where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

This article reviews the application of electric circuit methods for the analysis of pressure-driven microfluidic networks with an emphasis on concentration- and flow-dependent systems. The application of circuit methods to microfluidics is based on the analogous behaviour of hydraulic and electric circuits with correlations of pressure to voltage, volumetric flow rate to current, and hydraulic to electric resistance. Circuit analysis enables rapid predictions of pressure-driven laminar flow in microchannels and is very useful for designing complex microfluidic networks in advance of fabrication. This article provides a comprehensive overview of the physics of pressure-driven laminar flow, the formal analogy between electric and hydraulic circuits, applications of circuit theory to microfluidic network-based devices, recent development and applications of concentration- and flow-dependent microfluidic networks, and promising future applications. The lab-on-a-chip (LOC) and microfluidics community will gain insightful ideas and practical design strategies for developing unique microfluidic network-based devices to address a broad range of biological, chemical, pharmaceutical, and other scientific and technical challenges.

Design of pressure-driven microfluidic networks using electric circuit analogy

Mixing in microfluidic devices presents a challenge due to laminar flows in microchannels, which result from low Reynolds numbers determined by the channel's hydraulic diameter, flow velocity, and solution's kinetic viscosity. To address this challenge, novel methods of mixing enhancement within microfluidic devices have been explored for a variety of applications. Passive mixing methods have been created, including those using ridges or slanted wells within the microchannels, as well as their variations with improved performance by varying geometry and patterns, by changing the properties of channel surfaces, and by optimization via simulations. In addition, active mixing methods including microstirrers, acoustic mixers, and flow pulsation have been investigated and integrated into microfluidic devices to enhance mixing in a more controllable manner. In general, passive mixers are easy to integrate, but difficult to control externally by users after fabrication. Active mixers usually take efforts to integrate within a device and they require external components (e.g. power sources) to operate. However, they can be controlled by users to a certain degree for tuned mixing. In this article, we provide a general overview of a number of passive and active mixers, discuss their advantages and disadvantages, and make suggestions on choosing a mixing method for a specific need as well as advocate possible integration of key elements of passive and active mixers to harness the advantages of both types.

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Mixing in microfluidic devices and enhancement methods

Flow approaches towards sustainability

Micromixers are crucial components within micro biomedical systems. This article presents a comprehensive review of the main state-of-the art applications of micromixers in biomedical systems over the past ten years. The article commences by reviewing the fundamental fluidic behaviors involved in microfluidic mixing. The biomedical applications of micromixers are then described in regard to their use particularly for (1) sample concentration, (2) chemical synthesis, (3) chemical reaction, (4) polymerization, (5) extraction and purification, (6) biological analysis, and (7) droplet/emulsion processes and others. The review concludes with a brief statistical analysis of the published literature in the micromixer field and an overview of the relative advantages of passive micromixers compared to active micromixers.

Recent advances and applications of micromixers

The improvement on the transmission loss of a duct by adding Helmholtz resonators

The mixing and reaction performance of a split-and-recombine (SAR) microreactor was enhanced on modification of the geometric configuration. A rotation of fluid is induced on shrinking the structure of the splitting and reorientation region in alternate directions, thus improving the pattern of multi-lamination and enhancing the chaos of the fluid. To design and to analyze systematically the performance of the reactors, an effective method involving chaotic analysis and fluorescent resonant-energy transfer (FRET) is proposed. The structural design of a passive microreactor to generate an effective contact between the reagents is of great practical significance. SAR microreactors of four types with various microstructures were designed to illustrate the effects of geometric patterns (i.e., arrangement and dimensions) on mixing and reaction. Through analysis of the chaos, we revealed numerically the dynamic mixing governed by multi-lamination and chaotic mechanisms in the devices. The results show that specific structural designs induce rotation and rearrangement of fluids, thus elongating their material interface; the mixing of the fluids consequently improved. We investigated the hybridization of two complementarily labeled oligonucleotides in the devices by means of FRET. How the devices affected the rate of hybridization was thereby assessed, verifying that FRET is a technique capable of estimating the practical applicability of these devices.

Analysis of chaos and FRET reaction in split-and-recombine microreactors

Flash synthesis of carbohydrate derivatives in chaotic microreactors

We propose a novel technique that allows oligonucleotides with specific end-modification within a plug in a plug-based microfluidic device to undergo a locally enhanced concentration at the rear of the plug as the plug moves downstream. DNA was enriched and detected in situ upon exploiting a combined effect underlain by an entropic force induced through fluid shear (i.e. a hydrodynamic-repellent effect) and the interfacial adsorption (aqueous/oil interface) attributed to affinity. Flow fields within a plug were visualized quantitatively using micro-particle image velocimetry (micro-PIV); the distribution of the fluid shear strain rate explains how the hydrodynamic-repellent effect engenders a dumbbell-like region with an increased concentration of DNA. The concentration of FAM (6-carboxy-fluorescein)-labeled DNA (FC-DNA) and of TAMRA (tetramethyl-6-carboxyrhodamine)-labeled DNA (TC-DNA), respectively, and the hybridization of probe DNA (modified with FAM) with target DNA (modified with TAMRA) were investigated in devices; a confocal fluorescence microscope (CFM) was utilized to monitor the processes and to resolve the corresponding 2D patterns and 3D reconstruction of the DNA distribution in a plug. TC-DNA, but not FC-DNA, concentrating within a plug was affected by the combined effect so as to achieve a concentration factor (Cr) twice that of FC-DNA because of the lipophilicity of TAMRA. Using fluorescence resonance-energy transfer (FRET), we characterized the hybridization of the DNA in a plug; the detection limit of a system, improved by virtue of the proposed technique (the locally enhanced concentration), for DNA detection was estimated to be 20–50 nM. This technique enables DNA to concentrate locally in a nL–pL free-solution plug, the locally enhanced concentration to profit the hybridization efficiency and the detection of DNA, prospectively serving as a versatile means to accomplish a rapid DNA detection in a small volume for a Lab-on-a-Chip (LOC) system.

Locally enhanced concentration and detection of oligonucleotides in a plug-based microfluidic device

For the diagnosis of biochemical reactions, the investigation of microflow behavior, and the confirmation of simulation results in microfluidics, experimentally quantitative measurements are indispensable. To characterize the mixing and reaction of fluids in microchannel devices, we propose a mixing quality index (Mqi) to quantify the cross-sectional patterns (also called mixing patterns) of fluids, captured with a confocal-fluorescence microscope (CFM). The operating parameters of the CFM for quantification were carefully tested. We analyzed mixing patterns, flow advection, and mass exchange of fluids in the devices with overlapping channels of two kinds. The mixing length of the two devices derived from the analysis of Mqi is demonstrated to be more precise than that estimated with a commonly applied method of blending dye liquors. By means of fluorescence resonance-energy transfer (FRET), we monitored the hybridization of two complementary oligonucleotides (a FRET pair) in the devices. The captured patterns reveal that hybridization is a progressive process along the downstream channel. The FRET reaction and the hybridization period were characterized through quantification of the reaction patterns. This analytical approach is a promising diagnostic tool that is applicable to the real-time analysis of biochemical and chemical reactions such as polymerase chain reaction (PCR), catalytic, or synthetic processes in microfluidic devices.

/pdf/characterization-of-microfluidic-mixing-and-reaction-in-rnmh9avogv.pdf

Yu-Tzu Chen

Papers

The improvement on the transmission loss of a duct by adding Helmholtz resonators

Analysis of chaos and FRET reaction in split-and-recombine microreactors

Flash synthesis of carbohydrate derivatives in chaotic microreactors

Locally enhanced concentration and detection of oligonucleotides in a plug-based microfluidic device

Characterization of microfluidic mixing and reaction in microchannels via analysis of cross-sectional patterns.