This letter describes an experimental test of a simple argument that predicts the scaling of chaotic mixing in a droplet moving through a winding microfluidic channel. Previously, scaling arguments for chaotic mixing have been described for a flow that reduces striation length by stretching, folding, and reorienting the fluid in a manner similar to that of the baker's transformation. The experimentally observed flow patterns within droplets ͑or plugs͒ resembled the baker's transformation. Therefore, the ideas described in the literature could be applied to mixing in droplets to obtain the scaling argument for the dependence of the mixing time, tϳ(aw/U)log(Pe), where w ͓m͔ is the cross-sectional dimension of the microchannel, a is the dimensionless length of the plug measured relative to w, U This letter describes an experimental test of a simple argument that predicts the scaling of mixing of solutions by chaotic advection inside droplets moving through winding microfluidic channels.1 In microfluidic systems 2,3 operating at low values of the Reynolds number Re, streams of reagents flow laminarly. Diffusive mixing across laminar streams is slow because the mixing time t diff ͓s͔ is proportional to the square of the initial striation length stl(0) ͓m͔, the distance over which the mixing occurs by diffusion with a diffusion coefficient D ͓m 2 s Ϫ1 ͔:Mixing that occurs purely by diffusion is too slow for many applications of microfluidic systems, including highthroughput analysis and kinetic measurements. Methods designed to accelerate mixing aim to reduce the striation length, and several attractive approaches have been developed and reviewed. 2 Chaotic advection 4,5 enhances mixing by stretching and folding the fluid to give rise to an exponential decrease in the striation length stl. 4 In principle, presence of chaos does not guarantee widespread rapid mixing because poorly mixed islands can coexist with well-mixed chaotic regions.

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.

This paper analyzes the effect of mixing on nucleation of protein crystals. Nucleation is an important aspect of protein crystallization. 1 In-depth research has been conducted leading to insights into the mechanism of crystal nucleation as well as novel methods to control it 1,2 (e.g., work on nucleation at the liquid-liquid-phase boundary and on levitated droplets), but the effect of several factors affecting nucleation is not well understood. Mixing is proposed to be responsible for uncertainties in batch protein crystallization. 3 Mixing is also important in the nucleation of small molecule crystals 4 and selectivity of organic reactions, 5 but its effect on nucleation of protein crystals has not been studied experimentally. One barrier to this study is the difficulty of controlling and monitoring mixing, especially when using manual or robotic pipets. Crystal nucleation is a stochastic process, and to obtain statistically significant data, studies of nucleation necessitate a large number of experiments. The amount of the protein and labor required presents another barrier.Here we show that a plug-based microfluidic system 6 is suitable for observing mixing effects in crystal nucleation. The system is capable of setting up hundreds of crystallization experiments in a short period of time, 7 requiring little labor and ~1 μL samples of protein solutions. It relies on nL-volume aqueous plugs in a water-immiscible, fluorinated carrier fluid, where each plug acts as a microreactor in which a crystallization trial takes place. Mixing by chaotic advection in the system is well-controlled and characterized. 8 Chaotic advection has been pioneered in single-phase microfluidic devices. 9 The use of two-phase flows in plugs is attractive because it can transport solids, 10 such as precipitates that might arise during crystallization experiments.Mixing experiments were carried out by combining protein (thaumatin) and precipitant (2 M KNaC 4 H 4 O 6 ) solutions in a PDMS microfluidic channel. The solutions were separated by a thin stream of buffer to avoid contact 6 before forming plugs (Figure 1a). Mixing was changed by varying the total flow rate (higher flow rate corresponding to more rapid mixing in a winding channel). 8 The flow rate ratios between protein, buffer, and salt solutions were kept constant. Mixed plugs were collected in a glass capillary, 7 which was sealed and incubated at 18 °C. The number of crystals in each plug was monitored over time.Nucleation was sensitive to flow rate and mixing. Rapid nucleation took place at low flow velocities: i) precipitate was visible as the plugs were being mixed, and ii) these plugs yielded precipitation or showers of microcrystals after incubation for 8 h, indicating many nucleation events per plug. At high flow velocities, no precipitation was visible, and only a few large crystals grew after 8 h (Figure 1) of incubation, representing only a few nucleation events in each plug.E-mail: r-ismagilov@uchicago.edu. Supporting Information Available: Experimental details and a...

Protein crystallization is important for determining protein structures by X-ray diffraction. Nanolitersized plugs -aqueous droplets surrounded by a fluorinated carrier fluid -have been applied to the screening of protein crystallization conditions. Preformed arrays of plugs in capillary cartridges enable sparse matrix screening. Crystals grown in plugs inside a microcapillary may be analyzed by in situ X-ray diffraction. Screening using plugs, which are easily formed in PDMS microfluidic channels, is simple and economical, and minimizes consumption of the protein. This approach also has the potential to improve our understanding of the fundamentals of protein crystallization, such as the effect of mixing on the nucleation of crystals.

This article reports a functional chemical reaction network synthesized in a microfluidic device. This chemical network performs chemical 5000-fold amplification and shows a threshold response. It operates in a feedforward manner in two stages: the output of the first stage becomes the input of the second stage. Each stage of amplification is performed by a reaction autocatalytic in Co(2+). The microfluidic network is used to maintain the two chemical reactions away from equilibrium and control the interactions between them in time. Time control is achieved as described previously (Angew. Chem., Int. Ed. 2003, 42, 768) by compartmentalizing the reaction mixture inside plugs which are aqueous droplets carried through a microchannel by an immiscible fluorinated fluid. Autocatalytic reaction displayed sensitivity to mixing; more rapid mixing corresponded to slower reaction rates. Synthetic chemical reaction networks may help understand the function of biochemical reaction networks, the goal of systems biology. They may also find practical applications. For example, the system described here may be used to detect visually, in a simple format, picoliter volumes of nanomolar concentrations of Co(2+), an environmental pollutant.