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.

The development of assays that measure enzyme activities underlies much work in cell biology, clinical diagnostics, and drug discovery. Recent technical advances in microfluidic networks (µFNs) and in biochip microarrays have separately contributed to the development of assays that require few manipulations and that can simultaneously measure large numbers of activities. Microfluidic networks require small sample volumes and can integrate several sample processing steps on a single platform, 1 while biochips allow multiple assays to be performed on a single sample. 2 This paper reports a strategy for combining µFNs and biochip arrays to assay multiple enzyme activities in a sample.Microfluidic networks have most commonly been used to perform homogeneous phase assays, 3 but several recent examples have addressed solid-phase format assays. 4 These examples have emphasized immunoassays to detect, or quantitate, analytes. The use of µFN to assay multiple enzymatic activities is much less common, in part, because the labeling protocols required to identify these activities add several additional steps to the assays.We demonstrate the multi-analyte assay with a set of peptides that are selective substrates for a panel of kinase and phosphatase enzymes (Table 1). 5 The peptides contain a terminal cysteine residue, which permits immobilization to a self-assembled monolayer presenting maleimide groups. 6 To prepare the peptide arrays, we used a well-established "criss-cross" procedure for patterning. 7 A poly(dimethylsiloxane) (PDMS) stamp having six parallel channels in negative relief (500 µm width, 50 µm height) was applied to the monolayer, 8 and separate aqueous solutions each containing a different peptide (0.2 mM) were flowed into the channels in contact with the monolayer for 30 min ( Figure 1A). The channels were emptied, and the stamp was removed, washed, and reapplied to the monolayer in a perpendicular orientation so that each channel intersected each of the six immobilized peptides. Solutions containing each of the six kinases were next flowed over the monolayers for 1 h at 150 nL/min. 9 We then removed the stamp and used MALDI-TOF MS to analyze the 36 regions of the monolayer corresponding to treatment of each peptide with each of the kinases. 10,11 Spectra corresponding to regions where peptides had been immobilized but not exposed to kinases showed expected peaks for cysteine-mediated immobilization of the peptide substrate ( Figure 1B, ii). Only regions containing peptides that were exposed to specific kinases showed peaks corresponding to phosphorylation (iii). Figure 2A summarizes the specificity of each kinase for the panel of peptides. 12 The kinases showed the expected specificities toward the peptides. For example, the related kinases Abl and Src (and PKA and PKC) show a slight cross-reactivity for their peptide substrates. 5 We next illustrate that the peptide arrays can be used to identify enzyme activities in a mixture of kinases. Using the technique described above, we assayed kinase and inhi...