MICROFLUIDIC PRODUCTION OF DROPLET PAIRS

BACKGROUND OF THE INVENTION

[0001] In vitro compartmentalization (IVC) techniques [1], in which water-in-oil droplets are used as femtoliter to nanoliter reactors, allow as many as 10 ¹⁰ reactions to be performed in parallel in only one milliliter of emulsion. The small volumes of the reaction compartments enables the study of reactions at the single molecule, single gene, or single cell level [2, 3]. Combining IVC and microfluidics techniques [4, 5] promises to give an unprecedented level of control for high-throughput screening of chemical and biochemical processes [6]. Indeed, recent progress in the field of two-phase-flow microfluidic systems [7, 8] has enabled controlled operations on droplets in microchannels, such as the production of monodisperse emulsions [9], splitting of droplets [10], fusion of pairs of droplets [11, 12], and sorting [13].

[0002] In addition, the use of microfluidic systems in the synthesis of nanoparticles is attracting increasing attention. Compared to conventional bulk synthesis strategies, microfluidic systems allow more precise control of the reaction conditions which can lead to reductions in particle size and polydispersity [20]. A range of different nanoparticles have been synthesized in microfluidic systems: CdSe, CdS, TiO2, Boehmite, Au, Co, Ag, Pd, Cu, BaSO4, and CdSe-ZnS core-shell nanoparticles [20, 21]. So far, however, microfluidic synthesis of magnetic iron oxide nanoparticles has not been demonstrated. Spinel iron oxide nanocrystals have attracted attention for their use as high density data storage media, [22] or in biomedical applications, such as contrast enhancement agents for magnetic resonance imaging (MRI) and for drug delivery. [23, 24].

[0003] Controlling the synthesis conditions of these particles is critical since this determines their physical properties [25]. While single-phase microfluidic systems are subjected to diffusion-limited mixing and reagent dispersion, droplet-based microfluidic systems overcome these limitations by fast mixing in spatially isolated microreactors (droplets) containing well defined quantities of materials [26, 28] and, therefore, provide a high-level of control of the synthesis conditions [29, 30]. In droplet-based microfluidic systems, reagents are generally brought together in a co-flowing stream just before droplet formation, the reaction occurring later in the microdroplet [26]. However, this method is unsuitable for aggressive or fast reactants which generate precipitates. To study and control such reactions, it is necessary to initiate the

reaction by fusion of two droplets, each containing different reagents. The main limitation is then the accurate pairing of these droplets which is hindered by small variations in the channel depths or flow rates [26]. In order to overcome these limitations, strategies such as active control of droplet release based on electric fields, [31] or passive hydrodynamic coupling at a single nozzle have been proposed [32, 33]. Nevertheless, these approaches lack the control of droplet volume ratios required to optimize reaction stoichiometry and undesired coalescence occurs for certain flow rate regimes.

SUMMARY OF INVENTION

[0004] The present invention is directed to a novel microfluidic device for the production of droplet pairs based on hydrodynamic coupling of two spatially separated nozzles and uses thereof. Compared to prior systems, the present invention provides for reliable production of droplet pairs, with errors in pairing of only 10 ^~5 or less. Droplets are paired by the hydrodynamic coupling of two nozzles over a wide range of aqueous and non-aqueous flow rates. After formation, the droplet pairs, each containing separate reagents, are fused creating picoliter to nano liter reactors. Fast mixing of the contents of the droplets results in a homogenous distribution of reagents that do not require further mixing modules. The pre- compartmentalization of reagents into droplet pairs allows for increased control over the initiation and quenching of reactions, as well as a means for capturing solid precipitates or other solid objects formed after the fusion of droplet pairs. The device and methods of the present invention can be used to conduct and study chemical and biochemical reactions at the single molecule or single cell level, as well as formation of nanoparticles.

[0005] In one aspect, the present invention is directed to a novel microfluidic device comprising: a synchronization module and a coalescence module in fluid communication with the synchronization module. In one exemplary embodiment, the synchronization module comprises a central flow channel, a first and second lateral flow channel and a first and second nozzle. The central flow channel is in fluid communication with the first and second nozzles. The proximity of the two nozzles leads to a passive coupling of the two nozzles by this central flow channel allowing for the passive synchronization of droplet formation in the first and second nozzles. The first and second lateral flow channels run adjacent to the central flow channel on opposite sides and are in fluid communication with the first and second nozzles,

respectively. The coalescence module is in fluid communication with the first and second nozzles.

[0006] In one exemplary embodiment, the microfluidic device is placed in fluid communication with a flow control module. The flow control module may be integrated onto the microfluidic device ("on-chip"), or separable from the microfluidic device ("off-chip"). Whether located on-chip or off-chip, the flow control module is placed in fluid communication with the first and second lateral flow channels and the central flow channel. The flow control module may comprise any system suitable for the controlled injection of a liquid or gas phase into the lateral and central flow channels. In one non-limiting example, the flow control module comprises one or more syringe pumps.

[0007] In another exemplary embodiment, the microfluidic device further comprises a collection module in fluid communication with the coalescence module.

[0008] In one exemplary embodiment, the device of the present invention may further comprise a detection module in communication with the coalescence and/or collection modules for detection of the formation of fused droplet pairs.

[0009] In another exemplary embodiment, the device of the present invention may be connected in line with other microfluidic devices or modules for further processing of products made after fusion of droplet pairs. For example, a newly formed encapsulated nanoparticle may then be injected into the same or a separate device for fusion with an additional set of droplets to quench or further modify the newly formed particles.

[0010] In one exemplary embodiment, the first and second lateral flow channels may have a depth ranging from about 1 μm to about 1 mm, a width ranging from about 1 μm to about 1 mm, and a length ranging from about 1 μm to about 5 mm. In another exemplary embodiment, the lateral flow channels have a depth of 25 μm, a width of about 50 μm and a length of 3 mm.

[0011] In one exemplary embodiment, the central flow chamber may have a depth ranging from about 1 μm to about 1 mm, a width ranging from about 1 μm to about 1 mm and a length ranging from about 1 μm to about 5 mm. In one exemplary embodiment, the central flow chamber has a depth of 25 μm, a width of 100 μm, and a length of 3 mm.

[0012] In one exemplary embodiment, the first and second nozzles may have a depth ranging from about 1 μm to about 1 mm, a width ranging from about 1 μm to about 1 mm. In another exemplary embodiment, the first and second nozzles have a depth of 25 μm, a width of 50 μm. In one exemplary embodiment the distance between the first and second nozzles is about 1 μm to about 1 mm. In another exemplary embodiment, the distance between the first and second nozzles is 100 μm.

[0013] In one exemplary embodiment, the coalescence module may have a depth ranging from about 1 μm to about 1 mm, a width ranging from about 1 μm to about 1 mm, and a length of 1 μm to about 1 mm. In another exemplary embodiment, the coalescence module has a depth of 25 μm, a width of 60 μm. In yet another exemplary embodiment, the coalescence module may further comprise one or more electrodes connected to an electrical source. In another embodiment, the coalescence module may further comprise a microwave heating source.

[0014] The collection module may comprise any material and volume suitable for use in storing either temporarily, or for an extended time, the fused droplet pairs produced by the device of the present invention. In one exemplary embodiment, the collection module has a volume ranging from about 1 pL to about 5 L. In another exemplary embodiment the collection module further comprises a cooling means or a heating means. In yet another exemplary embodiment, the collection module further comprises a means for re -injecting the fused droplet into the first or second lateral channel of the device.

[0015] In another aspect, the present invention is directed to a method of forming nanoparticles comprising the steps of: a) formation of a first droplet set comprising a first reaction solution and a second droplet set comprising a second reaction solution; b) fusion of the first droplet set and second droplet set to form a fused droplet set, wherein fusion of the first and second droplet sets initiates synthesis of a nanoparticles; and c) collection of the fused droplet set.

[0016] Droplet formation can be accomplished using any of a number of prior art methods. The fusion of the first and second droplet set can be initiated by methods known in the art

including, but not limited to, electrocoalescense, passive fusion, change or absence of surfactant concentration, and heat.

[0017] In another aspect, the preset invention is directed to a method for forming and fusing droplet pairs using the device of the present invention to form picoliter to nanoliter reactors, the method comprising the steps of: a) injecting a first reaction solution into the first lateral flow chamber, a second reaction solution into the second lateral flow chamber, and a carrier solution into the central flow chamber; b) forming a first droplet set comprising the first reaction solution and a second droplet set comprising the second reaction solution at the first and second nozzles respectfully; c) fusion of the first and second droplet sets in the coalescence module to form a fused droplet set; and d) collection of the fused droplet set.

[0018] In one exemplary embodiment, the first and second reaction mixtures are aqueous phase reaction mixtures and the carrier solution comprises an oil phase solution. In another exemplary embodiment, the first and second reaction mixtures comprise oil phase reaction mixtures and the carrier solution comprises a aqueous phase solution.

[0019] In one exemplary embodiment the droplets produced have a volume ranging from about 10 pL to about 500 pL. In another exemplary embodiment, the droplets have a volume ratio between droplets ranging from about 1 : 1 to about 1 :7.

[0020] In one exemplary embodiment, the method is used to carry out a biochemical or chemical reaction. In another exemplary embodiment, the method is used to synthesize a nanoparticle.

[0021] In one exemplary embodiment the fusion of the first and second droplet initiates, quenches, or modifies a chemical or biological reaction. In another exemplary embodiment, the fusion of the first and second droplets, initiates, quenches, or modifies the synthesis of a nanoparticles.

[0022] The present invention provides a means for compartmentalizing and handling solid objects for further microfluidic processing. In one exemplary embodiment, the present invention can be used to functionalize the surface of a nanoparticle formed by the present method, or other means, by adding or exchanging a ligand or polymer coating present on the nanoparticle surface.

[0023] In another exemplary embodiment, the present invention may be used to prepare core/shell structures such as, but not limited to, quantum dots, metal/metaloxides, and alloys in order to provide improved or enhanced properties (e.g. fluorescence properties, magnetic properties, electrical properties, and/or catalytic properties).

[0024] The present invention may be used to form nanoparticles from materials including, but not limited to, metals, oxides, alloys, sulfides, ceramics, polymers, or a combination thereof. Nanoparticles that may be synthesized using the present invention include, but are not limited to, ZnS, CdS, CoPt, TiO ₂ , V ₂ O ₅ , SiO ₂ , PbSe, InAs, ZnIn ₂ S ₄ , ZnO, CoAu, Au, FePt, Ag, Pt, Pd, Ni, BaTiO ₃ , and CoFe ₂ O ₃ .

[0025] Nanoparticles synthesized according to the present invention may have shapes including, but not limited to, spherical, with or without a core shell structure, isopolygonal plates, sheets, rods, wires, tubes, or dendrites.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a schematic diagram of an embodiment of the device of the present invention

[0027] Figure 2 a-b is picture showing the synchronized formation of droplets in the nozzle arms of the present invention

[0028] Figure 3 is graph plotting the measurement of droplet frequency as a function of the carrier solution flow rate.

[0029] Figure 4 a-d are graphs plotting the measure of droplet production frequencies for the symmetric case and asymmetric case.

[0030] Figure 5 a is diagram showing splitting of the carrier solution flow in the asymmetric case

[0031] Figure 5 b-c are graphs showing decomposition of the asymmetric case into two symmetric cases.

[0032] Figure 5 d is graph showing the geometrical determination of the droplet production frequency in the asymmetric case.

[0033] Figure 6 is a graph showing the frequencies measured for various carrier solution flow rates and aqueous phases.

[0034] Figure 7 a-b is a picture showing the synchronization and coalescence modules of an embodiment of the presently claimed invention.

[0035] Figure 8 a-b is diagram showing the mixing of droplets in a co-flow and in-line droplet fusion micro fluidic set-up.

[0036] Figure 9 is a picture showing the formation of iron oxide nanoparticles after fusion of droplet pairs.

[0037] Figure 10 a is a TEM micrograph showing formation of iron oxide particles [0038] Figure 10 b is a HRTEM image of particle showing the particle's spinal plances

[0039] Figure 10 c is graph showing the electron diffraction pattern indicating the spinel structure.

DETAILED DESCRIPTION

[0040] Microfluidic systems are a powerful tool to study and optimize a wide range of biological and chemical reactions [19], and their use for the synthesis of nanoparticles is attracting increasing attention. Compared to conventional bulk synthesis strategies, microfluidic systems allow more precise control of the reaction conditions which can lead to reductions in nanoparticle size and polydispersity [20]. Controlling the synthesis conditions of these particles is critical since this determines their physical properties [25]. While single -phase microfluidic systems are subjected to diffusion- limited mixing and reagent dispersion, droplet-based microfluidic systems overcome these limitations by fast mixing in spatially isolated microreactors (droplets) containing well defined quantities of materials [26, 27, 28], and therefore provide a high-level of control of the synthesis conditions [29, 39]. In droplet-based microfluidic systems, reagents are generally brought together in a co-flowing stream just before

droplet formation, the reaction occurring later in the microdroplet [26]. However, this method is unsuitable for aggressive or fast reactants which generate precipitates.

[0041] To study and control such reactions, it is necessary to initiate the reaction by fusion of two droplets, each containing different reagents. The main limitation is then the accurate pairing of these droplets which is hindered by small variations in the channel depths or flow rates [12]. In order to overcome these limitations, strategies such as active control of droplet release based on electric fields [31], or passive hydrodynamic coupling at a single nozzle have been proposed [32, 33]. Nevertheless, these approaches lack the control of droplet volume ratios required to optimize reaction stoichiometry and undesired coalescence occurs for certain flow rate regimes.

[0042] The present invention utilizes the pre-compartmentalization of reagents into two separate droplet pairs, which are later fused to initiate synthesis of a nanoparticle. The compartmentalization of reagents into separate droplet pairs allows for increased control over the initiation of fast reactions. In addition, pre-compartmentalization avoids reagent interaction with the walls of a microfluidic device, as well as premature formation of channel clogging precipitants.

Microfluidic Devices

[0043] Fig 1. provides an embodiment of the device of the present invention. The device 100 comprises a synchronization module 109 and a coalescence module 106, which are in fluid communication with each other. The synchronization module 109 comprises two spatially separated nozzles arms 104 and 105, which are hydrodynamically coupled by the flow of fluid through the central flow channel 101. A first 102 and second 103 lateral flow channel run adjacent to the central flow channel and are in fluid communication with the first 104 and second 105 nozzle, respectively.

[0044] The device 100 may further comprises a flow control module 107 for introducing and controlling the flow rate of aqueous and non-aqueous fluids into the central and lateral flow channels. The flow control module may be integrated into the microfluidic device ("on-chip"), or separable from the microfluidic device ("off chip"). The flow control module may comprise any system suitable for the controlled injection of aqueous and/or oil based fluids into the lateral and central flow channels of the microfluidic device. In an exemplary embodiment, the flow control module comprises one or more syringe pumps.

[0045] The device 100 may also further comprise a collection module 108 in fluid communication with the coalescence module. The collection module may comprise any material and volume suitable for use in storing either temporarily, or for an extended time, the fused droplet pairs produced by the device of the present invention. In one exemplary embodiment, the collection module has a volume ranging from about 1 pL to 5 L or more. The capacity of the coalescence module is determined by the type and amount of product to by synthesized and can readily be determined by one of ordinary skill in the art. In another exemplary embodiment, the collection module, and/or microfluidic device, further comprises a cooling means or a heating means. In yet another exemplary embodiment, the collection module further comprises a means for re -injecting the fused droplet into the first or second lateral channel of the device.

[0046] The device 100 may optionally include a detection module for detecting the formation of particlulates or other reaction products. Suitable detection means include confocal microscopy, fluorescence detectors, magnetic detectors, or any other suitable means known in the art for monitoring nanoparticle formation. The type of detection system used will depend on the type of nanoparticles or other products being synthesized for which detection is desired.

[0047] To initiate formation of droplets in the device, a carrier solution is injected into the central flow channel and a first and second reaction solution are injected into the first and second lateral flow channels respectively. In one embodiment, the carrier solution is non-aqueous and the first and second reaction solutions are aqueous. Alternatively, the carrier solution may be an aqueous solution and the first and second reactions solutions are non-aqueous.

[0048] While not intended to be limited by the following, synchronization of droplet formation is believed to be promoted by the formation and presence of a droplet in one of the two nozzle arms forcing the carrier solution through the second arm. Above a certain size limit the influence of the droplet on the fluidic resistance [18] is strong enough to force droplet breakup in the opposite channel leading to an alternating carrier solution flow (see quantitative analysis carried out in Example 1). It is to be understood, that the design of the microfluidic device is channel and droplet size independent as long as the force generated by the fluidic resistance of a newly formed droplet in one nozzle arm is sufficient to hydrodynamically couple and force droplet breakup in the second nozzle. In terms of design, this can be achieved by

altering the proximity of the nozzles and/or smaller channel dimensions in order to increase the fluidic resistance of a created droplet.

[0049] The device of the present invention may be prepared using any standard microfabrication technique known in the art. The device may be prepared, for example, on poly(dimethylsiloxane) (PDMS) using a soft lithography technique. The device may also be fabricated from other substrates including, but not limited to, glass, silicon, and poly (methyl methylacyrlate).

Synthesis of Nanoparticles

[0050] The present invention provides a method for synthesizing a solid object, such as nanoparticles, on a microfluidic device. The method employs the use of pre- compartmentalization of reagents into two separate droplet pairs. This pre-compartmentalization prevents undesirable interactions between the wall of the microfluidic device, as well the premature formation of channel blocking precipitants. The pre-compartmentalization of reagents also allows for greater control over initiation and quenching of reactions through the controlled initiation of fusion between droplet pairs. The ability to synthesize solid objects, such as nanoparticles, in a compartmentalized form allows for further processing of products. For example the encapsulated nanoparticle can be reinjected into a microfluidic device and further processed and modified, such as required for the building of core-shell-particles. The separation of a bulk reactions into multiple identical small volume reactions also allows for increased homogeneity of the reaction. A correlation has been shown between the degree of homogeneity of nucleation and the degree of polydispersity of nanoparticles sizes in nanoparticle synthesis [42]. By increasing the homogeneity of the reaction, the present device allows for the production of nanoparticles of well defined structure and reduced polydispersity.

[0051] The methods of the present invention require the formation of a first and second set of droplet pairs comprising a first and second reaction solution respectively. The formation of separate droplet pairs may be carried out using any suitable microfluidic device, including the device of the present invention. The first and second droplet sets are then fused to initiate, quench, or modify a reaction between the reagents of the first and second reaction mixtures. Fusion between droplet pairs can be achieved using standard techniques in the art including, but

not limited to, electrocoalescence, heat, changes in concentration of absence of surfactant, or passive fusion (e.g. altering the geometry of a coalescence module).

[0052] The methods of the present invention may be used to synthesize nanoparticles. Nanoparticles that may be synthesized using the present invention include, but are not limited to, ZnS, CdS, CoPt, TiO ₂ , V ₂ O ₅ , SiO ₂ , PbSe, InAs, ZnIn ₂ S ₄ , ZnO, CoAu, Au, FePt, Ag, Pt, Pd, Ni, BaTiO ₃ , and CoFe ₂ O ₃ , CdSe, boehmite, iron oxide, Au, Co, Ag, Pd, Cu, BaSO ₄ , and CdSe-ZnS core shell nanoparticles. The type of nanoparticle to be synthesized will determine the selection of reagents for the first and second reaction solutions as well as an appropriate carrier solution. For example, in the synthesis of iron oxide nanoparticles, the first reaction solution may contain a mixture of FeCl ₂ and FeCl ₃ salts and the second reaction mixture may comprise a mixture of ammonium hydroxide. A suitable carrier solution may include a solution of a perfluorocarbon oil FC40 and a surfactant.

[0053] The methods of the present invention may be used to modulate the self-assembly of nanoparticles and the shape by mixing of charged nanoparticles with oppositely charged homopolymers, bloc copolymers or statistical copolymers. The shape of the nanoparticle can be designed by changing, over multiple fusions, reagent concentrations, ionic strength, pH, polymer length, solvent, surfactant/polymer structure, or reaction temperature. Rod like, dense aggregate, ramified aggregate, spherical (with or without a core shell structure), isopolygonal plates, sheets, rods, wires, tubes, or dendrites.

[0054] The methods of the present invention may be used to functionalize the surface of a nanoparticle by transferring it to a polar or non-polar solvent, by ligand exchange (e.g. citrates, oleic acids, CTAB, DTAB, TOPO) or polymer coating (e.g. polyvinylpyrolidone, polyacid acrylic, polylysine and polysine derivatives, polyethylene glycol and polyethylene glycol derivatives).

[0055] The methods of the present invention may also be used to prepare core/shell structures such as, but not limited to, quantum dots, metals/metaloxides and alloys, to combine physical properties or enhance properties such as fluorescence, magnetic properties, electrical properties, or catalytic properties.

[0056] In addition, the synthesis of solid objects, the methods of the present invention may be used to conduct biochemical and chemical reactions as well as provide a means for studying those reactions at the single molecule or single cell level.

[0057] Certain modifications and improvements will occur to those skilled in the art upon a reading of the foregoing description. It should be understood that all such modifications and improvements have been deleted herein for the sake of conciseness and readability but are properly within the scope of the following claims.

EXAMPLE 1

Experimental analysis of droplet production frequencies utilizing hydrodvnamic coupling from two spatially separated nozzles

Microfluidic devices with d=25 μm deep channels were prepared by standard soft- lithography techniques [16] in poly(dimethylsiloxane) (PDMS, Sylgard 184, Dow Corning). The PDMS was bound to a glass slide after treatment in an oxygen plasma. The channels were coated with a commercial surface coating agent (Aquapel, PPG Industries) to increase hydrophobicity and subsequently dried with N ₂ . Volumetric flow rates were controlled by syringe pumps (PHD2000, Harvard Apparatus). The microfluidic device consists of two adjacent nozzles coupled together by the use of a single central oil stream (Fig. 2). The oil stream comprised a perfluorocarbon oil FC40 (3M) with 2.5% (w/w) of surfactant, made of the ammonium salt of a perfluorinated polyether (PFPE) (Krytox FSL, Dupont) [17] and flowing at a rate Qo. Two aqueous phases, a mixture of phosphate buffered saline solution (PBS; Sigma) containing either 50 μM resorufm, or 10 μM fluorescein are dispensed through the lateral channels x and y at volumetric flow rate rates Qx and Qy. A 488nm laser source focused in the channels through a x40 microscope objective (Leica) excited the droplets. Fluorescent emission intensities were measured simultaneously on two photomultiplier tubes (Hammamatsu) in the range of 495- 520nm (green, fluorescein detection) and 578-657nm (orange, resorufin detection) respectively. Fluorescent detection coupled to a data-acquisition device (Labview - National Instruments) allowed signal processing for droplet frequency measurements and statistical analysis.

Additionally, sequences of images were recorded with a high speed camera (Phantom V4.2 at 2 - 10 ^λ 4 frames per second).

Qualitatively, the idea behind the design presented in Fig. 2 is that the synchronization is promoted by the formation and presence of a droplet in one of the two nozzle arms forcing the oil through the second arm. Above a certain size limit, the influence of the droplet on the fluidic resistance [18] is strong enough to force droplet breakup in the opposite channel leading to an alternating oil flow.

Quantitative analysis was performed by measuring droplet production frequencies for various oil flow rates Qo and equal aqueous flow rates Qx = Qy (symmetric case). A typical snapshot is displayed in Fig. 2 (a). Droplet pairing was obtained successfully until a flow rate limit Qo dependent on the aqueous flow rate (Fig. 3). Above this limit (i.e. beyond the points marked with a star in Fig. 3), the droplet production became erratic and lead to the creation of unpaired droplets. In the pairing regime, the droplet frequency fxx displays a linear relationship with the oil flow rate Qo (see Fig. 3) and a power law behavior with the aqueous flow rate Qx (see inset of Fig. 3) resulting in Eq. 1 :

fxx = a QoQx ^b (1)

where b ~ 0.82 and a =0.17 for flow rates expressed in nLs-1 and frequencies in s-1 . In order to understand the flow rate limit it is necessary to consider the volume V of the produced droplet. By inserting the mass conservation relationship V = Qx/fxx into Eq. 1 , the droplet production frequency reads:

fxx = V ^b/(1 - ^b) (aQo ) ^1/(1"b) (2)

The experimental limit of successful droplet pairing (stars in Fig. 3) corresponds to the line of constant volume V =40 pL (solid line of Fig. 3) for pancake-shaped droplets of height d =25 μ m and diameter = 45 μ m. This means, when the droplets become smaller than the channel width (w = 50 μm) they are too small to quantitatively alter the oil flow [15, 18]: the hydrodynamic coupling between the two nozzles vanishes and the droplets stop alternating. This result supports

the qualitative argument that droplet pairing is promoted by the interplay of droplet size and channel dimensions leading to an alternating oil flow between the two nozzle arms.

The asymmetric case (Qx Qy) was studied using the same method and, as before, the droplet production frequency was equal in both nozzle arms (Fig. 2 (b)). The aqueous flow rate ratio can reliably be varied between 5:1 and 1 :5 leading to a volume ratio of Vx/Vy = Qx/Qy due to mass conservation Vx,y = Qx,yfxy. By ramping up the oil flow rate at different Qx, Qy combinations the frequency presents a similar linear behavior as a function of Qo. The measured frequencies lie in between the frequencies obtained in the symmetric case with the corresponding aqueous flow rates (see Fig. 3). However, deriving an equivalent of the power-law of Eq. 1 for the asymmetric case is not straight-forward.

In order to explain the experimental data and generalize the power-law behavior with the aqueous flow rates to the asymmetric case, a model for the droplet alternation has been derived. In general, hydrodynamics calculations in the presence of droplets in channels is a complex problem [18]. Here, understanding the symmetric case is sufficient to predict the frequencies obtained in the asymmetric case, on the basis of geometrical arguments. At the nozzle, the oil flow splits into the two nozzle arms. In the symmetric case, the flow rate in each arm is on average Qo/ 2 - average should be understood as the mean oil flow rate over one period of droplet production - (see Fig. 4 (a), e = 1/2 by symmetry). In the asymmetric case, the oil flow splits unequally into two fractions of the total oil flow rate ( eQo and (1- e)Qo , 0 < e < 1/2, see Fig. 4 (b),(c)). The asymmetric case can be modeled as a combination of two symmetric cases: each side of the device behaves as a symmetric nozzle with oil flow rates 2 eQo and 2(1- e)Qo respectively. The frequency fxy (Qo ) is the solution of Eq. 3:

fxy (Qo ) = fxx (2 e Qo ) = fyy (2(1 - e )Qo ) (3)

Fig. 4(d) illustrates the geometrical interpretation of Eq. 3 leading to frequency determination: the distances BAxx and BAyy are equal. This construction has been applied to the experimental data of Fig. 3. In all studied cases, the geometrical construction predicts accurately the frequencies of the asymmetric case. In addition, an analytical expression for e is obtained by replacing Qo in Eq. 1 by the new oil flow rates and solving the right hand side of Eq. 3:

e = Qy / (Qx + Qy) (4)

The combination of Eq. 1 , 3 and 4 leads to the general expression for the droplet production frequencies as a function of oil and aqueous flow rates:

fxy = 2a Qo ^b Qx ^b / (Qo ^b + Qx ^b ) (5)

The relationship between fxy and the parameter QoQx ^b Qy ^b /(Qx ^b + Qy ^b ) has been compared to all experimental results obtained at various oil and aqueous flow rates in Fig. 6. The frequencies obtained experimentally collapse on a single master curve with an exponent of 1 , as predicted by Eq. 5 without any additional fitting parameters. The exponent b is that obtained experimentally in the symmetric case. Both the values of the symmetric and asymmetric case are overlaid in Fig. 6. Therefore, Eq. 5 is the generalized form of the power-law in Eq. 1, accounting for both the symmetric and the asymmetric case. In addition, Eq. 5 allows the frequency in the asymmetric case fxy to be described as the harmonic mean value of the frequencies in the symmetric cases fxx and fyy :

fxy =21 (1/fxx + 1/fyy) (6)

According to Fig. 5(d), there are an infinite number of e solutions that guarantee a split of the oil between the two arms, each of these solutions corresponding to different frequencies fyy and fxx; only one e solution corresponds to the same frequency for both arms. It should be noted that pressure calculations based on Poiseuille flow in both arms of the nozzle do not explain these values of e, since the presence of a droplet in the channel influences the pressure distribution in the channels [18]. This point demonstrates that the mechanism of alternation between the two nozzles is the result of the modification of the oil flow by droplets wider than the channel.

The present analysis demonstrates ability of Eq. 5 to accurately predict droplet production frequencies and that the dual nozzle is capable of producing droplet pairs over a large range of different flow rate combinations. Nevertheless, this pairing accuracy can be only obtained for two continuous aqueous phases on both arms of the nozzle. When replacing a

continuous stream by an emulsion of monodisperse droplets, both the flow rate Qx and the frequency fxy are fixed. Under these conditions, according to Fig. 5d, for a fixed Qy , there is only one flow rate Qo that guarantees that BAxx = BAyy : the coupling will occur only when the flow rates are properly tuned, coming back to the initial limitations of pumping rate and device depth heterogeneities. This is supported by experimental observations that no coupling occurred with reinjected emulsions (data not shown). Unless additional coupling strategies are applied, the presented analysis proves that it is not possible to obtain a self-triggered pairing device for a reinjected emulsion based on this coupling mechanism. However, the level of control and the accuracy in producing droplet pairs from continuous aqueous phases allows the realization of highly sensitive and reproducible experiments in microreactors, initiated by electrocoalescence of droplet pairs containing different reagents, that are not feasible in co-flow systems (Frenz et al. submitted). This design is therefore an additional tool for the control of (bio-)chemical reactions that complements the other pre-existing microfluidic modules for droplet manipulation. In summary, the present analysis characterizes a microfluidic module for the controlled production of droplet pairs. The size ratio between paired droplets is directly controlled by the flow rates of the aqueous streams. A well-defined regime of flow rates corresponding to droplet pairing can be achieved when the droplets are wider than the channel width. In this pairing regime, droplet production frequencies (and volumes) display a power-law behavior with the flow rates - determined experimentally in the symmetric case and generalized to the asymmetric case - which enable the prediction of frequencies and droplet volumes.

EXAMPLE 2

Synthesis of magnetic iron oxide nanoparticles

The 25 μm deep structures used for fluid channels and electrodes were patterned into poly(dimethylsiloxane) (PDMS) using soft-lithography [39]. Electrodes used for fusion were patterned into the same layer and in close vicinity to the fluidic channels [40]. A commercial surface coating agent (Aquapel, PPG Industries) was used to coat the channels. Harvard Apparatus syringe pumps (PHD2000) controlled the flow rates. The continuous oil phase was a perfluorocarbon oil FC40 (3M) with 2.5% (w/w) of surfactant, made of the ammonium salt of a perfluorinated poly ether (PFPE) (Krytox FSL - Dupont) [41]. As starting materials for the

precipitation of iron oxide nanoparticles FeC12-4H2O (Sigma-Aldrich) and FeC13-6H2O (Acros Organics) were used to form a first reaction solution; ammonium hydroxide solution (28% NH3 - Fluka) and hydrochloric acid (37% HCl- Acros Organics) of analytical grade were used form a second reaction solution. After degassing 0.5 m HCl in Milli-Q water with an argon flux for 1 h we added the iron chloride salts and kept this solution under argon. Two different solutions with FeIII /Fell = 2 ratio were tested: (Sl) 48OmM FeC13 + 24OmM FeC12 and (S2) 6OmM FeC13 + 3OmM FeC12. As a base we used a 2M ammonium hydroxide solution - also prepared using degassed Milli-Q water. In order to avoid oxidation of the Fell during the reaction process, the PDMS device was kept in a vacuum chamber over night before use, the oil was degassed with a nitrogen flux for 1 h, and collected using gas-impermeable polyethylene tubing (Becton Dickinson) into a nitrogen atmosphere. Electrocoalescence was achieved by an AC-voltage of U = 200V (Peak to peak) at 30 kHz, which was applied across the two electrodes positioned on each side of the microfluidics channel. TEM and HRTEM images were recorded with a TOPCON 002B transmission electron microscope, operating at 200 kV, with a point to point resolution of 0.18 nm. Magnetic measurements were performed using a Superconducting Quantum Interference Device Magnetometer (SQUID) magnetometer (Quantum Design MPMS- XL) at 200 K.

Magnetic spinel iron oxide nanoparticles were synthesized by co-precipitation of Fe ^π /Fe ^iπ salt solutions by addition of a base. This co-precipiatation leads first to magnetite (Fe3O4) which oxidizes readily subsequently to maghemite (gamma-Fe2 03) when in contact with air [24, 25]. The co-precipitation is so fast that it immediately forms particles and blocks the channels in a co-flow system especially at higher concentrations (data not shown). Droplet fusion can potentially overcome this problem [33], but in the absence of surfactant [33], it is extremely difficult to achieve controlled pairwise droplet fusion [36]. In the present system the two aqueous components never mix unintentionally, not even during the startup of the system, as the nozzles are spatially separated and the droplets are stabilized by surfactant. Controlled pairwise droplet-fusion is achieved by electrocoalescence. This approach enables an increase in the compound concentration by 2-3 orders of magnitude compared to earlier droplet-based microfluidic methods for the synthesis of nanoparticles. [33, 37] In detail, iron chloride solution was flushed into one arm of the nozzle and ammonium hydroxide into the second arm, which led to droplet pairs containing the two reagents. After electrocoalescence a precipitate of iron oxide

nanoparticles appeared within 2 ms (see Figure 9). Due to identical reaction conditions in all droplets, the kinetics of precipitation and its morphology was extremely similar in all droplets throughout the whole experiment.

Particle size measurements by transmission electron microscopy (TEM) (Figure 10) show that the average particle diameter is smaller for the fast microfluidic compound mixing (4 +/- 1 nm) compared to bulk mixing (9 +/- 3 nm). In addition, high resolution TEM (HRTEM) measurements (inset Figure 1Oa)) show that the nanoparticles are monocrystalline, no stacking faults being visible. They exhibit planes with interplanar distances of about 0.3nm characteristic of (220) spinel planes. The electron diffraction pattern measured from a large zone (Figure 9b) confirms the iron oxide spinel structure. Finally, the absence of hysteresis in the magnetization curve (Figure 9c)) of the nanoparticles synthesized, indicates that they are superparamagnetic, which is characteristic of spinel iron oxide nanoparticles smaller than 15 nm.

In summary, the present experiment demonstrates a robust and flexible microfluidic module for the controlled production of droplet pairs based on hydrodynamic coupling. The level of control obtained allows the realization of highly sensitive and reproducible experiments in microreactors, as demonstrated for the precipitation of iron oxide nanoparticles. Such on-chip synthesized particles could potentially be functionalized by an additional droplet fusion step to synthesize core-shell particles optimized for bio-compatibility, drug anchoring, and cell targeting [20]. For iron oxide this is of special interest, since magnetite (Fe3O4), which displays a higher saturation magnetization than maghemite (γ-Fe2O3), could then be preserved without oxidation to maghemite. This system can be used to control and study a wide range of millisecond kinetic reactions in chemistry and biology and is therefore an additional tool that extends the capabilities of and complements other preexisting microfluidic modules for droplet manipulation.

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