefficient at Re ::: = 0.2, while the new design exhibits rapid mixing at Re ::: = 0.2 and at Re of O(10−2). The new mixer design will benefit various microfluidic systems.
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paper_title: Mixing and hydrodynamic analysis of a droplet in a planar serpentine micromixer

paper_content:

In this work we combined numerical simulation with molecular-diffusion effect, high-tempo micro-particle image velocimetry (μ-PIV), and probability distribution function (PDF) analysis to investigate the chaotic mixing and hydrodynamics inside a droplet moving through a planar serpentine micromixer (PSM). Robust solutions for the distributions of interface and concentration of the droplets were obtained via computational fluid dynamics. The simulated fluid patterns are consistent with those measured with μ-PIV, which serves as a powerful nonintrusive diagnostic approach to observe the droplets. Two mechanisms are proposed to enhance the performance of mixing in a PSM—the deformation of droplets and the asymmetric recirculation within the droplets. On introducing alternating cross sections into a winding channel, this specific design of PSM is found to amplify the fluid disturbance and maximum vorticity difference. Data show that the PDF of the vorticity fields is modified and the fraction with larger vorticity is increased. Accordingly, the PSM is capable of achieving a mixing index 90% within 700 μm (Re = 2), which is eight times better than for a straight microchannel. The results not only demonstrate explicitly the fluid patterns within the droplets but also provide significant insight into the factors dominating the mixing efficiency.
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paper_title: Enhancement of Mixing in a Microchannel by Using AC-Electroosmotic Effect

paper_content:

This study has focused on optimizing the AC-electroosmotic micro-mixer, which is composed of a microchannel with an array of rectangular electrodes attached on the bottom wall. The electrode array is spatial-periodically arranged in pairs symmetric with respect to the longitudinal central line. An AC electrode field is applied to the electrodes, which drives the secondary transverse flow in a circulating cell mode near the electrodes. The main flow along the channel longitudinal direction plus this secondary transverse flow contribute to the stretching and folding of the fluid flow, that is the chaotic behavior, and thus to the enhancement of the fluid mixing. To design the better micro-mixer, numerical simulations have been performed by using a commercial code (CFX 10). In the simulations, the concept of mixing index is employed to evaluate the mixing performance as well as to optimize the size and spacing of each electrode in one pair. It is found that the optimum design of one electrode pair, which leads to the best mixing performance, is not simply harmonic one. When the length ratio of the two electrodes in a pair closes to 2:1, the best mixing effect can be attained. The flow pattern was visualized. Furthermore, the velocity field will be measured with a PTV technique to validate the numerical simulations.Copyright © 2008 by ASME
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paper_title: Design of mixing in microfluidic liquid slugs based on a new dimensionless number for precise reaction and mixing operations

paper_content:

Abstract This paper reports mixing characteristics inside a microfluidic liquid slug using the computational fluid dynamics (CFD) simulations. Each slug is modeled as a single-phase flow domain. Slug-based microfluidics offers rapid mixing by internal circulation and transport with narrow residence time distribution, making it suitable for precise reaction and mixing operations. Miniaturizing the slug size to microscale allows high interactions between the slug internal fluid and the channel wall, leading to a highly effective internal circulation. However, quantitative understanding of mixing characteristics and the influences of operating parameters on mixing rate is crucial for the design of a liquid slug that ensures desired mixing rates. The simulation results provide insights into the influences of operating parameters on slug-based mixing rates. Based on the simulation results, the modified Peclet number, Pe * = U s d s 2 / lD , is proposed for designing mixing in liquid slugs. A novel method using Pe * to estimate mixing rates and design liquid slugs to obtain desired mixing rates is discussed. Using this method, both short (ms) and long (min) mixing timescales can be accessed in the same microfluidic device by simply varying the slug velocity.
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paper_title: Drop mixing in a microchannel for lab-on-a-chip platforms.

paper_content:

We present theory, simulations, and experiments for discrete drop mixing in microchannels. The drops are placed sequentially in a channel and then moved at a set velocity to achieve mixing. The mixing occurs in three different regimes (diffusion-dominated, dispersion-dominated, and convection-dominated) depending on the Peclet number (Pe) and the drop dimensions. Introducing the modified Peclet number (Pe*), we show asymptotic curves that can be used to predict the mixing time and the required distance for mixing for any of the three regimes. Simulations of the mixing experiments using COMSOL agree with the theoretical limits. In our experimental work, we used a polydimethylsiloxane (PDMS) microchannel with a membrane air bypass valve to remove the air between drops. This approach enables precise control of the mixing and merging site. Experimental, simulation, and theoretical results all agree and show that mixing can occur in fractions of a second to hours, depending on the parameters used.
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paper_title: Mixing of miscible liquids in gas-segmented serpentine channels

paper_content:

The chaotic mixing of miscible liquids in gas-segmented serpentine channels is studied computationally in a two-dimensional setting. Passive tracer particles are used to visualize and quantify the mixing. The molecular diffusion is ignored and only the mixing due to chaotic stirring is considered. Mixing is quantified using the entropy and intensity of segregation measures. The effects of various non-dimensional parameters on the quality of mixing are investigated and it is found that the relative bubble size, the capillary number and the non-dimensional channel corrugation length are the most important parameters influencing the mixing. The mixing is found to be weakly dependent on Reynolds number and nearly independent of viscosity ratio.
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paper_title: Mixing Crowded Biological Solutions in Milliseconds

paper_content:

In vitro studies of biological reactions are rarely performed in conditions that reflect their native intracellular environments where macromolecular crowding can drastically change reaction rates. Kinetics experiments require reactants to be mixed on a time scale faster than that of the reaction. Unfortunately, highly concentrated solutions of crowding agents such as bovine serum albumin and hemoglobin that are viscous and sticky are extremely difficult to mix rapidly. We demonstrate a new droplet-based microfluidic mixer that induces chaotic mixing of crowded solutions in milliseconds due to protrusions of the microchannel walls that generate oscillating interfacial shear within the droplets. Mixing in the microfluidic mixer is characterized, mechanisms underlying mixing are discussed, and evidence of biocompatibility is presented. This microfluidic platform will allow for the first kinetic studies of biological reactions with millisecond time resolution under conditions of macromolecular crowding simil...
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paper_title: Mixing in a drop moving through a serpentine channel: A computational study

paper_content:

The chaotic mixing in a drop moving through a winding channel is studied computationally in a two-dimensional setting. The molecular mixing is ignored and only the mixing due to the chaotic advection is considered. Passive tracer particles are used to visualize the mixing patterns and mixing is quantified by two distinct methods. It is found that both the quantification methods are consistent with visual observations as well as with each other. The effects of various non-dimensional parameters on the quality of mixing are studied and it is found that the capillary number, the ratio of the drop phase fluid viscosity to that of the ambient fluid and the relative size of the drop compared to the average channel width are the most critical parameters influencing the mixing. The mixing is found to be weakly dependent on Reynolds number.
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paper_title: Mixing characterization inside micro-droplets engineered on a microcoalescer

paper_content:

Abstract We use a microdevice where microdroplets of reagents are generated and coalesce in a carrier continuous phase. The work focuses on the characterization of the mixing step inside the droplets, in the perspective to use them for chemical kinetic data acquisition. A dye and water are used, and an acid–base instantaneous chemical reaction is monitored thanks to a colored indicator. Acquisitions are done with a high-speed camera coupled to a microscope and a mixing parameter is calculated by image analysis. Different angles of bended channels and different ways of coalescence are compared. It is shown that the homogenization of the droplets can be reached in less than 10 ms after coalescence. This is achieved by forcing the droplets to coalesce in a “shifted” way, and later by adding 45 ∘ angle bends along the channel.
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paper_title: Controlled mixing in microfluidic systems using bacterial chemotaxis.

paper_content:

We demonstrate the use of Escherichia coli and their chemotactic characteristics to enhance mixing in a microchannel in a controlled and bi-directional manner. The presence of a chemoattractant in one arm of a three-junction microchannel results in an asymmetric increase in the effective diffusion coefficient of extremely high molecular weight TMR-Dextran (MW 2 000 000), which rises linearly with the concentration of attractant from a baseline value of 8-42 microm(2)/s at a concentration of 0.1 M. The response to a repellent is similar, with the opposite bias.
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paper_title: A numerical study on the flow and mixing in a microchannel using magnetic particles

paper_content:

We have numerically investigated the characteristics of the flow and mixing in a microchannel using magnetic particles. The main flow is driven by the pressure gradient along the channel, while the secondary flow for the mixing is induced by the drag forces of the particles. Here, the particles can move in the flow due to the strong attraction under the periodically-varying magnetic field generated by electromagnets. For the study, the fractional step method based on the finite volume method is used to obtain the velocity field of the fluid and the trajectories of the particles. This study aims at achieving good mixing by periodically changing the direction of magnetic actuation force in time to activate the interaction between the particles and the flow. The quality of mixing is estimated by considering the mixing index and Poincare section. In this study, parameter studies on the switching frequency, the magnetic actuation force, the number of magnetic particles and so on are performed to understand their effects on the flow and mixing. Results show that the clustering of magnetic particles during the magnetic actuation plays an important part in good mixing. It is also found that the magnetic force magnitude and switching frequency are the two main parameters that make a combined influence on the mixing efficiency. Such a mixing technique using magnetic particles would be an alternative, effective application for the flow and mixing in a microchannel.
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paper_title: Paramagnetic particles and mixing in micro-scale flows.

paper_content:

Mixing in microscale flows with rotating chains of paramagnetic particles can be enhanced by adjusting the ratio of viscous to magnetic forces so that chains dynamically break and reform. Lattice Boltzmann (LB) simulations were used to calculate the interaction between the fluid and suspended paramagnetic particles under the influence of a rotating magnetic field. Fluid velocities obtained from the LB simulations are used to solve the advection diffusion equation for massless tracer particles. At relatively high Mason numbers, small chains result in low edge velocities, and hence mixing is slower than at other Mason numbers. At low Mason numbers, long, stable chains form and produce little mixing toward the center of the chains. A peak in mixing rate is observed when chains break and reform. The uniformity of mixing is greater at higher Mason numbers because more small chains result in a larger number of small mixing areas.
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paper_title: Batch-mode mixing on centrifugal microfluidic platforms.

paper_content:

We present two novel fluidic concepts to drastically accelerate the process of mixing in batch-mode (stopped-flow) on centrifugal microfluidic platforms. The core of our simple and robust setup exhibits a microstructured disk with a round mixing chamber rotating on a macroscopic drive unit. In the first approach, magnetic beads which are prefilled into the mixing chamber are periodically deflected by a set of permanent magnets equidistantly aligned at spatially fixed positions in the lab-frame. Their radial positions alternatingly deviate by a slight positive and negative offset from the mean orbit of the chamber to periodically deflect the beads inbound and outbound during rotation. Advection is induced by the relative motion of the beads with respect to the liquid which results from the magnetic and centrifugal forces, as well as inertia. In a second approach--without magnetic beads--the disk is spun upon periodic changes in the sense of rotation. This way, inertia effects induce stirring of the liquids. As a result, both strategies accelerate mixing from about 7 minutes for mere diffusion to less than five seconds. Combining both effects, an ultimate mixing time of less than one second could be achieved.
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paper_title: Magnetic microsphere-based mixers for microdroplets

paper_content:

While droplet-based microfluidic systems have several advantages over traditional flow-through devices, achieving adequate mixing between reagents inside droplet-based reactors remains challenging. We describe an active mixing approach based on the magnetic stirring of self-assembled chains of magnetic microspheres within the droplet as these stirrers experience a rotating magnetic field. We measure the mixing of a water-soluble dye in the droplet in terms of a dimensional mixing parameter as the field-rpm, fluid viscosity, and microsphere loading are parametrically varied. These show that the mixing rate has a maximum value at a critical Mason number that depends upon the operating conditions.
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paper_title: An immersed‐boundary finite‐volume method for direct simulation of flows with suspended paramagnetic particles

paper_content:

In the present study, we have proposed an immersed-boundary finite-volume method for the direct numerical simulation of flows with inertialess paramagnetic particles suspended in a nonmagnetic fluid under an external magnetic field without the need for any model such as the dipole–dipole interaction. In the proposed method, the magnetic field (or force) is described by the numerical solution of the Maxwell equation without current, where the smoothed representation technique is employed to tackle the discontinuity of magnetic permeability across the particle–fluid interface. The flow field, on the other hand, is described by the solution of the continuity and momentum equations, where the discrete-forcing-based immersed-boundary method is employed to satisfy the no-slip condition at the interface. To validate the method, we performed numerical simulations on the two-dimensional motion of two and three paramagnetic particles in a nonmagnetic fluid subjected to an external uniform magnetic field and then compared the results with the existing finite-element and semi-analytical solutions. Comparison shows that the proposed method is robust in the direct simulation of such magnetic particulate flows. This method can be extended to more general flows without difficulty: three-dimensional particulate flows, flows with a great number of particles, or flows under an arbitrary external magnetic field. Copyright © 2010 John Wiley & Sons, Ltd.
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paper_title: Passive micromixers for applications in the microreactor and μTAS fields

paper_content:

An overview is given of current developments in micromixing technology, where the emphasis is on liquid mixing in passive micromixers. The mixers presented are differentiated by the hydrodynamic principle employed, and four important principles are discussed in some detail: hydrodynamic focusing, flow separation, chaotic advection, and split-and-recombine flows. It is shown that these principles offer excellent mixing performance in various dynamical regimes. Hydrodynamic focusing is a concept working very much independently of the Reynolds number of the flow. Flow separation offers rich dynamical behavior over a Reynolds number scale of several hundred, with superior performance compared to purely diffusive mixing already found at low Reynolds numbers. For chaotic advection, different implementations tailor-made for low and comparatively high Reynolds numbers exist, both leading to an exponential increase of the interface between two fluids. Split-and-recombine flows can only be realized in a close-to-ideal form in the low Reynolds number regime. Corresponding mixers can be equipped with comparatively wide channels, enabling a favorable ratio of throughput to pressure drop. The overview given in this article should enable a potential user of micromixing technology to select the most favorable concept for the application envisaged, especially in the field of chemical process technology
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Title: A Review on Mixing in Microfluidics

Section 1: Introduction
Description 1: Summarize the importance and challenges of mixing in microfluidic applications, and outline the review's scope and objectives.

Section 2: Principles and Terminology of Fluid Mixing
Description 2: Explain the fundamental principles and terminology associated with fluid mixing, including the mechanisms of stirring, diffusion, and the importance of low Reynolds-number flows.

Section 3: Review on Various Mixer Designs for Microfluidic Applications
Description 3: Provide a comprehensive review of different microfluidic mixer designs reported since 2005, classified by the underlying physical mechanisms.

Section 4: Hydrodynamic Focusing
Description 4: Discuss the hydrodynamic focusing technique, its designs, and advantages, as well as any associated complexities and challenges.

Section 5: Alternate-Injection or Pulsed-Flow Mixing
Description 5: Describe the alternate-injection or pulsed-flow mixing methods, including their benefits, design simplicity, and potential drawbacks.

Section 6: Geometry Effect
Description 6: Explore how varying channel geometries can enhance mixing, covering specific designs and the challenges related to their fabrication.

Section 7: Electrokinetic Method
Description 7: Investigate the use of electrokinetic methods for mixing, including the role of microelectrodes and electrokinetic instability in enhancing mixing.

Section 8: Mixing by Droplets
Description 8: Outline the advantages of droplet-based mixing methods, detailing various channel designs and their mixing performance.

Section 9: Stirring by Particles
Description 9: Discuss mixing methods that utilize magnetic or biological particles, addressing the mechanisms and limitations of such designs.

Section 10: Conclusions
Description 10: Summarize the key findings of the review, highlighting the comparative advantages and disadvantages of different mixing designs and offering recommendations for specific applications.