Introduction: mixing in microfluidics

Magnetic stabilization and vorticity in submillimeter paramagnetic liquid tubes

It is possible to suppress convection and dispersion of a paramagnetic liquid by means of a magnetic field. A tube of paramagnetic liquid can be stabilized in water along a ferromagnetic track in a vertical magnetic field, but not in a horizontal field. Conversely, an "antitube" of water can be stabilized in a paramagnetic liquid along the same track in a transverse horizontal field, but not in a vertical field. The stability arises from the interaction of the induced moment in the solution with the magnetic field gradient in the vicinity of the track. The magnetic force causes the tube of paramagnetic liquid to behave as if it were encased by an elastic membrane whose cross-section is modified by gravitational forces and Maxwell stress. Convection from the tube to its surroundings is inhibited, but not diffusion. Liquid motion within the paramagnetic tube, however, exhibits vorticity in tubes of diameter 1 mm or less--conditions where classical pipe flow would be perfectly streamline, and mixing extremely slow. The liquid tube is found to slide along the track almost without friction. Paramagnetic liquid tubes and antitubes offer appealing new prospects for mass transport, microfluidics, and electrodeposition.

Design and evaluation of a passive alcove-based microfluidic mixer

A novel passive microfluidic silicon mixer has been designed, optimized and fabricated. The architecture of the mixer consists of a simple "T" junction, made up by a 20 microm wide by 82 microm deep channel, followed by three repeats of an alcove, each with a triangular obstruction, arranged in a zigzag fashion. Numerical simulations were employed to optimize the geometry, particularly the dimensions of the alcoves, the relative orientation and the spacing between them, and the degree of intrusion associated with them. The simulation results demonstrate that chaotic flow due to recirculation within the alcoves results in transverse velocity that promotes effective fluid mixing. The microfluidic mixer with the simulation-optimized geometry was fabricated with photolithographic techniques and characterized by optical imaging, fluorescence, and Raman microscope spectroscopy. At a sample flow rate of 20 microL/s, the mixer exhibits a short mixing deadtime of approximately 22 micros and a high mixing efficiency under both low and high viscosity conditions. The alcove-based microfluidic silicon mixer offers unique advantages for its short deadtime and slow sample consumption rate. In addition, it provides a valuable component for laboratory-on-a-chip applications for its ease of development into multiple networks for massively parallel analytical processes.

A versatile microfluidic chip for millisecond time-scale kinetic studies by electrospray mass spectrometry

An electrospray coupled microfluidic reactor for the measurement of millisecond time-scale, solution phase kinetics is introduced. The device incorporates a simple two-channel design that is etched into polymethyl methacrylate (PMMA) by laser ablation. The outlet of the device is laser cut to a sharp tip, facilitating low dead volume 'on chip' electrospray. Fabrication is fast, straightforward and highly reproducible, supporting rapid prototyping and large-scale reproduction. Device performance is characterized using a cytochrome c unfolding reaction. Unfolding processes with rates in excess of 30 s(-1) are easily measured, including the appearance of a 'native-like' intermediate that is maximally populated 180 ms post reaction initiation. To extract reliable rates from the data, a theoretical framework for the analysis of kinetics acquired under square-channel laminar flow is introduced.

Using TIRF microscopy to quantify and confirm efficient mass transfer at the substrate surface of the chemistrode

This paper describes experiments for characterizing mass transfer at the hydrophilic surface of the substrate in a chemistrode. The chemistrode uses microfluidic plugs to deliver pulses of chemicals to a substrate with high temporal resolution, which requires efficient mass transfer between the wetting layer and the hydrophilic surface of the substrate. Here, total internal reflection fluorescence microscopy (TIRFM) was used to image the hydrophilic surface of the substrate as plugs were made to flow over it. The surface of the substrate was rapidly saturated with a fluorescent dye as the fluroesecent plugs passed over the substrate, confirming effective mass transfer between the wetting layer and the surface of the substrate. The dynamics of saturation are consistent from cycle to cycle, indicating that the chemistrode can stimulate surfaces with high reproducibility. The number of plugs required to reach 90% saturation of the hydrophilic surface of the substrate, ϕ(90%), only weakly depended on experimental conditions (the Péclet number or the capillary number). Furthermore, over a wide range of operating conditions, ϕ(90%) was less than 4. These results are useful for improving the chemistrode and for understanding other phenomena that involve diffusional transfer in multiphase or recirculating flows near surfaces.

In situ assembly of linked geometrically coupled microdevices

Complex systems require their distinct components to function in a dynamic, integrated, and cooperative fashion. To accomplish this in current microfluidic networks, individual valves are often switched and pumps separately powered by using macroscopic methods such as applied external pressure. Direct manipulation and control at the single-device level, however, limits scalability, restricts portability, and hinders the development of massively parallel architectures that would take best advantage of microscale systems. In this article, we demonstrate that local geometry combined with a simple global field can not only reversibly drive component assembly but also power distinct devices in a parallel, locally uncoupled, and integrated fashion. By employing this single approach, we assemble and demonstrate the operation of check valves, mixers, and pistons within specially designed microfluidic environments. In addition, we show that by linking these individual components together, more complex devices such as pumps can be both fabricated and powered in situ.

Simple modeling of the physical sample dispersion process in rectangular meso (micro) channels with pressure-driven flows

The present paper reports the modeling and characterization of the physical sample dispersion process observed in rectangular microchannels when pressure-driven pumping is used. To explain experimental results provided by the silicon fluidic device constructed, two different mathematical models were tested. The first one is based on the diffusion-convection model, and the second one is based on the combination of ideal reactors. The silicon designed and constructed chip includes a microfluidic manifold with four inlet-outlet ports and a monolithically integrated optical flow cell. The microchannels, the optical flow cell, and the input-output ports were micromachined on a silicon wafer and then sealed with Pyrex glass anodically bonded. Optical windows were integrated in the chip, allowing simple absorbance-transmission measurements. Pressure-driven flows through fluidic channels were controlled via three-way solenoid valves and provided by an automatic microburette operating in aspiration mode. Experimentally obtained results demonstrate that the physical sample dispersion process can be easily modeled as a combination of a continuous stirred tank reactor and a plug-flow reactor.

Formation of miscible fluid microstructures by hydrodynamic focusing in plane geometries

We experimentally investigate the flow structures formed when two miscible fluids that have large viscosity contrasts are injected and hydrodynamically focused in plane microchannels. Parallel viscous flows composed of a central stream surrounded by symmetric sheath streams are examined as a function of the flow rates, fluid viscosities, and rates of molecular diffusion. We study miscible interfacial morphologies and show a route for manipulating viscous flow-segregation processes in plane microsystems. The diffusion layer at the boundary of an ensheathed fluid grows as function of the distance downstream and depends on the Péclet number. In particular, we observe diffusion-enhanced viscous ensheathing processes. In the presence of a constriction, we investigate the formation of a lubricated viscous thread in the converging flow and also the buckling morphologies of the thread in the diverging flow. This study, relevant to multifluid flow between a "thick" material and a "thin" solvent, demonstrates the possibility to further control steady and oscillatory miscible fluid microstructures.

Laser-induced cavitation based micropump

Lab-on-a-chip devices are in strong demand as versatile and robust pumping techniques. Here, we present a cavitation based technique, which is able to pump a volume of 4000 microm3 within 75 micros against an estimated pressure head of 3 bar. The single cavitation event is created by focusing a laser pulse in a conventional PDMS microfluidic chip close to the channel opening. High-speed photography at 1 million frames s(-1) resolves the flow in the supply channel, pump channel, and close to the cavity. The elasticity of the material affects the overall fluid flow. Continuous pumping at repetition rates of up to 5 Hz through 6 mm long square channels of 20 microm width is shown. A parameter study reveals the key-parameters for operation: the distance between the laser focus and the channel, the maximum bubble size, and the chamber geometry.

A practical guide to the staggered herringbone mixer

An analytical model of mixing in the staggered herringbone mixer (SHM) was derived to estimate mixing parameters and provide practical expressions to guide mixer design and operation for a wide range of possible solutes and flow conditions. Mixing in microfluidic systems has historically been characterized by the mixing of a specific solute system or by the redistribution of flow streams; this approach does not give any insight into the ideal operational parameters of the mixer with an arbitrary real system. For Stokes-flow mixers, mixing can be computed from a relationship between solute diffusivity, flow rate, and mixer length. Confocal microscopy and computational fluid dynamics (CFD) modeling were used to directly determine the extent of mixing for several solutes in the staggered herringbone mixer over a range of Reynolds numbers (Re) and Péclet numbers (Pe); the results were used to develop and evaluate an analytical model of its behavior. Mixing was found to be a function of only Pe and downstream position in the mixer. Required mixer length was proportional to log(Pe); this analytical model matched well with the confocal data and CFD model for Pe<5 x 10(4), at which point the experiments reached the limit of resolution. For particular solutes, required length and mixing time depend upon Re and diffusivity. This analytical model is applicable to other solute systems, and possibly to other embodiments of the mixer, to enable optimal design, operation, and estimation of performance.

Rate of mixing controls rate and outcome of autocatalytic processes: theory and microfluidic experiments with chemical reactions and blood coagulation

This article demonstrates that the rate of mixing can regulate the rate and outcome of both biological and nonbiological autocatalytic reaction systems that display a threshold response to the concentration of an activator. Plug-based microfluidics was used to control the timing of reactions, the rate of mixing, and surface chemistry in blood clotting and its chemical model. Initiation of clotting of human blood plasma required addition of a critical concentration of thrombin. Clotting could be prevented by rapid mixing when thrombin was added near the critical concentration, and mixing also affected the rate of clotting when thrombin was added at concentrations far above the critical concentration in two clinical clotting assays for human plasma. This phenomenon was modeled by a simple mechanism--local and global competition between the clotting reaction, which autocatalytically produces an activator, and mixing, which removes the activator. Numerical simulations showed that the Damköhler number, which describes this competition, predicts the effects of mixing. Many biological systems are controlled by thresholds, and these results shed light on the dynamics of these systems in the presence of spatial heterogeneities and provide simple guidelines for designing and interpreting experiments with such systems.

Shear-induced particle migration in one-, two-, and three-dimensional flows

We investigate the segregation resulting from the competition between advection and shear-induced migration of suspensions in steady open flows. Herringbone channels form a concentration profile deviating from the particle focusing found in straight channels. Transients can result from a buckling instability during the onset of migration when particle-depleted fluid is injected into particle-rich fluid. In chaotic flows, the better mixing found at low bulk volume fraction is not seen at higher bulk volume fraction. Thus, the ability of static mixers to reduce the effects of shear-induced migration is significantly limited.

Topology of advective-diffusive scalar transport in laminar flows

The present study proposes a unified Lagrangian transport template for topological description of advective fluid transport and advective-diffusive scalar transport in laminar flows. The key to this unified description is the expression of scalar transport as purely advective transport by the total scalar flux. This admits generalization of the concept of transport topologies known from laminar mixing studies to scalar transport. The study is restricted to two-dimensional systems and the fluid and scalar transport topologies, as a consequence, prove to be Hamiltonian. The unified Lagrangian transport template is demonstrated and investigated for a heat-transfer problem with nonadiabatic boundaries, representing generic scalar transport with permeable boundaries. The fluid and thermal transport topologies under steady conditions both accommodate islands (constituting isolated flow and thermal regions) that undergo Hamiltonian disintegration into chaotic seas upon introducing time periodicity. The thermal transport topology invariably comprises transport conduits that connect the nonadiabatic boundaries and facilitate wall-wall and wall-fluid heat transfer. For steady conditions these transport conduits are regular; for time-periodic conditions these conduits may, depending on degree of diffusion, be regular or chaotic. Regular conduits connect nonadiabatic walls only with specific flow regions; chaotic heat conduits establish connection (and thus heat exchange) of the nonadiabatic walls with the entire flow domain.

Electrohydrodynamic instabilities in microchannels with time periodic forcing

In microfluidic applications it has been observed that flows with spatial gradients in electrical conductivity are unstable under the application of sufficiently strong electric fields. These electrohydrodynamic instabilities can drive a nonlinear flow despite the low Reynolds number. Such flows hold promise as a simple mechanism for mixing fluids. In this work, the effect of a time periodic electric field on the instability is explored. The case where an electric field is applied across a diffuse interface of two fluids with varying electrical conductivity is considered. Frequency-dependent behavior is found only in the regime where the instability growth rates are very slow and cannot outpace mixing by molecular diffusion. Improving mixing by modulation of the electric body force is not a viable strategy in this geometry.

Laser-Induced Mixing in Microfluidic Channels

We demonstrate a novel strategy for mixing solutions and initiating chemical reactions in microfluidic systems. This method utilizes highly focused nanosecond laser pulses from a Q-switched Nd:YAG laser at lambda = 532 nm to generate cavitation bubbles within 100- and 200-microm-wide microfluidic channels containing the parallel laminar flow of two fluids. The bubble expansion and subsequent collapse within the channel disrupts the laminar flow of the parallel fluid streams and produces a localized region of mixed fluid. We use time-resolved imaging and fluorescence detection methods to visualize the mixing process and to estimate both the volume of mixed fluid and the time scale for the re-establishment of laminar flow. The results show that mixing is initiated by liquid jets that form upon cavitation bubble collapse and occurs approximately 20 micros following the delivery of the laser pulse. The images also reveal that mixing occurs on the millisecond time scale and that laminar flow is re-established on a 50-ms time scale. This process results in a locally mixed fluid volume in the range of 0.5-1.5 nL that is convected downstream with the main flow in the microchannel. We demonstrate the use of this mixing technique by initiating the horseradish peroxidase-catalyzed reaction between hydrogen peroxide and nonfluorescent N-acetyl-3,7-dihydroxyphenoxazine (Amplex Red) to yield fluorescent resorufin. This approach to generate the mixing of adjacent fluids may prove advantageous in many microfluidic applications as it requires neither tailored channel geometries nor the fabrication of specialized on-chip instrumentation.

Geometrical optimization of helical flow in grooved micromixers

Owing to the enhancement of surface effects at the micro-scale, patterned grooves on a micro-channel floor remain a powerful method to induce helical flows within a pressure driven system. Although there have been a number of numerical studies on geometrical effects concerning fluid mixing within the staggered herringbone mixer, all have focused mainly on the groove angle and depth, two factors that contribute greatly to the magnitude of helical flow. Here we present a new geometrical factor that significantly affects the generation of helical flow over patterned grooves. By varying the ratio of the length of the grooves to the neighboring ridges, helical flow can be optimized for a given groove depth and channel aspect ratio, with up to 50% increases in transverse flow possible. A thorough numerical study of over 700 cases details the magnitude of helical flow over unsymmetrical patterned grooves in a slanted groove micro-mixer, where the optimized parameters for the slanted groove mixer can be translated to the staggered herringbone mixer. The optimized groove geometries are shown to have a large dependence on the channel aspect ratio, the groove depth ratio, and the ridge length.

Mixing in 384-Well Plates: Issues, Measurements, and Solutions

Mixing in standard 384-well plates is different from mixing in 96-well formats. The aspect ratio of a typical well, the balance of surface tension and mass of the fluids, and the scale of diffusion all add to the increased difficulty in mixing fluids in higher-density plates. Here we examine two methods to measure mixing and some common techniques for mixing in 384-well plates. While conventional shaking can suffice, alternative methods can accelerate and improve the efficiency of mixing in 384-well plates.

Triggering and enhancing chaos with a prescribed target Lyapunov exponent using optimized perturbations of minimum power

The objective of the present work is to propose a method for nonfeedback anticontrol of chaos with perturbations of minimum power for a preset control goal. The noted Lorenz system is employed as the test model for chaotification with the target state specified by a prescribed positive value of the largest Lyapunov exponent (LLE), lambda[over ]>0 . Periodic and quasiperiodic perturbations are used as control signals, and the signals parameters are optimized using a genetic algorithm under restriction of minimum power. Performance of the optimized signals in triggering chaos at an ordered state, fixed point or periodic, as well as further enhancing chaoticity at a chaotic state is explored. The present numerical experiments reveal the following interesting physics about chaotification. In general, the power for chaotification increases with the preset value of lambda and quasiperiodic signals can achieve the control goal with a lower power than periodic ones. Given the same increment of LLE from that of the uncontrolled state (lambda1,0) , i.e., Deltalambda=lambda-lambda1,0, the further enhancement of chaoticity in a chaotic state needs a higher control power than the triggering of chaos from an ordered state. The minimum power required for chaotification of an ordered state increases relatively slowly for lower lambda[over ] but increases drastically as the preset target LLE reaches a certain critical value. Most strikingly, the numerical experiments demonstrate that this critical value of lambda corresponds to LLE of the nearest chaotic state in the neighborhood of the uncontrolled state. Robustness of applying the present method in the presence of external noise is also demonstrated.

Low power laser induced microfluidic mixing through localized surface plasmon

we present a new optical microfluidic mixing approach via surface tension driven force sustained by the localized surface plasmon (LSP) energy. The phonon energy associated with the non-radiative damping of LSP on an Au nanostructure creates thermal gradients capable of actuating a convective fluid flow. Experimental evidence and modeling results both show that LSP from the Au nanostructure is crucial to establish a temperature gradient with sufficient magnitude to induce the convective flow when using a low-power laser source.

Development of a microfluidic immobilised enzyme reactor

A microfluidic immobilised enzyme reactor consisting of a catalytically functionalised microstructure fabricated from silicone rubber material was used for steady-state kinetic characterisation of a thermophilic beta-glycosidase under pressure-driven flow conditions and continuous conversion of lactose by this enzyme at 80 degrees C.

Control and detection of chemical reactions in microfluidic systems

Recent years have seen considerable progress in the development of microfabricated systems for use in the chemical and biological sciences. Much development has been driven by a need to perform rapid measurements on small sample volumes. However, at a more primary level, interest in miniaturized analytical systems has been stimulated by the fact that physical processes can be more easily controlled and harnessed when instrumental dimensions are reduced to the micrometre scale. Such systems define new operational paradigms and provide predictions about how molecular synthesis might be revolutionized in the fields of high-throughput synthesis and chemical production.

Multivortex micromixing

The ability to mix liquids in microchannel networks is fundamentally important in the design of nearly every miniaturized chemical and biochemical analysis system. Here, we show that enhanced micromixing can be achieved in topologically simple and easily fabricated planar 2D microchannels by simply introducing curvature and changes in width in a prescribed manner. This goal is accomplished by harnessing a synergistic combination of (i) Dean vortices that arise in the vertical plane of curved channels as a consequence of an interplay between inertial, centrifugal, and viscous effects, and (ii) expansion vortices that arise in the horizontal plane due to an abrupt increase in a conduit's cross-sectional area. We characterize these effects by using confocal microscopy of aqueous fluorescent dye streams and by observing binding interactions between an intercalating dye and double-stranded DNA. These mixing approaches are versatile and scalable and can be straightforwardly integrated as generic components in a variety of lab-on-a-chip systems.

Microchemical systems for discovery and development

Applications of silicon-based microreactors are summarized starting with systems for single-phase organic transformations and progressing through multiphase catalytic systems to microsystems for multistep chemical synthesis. The latter systems involve extraction and gas-liquid separation processes designed to take advantage of the dominance of surface tension effects in microfluidic devices. Integration of physical sensors (e.g., for pressure, temperature, and flow) and measurements of chemical species further enhances the utility of microreactors by enabling chemical kinetic studies and optimization of optimal operating conditions. A brief description of synthesis and handling of solid particulates is included, with particular emphasis on multistep processing of colloidal nanoparticles. Finally, scale-up issues and challenges to the adoption of microreaction technology are discussed.

Small-volume rapid-mix device for subsecond kinetic analysis in flow cytometry

BACKGROUND

Rapid-mix flow cytometry has emerged as a powerful tool for mechanistic analysis of ligand binding, cell response, and molecular assembly. Although progress has come from improving sample delivery capabilities, little attention has been paid to the volumetric requirements associated with precious biological reagents.

METHODS

By using programmable syringes, valves, and other fluidic components, we created a modular, precisely regulated rapid-mix device for the delivery of small-volume samples to the flow cytometer. The device was tested using a bead-based assay in which the binding kinetics between native biotin and fluorescein biotin-bearing beads were characterized.

RESULTS

Bead suspensions and reagents paired in 35- to 45-microl aliquots were efficiently mixed by the device and delivered to the flow cytometer. Kinetic data associated with the fluorescein biotin beads were analyzed and used to calibrate the performance characteristics of the device in terms of sample delivery and mixing efficiency.

CONCLUSION

The rapid-mix device is capable of detecting subsecond kinetics of biological reactions using microliter volume of samples. Dimensions of the device have been minimized, and the quantitative aspects of sample delivery and analysis have been optimized. Further, the modular design has been optimized for adaptation to a variety of experimental protocols.

A microfluidic-based enzymatic assay for bioactivity screening combined with capillary liquid chromatography and mass spectrometry

The design and implementation of a continuous-flow microfluidic assay for the screening of (complex) mixtures for bioactive compounds is described. The microfluidic chip featured two microreactors (1.6 and 2.4 microL) in which an enzyme inhibition and a substrate conversion reaction were performed, respectively. Enzyme inhibition was detected by continuously monitoring the products formed in the enzyme-substrate reaction by electrospray ionization mass spectrometry (ESI-MS). In order to enable the screening of mixtures of compounds, the chip-based assay was coupled on-line to capillary reversed-phase high-performance liquid chromatography (HPLC) with the HPLC column being operated either in isocratic or gradient elution mode. In order to improve the detection limits of the current method, sample preconcentration based on a micro on-line solid-phase extraction column was employed. The use of electrospray MS allowed the simultaneous detection of chemical (MS spectra) and biological parameters (enzyme inhibition) of ligands eluting from the HPLC column. The present system was optimized and validated using the protease cathepsin B as enzyme of choice. Inhibition of cathepsin B is detected by monitoring three product traces, obtained by cleavage of the substrate. The two microreactors provided 32 and 36 s reaction time, respectively, which resulted in sufficient assay dynamics to enable the screening of bioactive compounds. The total flow rate was 4 microL min-1, which a 25-fold decrease was compared with a macro-scale system described earlier. Detection limits of 0.17-2.6 micromol L-1 were obtained for the screening of inhibitors, which is comparable to either microtiter plate assays or continuous-flow assays described in the literature.

Chaotic mixing in a steady flow in a microchannel

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.

Microfluidic systems for chemical kinetics that rely on chaotic mixing in droplets

This paper reviews work on a microfluidic system that relies on chaotic advection to rapidly mix multiple reagents isolated in droplets (plugs). Using a combination of turns and straight sections, winding microfluidic channels create unsteady fluid flows that rapidly mix the multiple reagents contained within plugs. The scaling of mixing for a range of channel widths, flow velocities and diffusion coefficients has been investigated. Due to rapid mixing, low sample consumption and transport of reagents with no dispersion, the system is particularly appropriate for chemical kinetics and biochemical assays. The mixing occurs by chaotic advection and is rapid (sub-millisecond), allowing for an accurate description of fast reaction kinetics. In addition, mixing has been characterized and explicitly incorporated into the kinetic model.

Foundations of chaotic mixing

The simplest mixing problem corresponds to the mixing of a fluid with itself; this case provides a foundation on which the subject rests. The objective here is to study mixing independently of the mechanisms used to create the motion and review elements of theory focusing mostly on mathematical foundations and minimal models. The flows under consideration will be of two types: two-dimensional (2D) 'blinking flows', or three-dimensional (3D) duct flows. Given that mixing in continuous 3D duct flows depends critically on cross-sectional mixing, and that many microfluidic applications involve continuous flows, we focus on the essential aspects of mixing in 2D flows, as they provide a foundation from which to base our understanding of more complex cases. The baker's transformation is taken as the centrepiece for describing the dynamical systems framework. In particular, a hierarchy of characterizations of mixing exist, Bernoulli --> mixing --> ergodic, ordered according to the quality of mixing (the strongest first). Most importantly for the design process, we show how the so-called linked twist maps function as a minimal picture of mixing, provide a mathematical structure for understanding the type of 2D flows that arise in many micromixers already built, and give conditions guaranteeing the best quality mixing. Extensions of these concepts lead to first-principle-based designs without resorting to lengthy computations.