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Self-coalescing flows in microfluidics for pulse-shaped delivery of reagents


Microfluidic systems can deliver portable point-of-care diagnostics without the need for external equipment or specialist operators, by integrating all reagents and manipulations required for a particular assay in one device1. A key approach is to deposit picogram quantities of dried reagents in microchannels with micrometre precision using specialized inkjet plotters2,3,4,5. This means that reagents can be stored for long periods of time and reconstituted spontaneously when adding a liquid sample. But it is challenging to carry out complex operations using multiple reagents, because shear flow enhances their dispersion and they tend to accumulate at moving liquid fronts, resulting in poor spatiotemporal control over the concentration profile of the reconstituted reagents6. One solution is to limit the rate of release of reagents into the liquid7,8,9,10. However, this requires the fine-tuning of different reagents, conditions and targeted operations, and cannot readily produce the complex, time-dependent multireagent concentration pulses required for sophisticated on-chip assays. Here we report and characterize a capillary flow phenomenon that we term self-coalescence, which is seen when a confined liquid with a stretched air–liquid interface is forced to ‘zip’ back onto itself in a microfluidic channel, thereby allowing reagent reconstitution with minimal dispersion. We provide a comprehensive framework that captures the physical underpinning of this effect. We also fabricate scalable, compact and passive microfluidic structures—‘self-coalescence modules’, or SCMs—that exploit and control this phenomenon in order to dissolve dried reagent deposits in aqueous solutions with precise spatiotemporal control. We show that SCMs can reconstitute multiple reagents so that they either undergo local reactions or are sequentially delivered in a flow of liquid. SCMs are easily fabricated in different materials, readily configured to enable different reagent manipulations, and readily combined with other microfluidic technologies, so should prove useful for assays, diagnostics, high-throughput screening and other technologies requiring efficient preparation and manipulation of small volumes of complex solutions.

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Fig. 1: Description and modelling of self-coalescence in a microchannel.
Fig. 2: SCM for reagent reconstitution.
Fig. 3: Scalability of SCMs.
Fig. 4: Reagent pulse shaping and generation of complex concentration profiles.
Fig. 5: Biochemical reactions in SCMs.

Data availability

The data that support the findings of this study are available from the corresponding authors on request.

Code availability

The code for the Schwarz–Christoffel mapping of self-coalescence (using Matlab), as well as the code for reagent pulse shaping (using Maple), is available on request from T.G.


  1. Yager, P. et al. Microfluidic diagnostic technologies for global public health. Nature 442, 412–418 (2006).

    Article  CAS  ADS  Google Scholar 

  2. Hughes, T. R. et al. Expression profiling using microarrays fabricated by an ink-jet oligonucleotide synthesizer. Nat. Biotechnol. 19, 342–347 (2001).

    Article  CAS  Google Scholar 

  3. Derby, B. Printing and prototyping of tissues and scaffolds. Science 338, 921–926 (2012).

    Article  CAS  ADS  Google Scholar 

  4. Sirringhaus, H. et al. High-resolution inkjet printing of all-polymer transistor circuits. Science 290, 2123–2126 (2000).

    Article  CAS  ADS  Google Scholar 

  5. Gökçe, O., Mercandetti, C. & Delamarche, E. High-content optical codes for protecting rapid diagnostic tests from counterfeiting. Anal. Chem. 90, 7383–7390 (2018).

    Article  Google Scholar 

  6. Hitzbleck, M. & Delamarche, E. Reagents in microfluidics: an ‘in’ and ‘out’ challenge. Chem. Soc. Rev. 42, 8494–8516 (2013).

    Article  CAS  Google Scholar 

  7. Fridley, G. E., Le, H. Q., Fu, E. & Yager, P. Controlled release of dry reagents in porous media for tunable temporal and spatial distribution upon rehydration. Lab Chip 12, 4321–4327 (2012).

    Article  CAS  Google Scholar 

  8. Beck, M. et al. On-chip sample preparation by controlled release of antibodies for simple CD4 counting. Lab Chip 12, 167–173 (2012).

    Article  CAS  Google Scholar 

  9. Hitzbleck, M., Gervais, L. & Delamarche, E. Controlled release of reagents in capillary-driven microfluidics using reagent integrators. Lab Chip 11, 2680–2685 (2011).

    Article  CAS  Google Scholar 

  10. Garcia, E., Kirkham, J. R., Hatch, A. V., Hawkins, K. R. & Yager, P. Controlled microfluidic reconstitution of functional protein from an anhydrous storage depot. Lab Chip 4, 78–82 (2004).

    Article  CAS  Google Scholar 

  11. Hele-Shaw, H. S. The flow of water. Nature 58, 34–36 (1898).

    Article  ADS  Google Scholar 

  12. Oliver, J. F., Huh, C. & Mason, S. G. Resistance to spreading of liquids by sharp edges. J. Colloid Interface Sci. 59, 568–581 (1977).

    Article  CAS  ADS  Google Scholar 

  13. de Gennes, P. G., Brochard-Wyart, F. & Quéré, D. Capillary Wetting Phenomena: Drops, Bubbles, Pearls, Waves 225–226 (Springer, 2004).

  14. Howison, S. Complex variable methods in Hele-Shaw moving boundary problems. Eur. J. Appl. Math. 3, 209–224 (1992).

    Article  MathSciNet  Google Scholar 

  15. Goyette, P.-A. et al. Microfluidic multipoles theory and applications. Nat. Commun. 10, 1781 (2019).

    Article  ADS  Google Scholar 

  16. Driscoll, T. A. & Trefethen, L. N. Schwarz–Christoffel Mapping (Cambridge Univ. Press, 2002).

  17. Bensimon, D., Kadanoff, L. P., Liang, S., Shraiman, B. I. & Tang, C. Viscous flow in two dimensions. Rev. Mod. Phys. 58, 977–999 (1986).

    Article  ADS  Google Scholar 

  18. Zimmermann, M., Schmid, H., Hunziker, P. & Delamarche, E. Capillary pumps for autonomous capillary systems. Lab Chip 7, 119–125 (2007).

    Article  CAS  Google Scholar 

  19. Vulto, P. et al. Phaseguides: a paradigm shift in microfluidic priming and emptying. Lab Chip 11, 1596–1602 (2011).

    Article  CAS  Google Scholar 

  20. Safavieh, R. & Juncker, D. Capillarics: pre-programmed, self-powered microfluidic circuits built from capillary elements. Lab Chip 13, 4180–4189 (2013).

    Article  CAS  Google Scholar 

  21. Zhao, B., Moore, J. S. & Beebe, D. J. Surface-directed liquid flow inside microchannels. Science 291, 1023–1026 (2001).

    Article  CAS  ADS  Google Scholar 

  22. Weiner, A. M. Femtosecond pulse shaping using spatial light modulators. Rev. Sci. Instrum. 71, 1929–1960 (2000).

    CAS  ADS  Google Scholar 

  23. Guilbault, G. G. & Kramer, D. N. Fluorometric procedure for measuring the activity of dehydrogenases. Anal. Chem. 37, 1219–1221 (1965).

    Article  CAS  Google Scholar 

  24. LaRue, N. et al. Comparison of quantitative and qualitative tests for glucose-6-phosphate dehydrogenase deficiency. Am. J. Trop. Med. Hyg. 91, 854–861 (2014).

    Article  CAS  Google Scholar 

  25. Cappellini, M. & Fiorelli, G. Glucose-6-phosphate dehydrogenase deficiency. Lancet 371, 64–74 (2008).

    Article  CAS  Google Scholar 

  26. Piepenburg, O., Williams, C. H., Stemple, D. L. & Armes, N. A. DNA detection using recombination proteins. PLoS Biol. 4, e204 (2006).

    Article  Google Scholar 

  27. Paegel, B. M., Hutt, L. D., Simpson, P. C. & Mathies, R. A. Turn geometry for minimizing band broadening in microfabricated capillary electrophoresis channels. Anal. Chem. 72, 3030–3037 (2000).

    Article  CAS  Google Scholar 

  28. Schindelin, J. et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012).

    Article  CAS  Google Scholar 

  29. Zimmermann, T. Spectral imaging and linear unmixing in light microscopy. Adv. Biochem. Eng. Biotechnol. 95, 245–265 (2005).

    PubMed  Google Scholar 

  30. Seaman, W. T. et al. Detection and quantitation of HPV in genital and oral tissues and fluids by real time PCR. Virol. J. 7, 194 (2010).

    Article  Google Scholar 

  31. Glock, G. E. & McLean, P. Further studies on the properties and assay of glucose 6-phosphate dehydrogenase and 6-phosphogluconate dehydrogenase of rat liver. Biochem. J. 55, 400–408 (1953).

    Article  CAS  Google Scholar 

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O.G., Y.T. and E.D. thank W. Riess for continuous support, and acknowledge partial funding from the European Union’s 7th Framework programme Chips4Life project (278720) and the IBM Research Frontiers Institute. O.G. and E.D. thank Coris BioConcept for discussions on DNA-amplification technologies, and microfluidic ChipShop for the fabrication of polymer prototypes using injection moulding. T.G. thanks C. Boudoux and S. Prudhomme (from the École Polytechnique de Montréal) for useful discussions. T.G. acknowledges support from the Natural Sciences and Engineering Council of Canada (NSERC; RGPIN2014-06409), the Fonds de Recherche du Québec–Nature et Technologies (FRQNT), and CMC microsystems.

Author information

Authors and Affiliations



E.D. conceived the research. O.G. discovered self-coalescing flows, designed SCMs and experiments, and conducted the experiments. T.G. developed the theoretical framework and contributed to the experimental design. S.C. performed the conformal mapping calculations and the numerical simulations, and contributed to the theoretical framework. O.G., S.C. and T.G. analysed the data. Y.T. fabricated microfluidic chips and documented them using scanning electron microscopy. O.G., T.G. and E.D. wrote the manuscript. All authors discussed and provided input to the manuscript.

Corresponding authors

Correspondence to Thomas Gervais or Emmanuel Delamarche.

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Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature thanks Piotr Garstecki and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Fig. 1 Characterization of reagent dissolution in SCMs and control experiments.

a, Bright-field microscope images of microfluidic chips in silicon, each chip being composed of a rounded inlet (left), an SCM (middle), and a meandering channel (right) used for conveniently measuring the concentration profile of the solution exiting the SCM. b, Amaranth solutions from an SCM (left) and in a control microchannel (right) are readily visualized using the meandering channels. c, Calibration curve for quantification of the concentration of reconstituted amaranth (n = 4 for each concentration). Error bars represent standard error of the mean. d, Concentration profiles of amaranth solution reconstituted in SCMs or control microchannels (Qin = 500 nl min−1). Means of individual acquisitions are displayed with dark coloured lines and individual acquisitions with a lighter shading. Amaranth solution was inkjet spotted into SCMs at 100 ng mm−1 (250-µm pitch). The reagent accumulation in the control was so strong that the amaranth solution was diluted ×30 before deposition to keep the absorbance signal in the dynamic range of the camera. The concentration profile from control experiments shown in Fig. 2d is scaled up from this diluted signal.

Extended Data Fig. 2 Fabrication steps for SCMs with depressed barriers, and scanning electron microscopy images of representative SCMs.

a, Silicon wafers are processed by standard photolithography and multiple steps of deep reactive-ion etching (DRIE). Specifically, a 1.2-µm-thick AZ 6612 photoresist layer is patterned (step 1) to mask the SiO2 layer during etching in buffered hydrofluoric acid (BHF; step 2). A new layer of AZ 6621 is patterned (step 3), exposing the areas that are etched to form the trenches during the first DRIE step (step 4). Later, using the patterned SiO2 layer as the mask, a second DRIE step forms the microchannels while preserving the trenches (step 5). After dicing, the chips are cleaned and silanized in trichloro(octyl)silane solution (step 6). After reagent deposition, chips are sealed with a layer of polydimethylsiloxane (PDMS; step 7). b, Image of an SCM fabricated in silicon, with yellow frames highlighting particular regions shown below. c, The leading barrier with a trench geometry. Here, for visual clarity, the trench width is 20 µm, but 5-µm-wide trenches were used in experiments. The curved end of the leading barrier facilitates the initiation of self-coalescing flow. d, Diversion barrier with a step-down geometry. e, Raised vertical CPLs at the entrance of the SCM help to keep the meniscus away from the side wall coloured in blue. f, The barrier at the vent entrance (arrowhead) ensures that liquid does not enter the vent. The depths of the SCM (HSCM), outlet (Houtlet) and barriers (Hbarrier) are shown on the images. g, h, Scanning electron microscopy (SEM) images of the devices used in G6PDH reactions (g) and in RPA reactions (h). (The numbers 1-2 and 1-4 are device numbers.).

Extended Data Fig. 3 SCM volume scaling experiments.

a, Bright-field microscope images of devices fabricated in silicon (numbered 1-1 to 1-5) in which volume scaling experiments were performed. As discussed in Fig. 1d, the velocity of the self-coalescing flow decays more quickly in narrower than in wider SCMs. In order to maintain a quick decay of the self-coalescing flow velocity in wide SCMs, the leading barrier is simply shifted towards the area in which reagents are deposited. Amaranth is deposited at 100 ng mm−1 (250-µm pitch). A spotting alignment mark is used to align the inkjet spotter head with the microfluidic chips for precise targeting of the deposition location. b, Bright-field microscope images showing the amaranth solution in the meandering channels, reconstituted in the SCMs shown in panel a. c, Time series of bright-field microscope images showing the reconstitution of amaranth in a 1-mm-wide SCM (Qin = 500 nl min−1). Typically, in wide SCMs (wider than 0.5 mm), lateral homogenization of the reconstituted reagent is complete at the narrow outlet of the SCM (as seen here), and can be enhanced, if necessary, by adding a Dean vortex mixer, a chaotic mixer, or a simple meandering channel. Larger volumes of solution with reconstituted reagents can also be achieved using an array of parallel SCMs. SCMs are easily scaled; however, making them longer decreases the maximum filling flow rate because the pressure at the inlet needs to be lower than the Laplace pressure over the CPL.

Extended Data Fig. 4 Assessment of the stability of the leading barrier.

a, During longitudinal flow, the hydraulic pressure (Phydraulic) increases as the hydraulic resistance (Rhydraulic) increases with the distance travelled by the liquid. The leading barrier is able to preserve the longitudinal flow as long as the pinning forces (PLaplace) can balance the increasing hydraulic pressure and the pressure exerted by the resistance to wetting (Rwetting). In order to investigate this effect, the width (W = 75, 100, 125, 150, 175 or 200 µm) and the height (H = 30, 45 or 90 µm) of the longitudinal flow area and the filling flow rate (Qin = 0.75, 1.5 or 3.0 µl min−1) were varied. During experiments, the maximum distance along which the liquid remains pinned was measured. b, Bright-field (left) and SEM (right) images of devices in which stability-assessment experiments are performed. c, Experimental data support theoretical predictions that: first, a smaller liquid–vapour interface can bear a higher hydraulic pressure; second, the hydraulic radius of the longitudinal flow area needs to be large in order to fill deeper structures or for high filling flow rates; and third, the flow rate challenges the stability of the leading barrier. Data points are means of experiments (n = 8 or more; error bars represent standard error of the mean). Conditions in which the liquid was not pinned at the CPL (longitudinal flow length = 0  mm) or the liquid travelled to the end of the test device (longitudinal flow length = 65 mm) are excluded from the plot.

Extended Data Fig. 5 Predicted complex concentration profiles from diffusion–dispersion models.

a, Illustration of the experimental method for analysing dispersion in SCMs and in downstream channels at distance d. C, concentration. bg, Predicted concentration profiles for experiments shown in Fig. 4 (C(t) in arbitrary units). b, c, Results of controlling the spotting pitch to generate spiked (b) or flat (c) concentration pulses at optimal (Pé = 5.6; top panels) and large (Pé = 100; lower panels) Péclet numbers, at constant spotted reagent mass. d, Signal decorrelation over time due to Taylor–Aris dispersion for several positions of the detection zone (Pé = 13). e, Pulsing of two spatially resolved different reagents (Pé = 13). f, Pulsing of a flat profile of two mixed reagents by alternated spotting and flow control (Pé = 13). g, Pulsing of two linear concentration gradients to a detection zone (Pé = 13).

Extended Data Fig. 6 Release of reconstituted reagents from an SCM with time delays.

A chamber of volume Vdelay at the entrance of the vent adds a delay before a liquid leaves the SCM. a, Time series of images showing filling of the delay chamber while reconstituted amaranth diffuses. Reagents in area A, but not in area B, have additional time to reconstitute/diffuse while the rest of the SCM fills (t = 0 s). If needed, using a delay chamber gives additional time for the reconstitution/diffusion of the B reagents. Arrowheads mark the liquid filling front in the delay chamber. b, Effect of delay on the concentration profile of points A and B. Without any delay, point B disperses more than it does with a delay, and its profile is broader (n = 9; Qin = 200 nl min−1). c, Measured delay provided by different delay chambers. The dashed line is the identity line; error bars represent standard error of the mean; n = 6; Qin = 200 nl min−1.

Extended Data Fig. 7 Optimization and calibration of RPA reactions in SCMs.

a, b, Optimization data for SYBR Green concentration (a; four experiments) and Mg2+ concentration (b; five experiments) for amplification of ten copies per microlitre of HPV-18 DNA. c, DNA concentration calibration (seven experiments) for HPV-18 DNA quantification. Plots show amplification onset time extracted from SYBR Green fluorescence signals. Error bars represent standard errors of the mean.

Extended Data Fig. 8 Characterization of dissolution of multiple reagents in SCMs.

a, Bright-field image of the device in which reagent pulse shaping and complex profile generation experiments were performed. The diversion barrier of these SCMs has a trench geometry in order to keep the dimensions of the dispersion analysis channel identical to the dimensions of the SCM. b, Absorbance calibration curve, and, c, the calibration curve after linear spectral unmixing of the amaranth signal. d, e, As for panels b, c, but for the brilliant blue signal. n = 6 for each data point. Error bars represent standard errors of the mean.

Extended Data Fig. 9 Experimental setup.

a, The setup for filling SCMs and documenting the dissolution of food dyes. b, Filling SCMs manually using a micropipette for G6PDH quantification experiments. c, Measuring the fluorescence signal from G6PDH and RPA reactions using a microtitre plate reader fitted with a custom-made aluminium adaptor.

Extended Data Table 1 The parameters used in simulations

Supplementary information

Supplementary Information

This file contains additional information and equations on the theoretical framework.

Video 1: Fluorescent microspheres revealing the streamlines of a self-coalescing flow.

4.8 µm fluorescent microspheres suspended in a liquid are injected into an SCM (0.5-mm-wide) at 0.5 µl min−1 flow rate. The video is in real time with each frame acquired over a 60 ms exposure.

Video 2: Reagent reconstitution in an SCM.

An SCM (L×W×D, 5 mm × 0.5 mm × 50 µm) spotted with amaranth dye is filled with water at 0.5 µl min−1 flow rate. The video is accelerated (3×).

Video 3: Self-coalescence and Saffman–Taylor viscous fingering.

Filling of an SCM observed using fluorescent microparticles. The experimental image is only the top half of the video. The part below the central mirror symmetry line (located at the device wall) is simply a reflection of the upper half made to highlight a similitude between self-coalescence and Saffman–Taylor viscous fingering. The height of the SCM is 50 µm and its width is 500 µm with a flow rate of 0.5 µL min−1 and λ = 1/2. The video is shown along with the discussion in Supplementary Information, section 1.5.2

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Gökçe, O., Castonguay, S., Temiz, Y. et al. Self-coalescing flows in microfluidics for pulse-shaped delivery of reagents. Nature 574, 228–232 (2019).

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