Droplet breakup in microfluidic junctions of arbitrary angles

Passive breakups of isolated drops and one-dimensional assemblies of drops in microfluidic geometries: experiments and models

Using two different geometries, rectangular obstacles and asymmetric loops, we investigate the breakup dynamics of deformable objects, such as drops and bubbles, confined in microfluidic devices. We thoroughly study two distinct flow configurations that depend on whether object-to-object hydrodynamic interactions are allowed. When such interactions are introduced, we find that the volumes of the daughter objects created after breakup solely depend on the geometrical features of the devices and are not affected by the hydrodynamic and physicochemical variables; these results are in sharp contrast with those obtained for non-interacting objects. For both configurations, we provide simple phenomenological models that capture well the experimental findings and predict the evolution of the volumes of the daughter objects with the controlling dimensionless quantities that are identified. We introduce a mean-field approximation, which permits accounting for the interactions between objects during breakup and we discuss its conditions of validity.

Path selection rules for droplet trains in single-lane microfluidic networks

We investigate the transport of periodic trains of droplets through microfluidic networks having one inlet, one outlet, and nodes consisting of T junctions. Variations of the dilution of the trains, i.e., the distance between drops, reveal the existence of various hydrodynamic regimes characterized by the number of preferential paths taken by the drops. As the dilution increases, this number continuously decreases until only one path remains explored. Building on a continuous approach used to treat droplet traffic through a single asymmetric loop, we determine selection rules for the paths taken by the drops and we predict the variations of the fraction of droplets taking these paths with the parameters at play including the dilution. Our results show that as dilution decreases, the paths are selected according to the ascending order of their hydrodynamic resistance in the absence of droplets. The dynamics of these systems controlled by time-delayed feedback is complex: We observe a succession of periodic regimes separated by a wealth of bifurcations as the dilution is varied. In contrast to droplet traffic in single asymmetric loops, the dynamical behavior in networks of loops is sensitive to initial conditions because of extra degrees of freedom.

Breakup of microdroplets in asymmetric T junctions

Symmetric T junctions have been used widely in microfluidics to generate equal-sized microdroplets, which are applicable in drug delivery systems. A newly proposed method for generating unequal-sized microdroplets at a T junction is investigated theoretically and experimentally. Asymmetric T junctions with branches of identical lengths and different cross sections are utilized for this aim. An equation for the critical breakup of droplets at asymmetric T junctions and one for determining the breakup point of droplets are developed. A good agreement was observed between the theories (present and previous) and the experiments.

Droplet-based microfluidics

Droplet-based microfluidics or digital microfluidics is a subclass of microfluidic devices, wherein droplets are generated using active or passive methods. The active method for generation of droplets involves the use of an external factor such as an electric field for droplet generation. Two techniques that fall in this category are dielectrophoresis (DEP) and electrowetting on dielectric (EWOD). In passive methods, the droplet generation depends on the geometry and dimensions of the device. T-junction and flow focusing methods are examples of passive methods used for generation of droplets. In this chapter the methods used for droplet generation, mixing of contents of droplets, and the manipulation of droplets are described in brief. A review of the applications of digital microfluidics with emphasis on the last decade is presented.

End-on microtubule-dynein interactions and pulling-based positioning of microtubule organizing centers

During important cellular processes such as centrosome and spindle positioning, dynein at the cortex interacts with dynamic microtubules in an apparent "end-on" fashion. It is well-established that dynein can generate forces by moving laterally along the microtubule lattice, but much less is known about dynein's interaction with dynamic microtubule ends. In this paper, we review recent in vitro experiments that show that dynein, attached to an artificial cortex, is able to capture microtubule ends, regulate microtubule dynamics and mediate the generation of pulling forces on shrinking microtubules. We further review existing ideas on the involvement of dynein-mediated cortical pulling forces in the positioning of microtubule organizing centers such as centrosomes. Recent in vitro experiments have demonstrated that cortical pulling forces in combination with pushing forces can lead to reliable centering of microtubule asters in quasi two-dimensional microfabricated chambers. In these experiments, pushing leads to slipping of microtubule ends along the chamber boundaries, resulting in an anisotropic distribution of cortical microtubule contacts that favors centering, once pulling force generators become engaged. This effect is predicted to be strongly geometry-dependent, and we therefore finally discuss ongoing efforts to repeat these experiments in three-dimensional, spherical and deformable geometries.

Microfluidic breakups of confined droplets against a linear obstacle: The importance of the viscosity contrast

Combining experiments and theory, we investigate the break-up dynamics of deformable objects, such as drops and bubbles, against a linear micro-obstacle. Our experiments bring the role of the viscosity contrast Δη between dispersed and continuous phases to light: the evolution of the critical capillary number to break a drop as a function of its size is either nonmonotonic (Δη>0) or monotonic (Δη≤0). In the case of positive viscosity contrasts, experiments and modeling reveal the existence of an unexpected critical object size for which the critical capillary number for breakup is minimum. Using simple physical arguments, we derive a model that well describes observations, provides diagrams mapping the four hydrodynamic regimes identified experimentally, and demonstrates that the critical size originating from confinement solely depends on geometrical parameters of the obstacle.

Behavior of liquid plugs at bifurcations in a microfluidic tree network

Flows in complex geometries, such as porous media or biological networks, often contain plugs of liquid flowing within air bubbles. These flows can be modeled in microfluidic devices in which the geometric complexity is well defined and controlled. We study the flow of wetting liquid plugs in a bifurcating network of micro-channels. In particular, we focus on the process by which the plugs divide as they pass each bifurcation. The key events are identified, corresponding to large modifications of the interface curvature, the formation of new interfaces, or the division of a single interface into two new ones. The timing of the different events and the amplitude of the curvature variations are analyzed in view of the design of an event-driven model of flow in branching micro-networks. They are found to collapse onto a master curve dictated by the network geometry.

Surfactants in droplet-based microfluidics

Surfactants are an essential part of the droplet-based microfluidic technology. They are involved in the stabilization of droplet interfaces, in the biocompatibility of the system and in the process of molecular exchange between droplets. The recent progress in the applications of droplet-based microfluidics has been made possible by the development of new molecules and their characterizations. In this review, the role of the surfactant in droplet-based microfluidics is discussed with an emphasis on the new molecules developed specifically to overcome the limitations of 'standard' surfactants. Emulsion properties and interfacial rheology of surfactant-laden layers strongly determine the overall capabilities of the technology. Dynamic properties of droplets, interfaces and emulsions are therefore very important to be characterized, understood and controlled. In this respect, microfluidic systems themselves appear to be very powerful tools for the study of surfactant dynamics at the time- and length-scale relevant to the corresponding microfluidic applications. More generally, microfluidic systems are becoming a new type of experimental platform for the study of the dynamics of interfaces in complex systems.

Droplet based microfluidics

Droplet based microfluidics is a rapidly growing interdisciplinary field of research combining soft matter physics, biochemistry and microsystems engineering. Its applications range from fast analytical systems or the synthesis of advanced materials to protein crystallization and biological assays for living cells. Precise control of droplet volumes and reliable manipulation of individual droplets such as coalescence, mixing of their contents, and sorting in combination with fast analysis tools allow us to perform chemical reactions inside the droplets under defined conditions. In this paper, we will review available drop generation and manipulation techniques. The main focus of this review is not to be comprehensive and explain all techniques in great detail but to identify and shed light on similarities and underlying physical principles. Since geometry and wetting properties of the microfluidic channels are crucial factors for droplet generation, we also briefly describe typical device fabrication methods in droplet based microfluidics. Examples of applications and reaction schemes which rely on the discussed manipulation techniques are also presented, such as the fabrication of special materials and biophysical experiments.

Fabrication of advanced particles and particle-based materials assisted by droplet-based microfluidics

Recent advances in the fabrication of complex particles and particle-based materials assisted by droplet-based microfluidics are reviewed. Monodisperse particles with expected internal structures, morphologies, and sizes in the range of nanometers to hundreds of micrometers have received a good deal of attention in recent years. Due to the capability of generating monodisperse emulsions and of executing precise control and operations on the suspended droplets inside the microchannels, droplet-based microfluidic devices have become powerful tools for fabricating complex particles with desired properties. Emulsions and multiple-emulsions generated in the microfluidic devices can be composed of a variety of materials including aqueous solutions, gels, polymers and solutions containing functional nanoparticles. They are ideal microreactors or fine templates for synthesizing advanced particles, such as polymer particles, microcapsules, nanocrystals, and photonic crystal clusters or beads by further chemical or physical operations. These particles are promising materials that may be applicable for many fields, such as photonic materials, drug delivery systems, and bio-analysis. From simple to complex, from spherical to nonspherical, from polymerization and reaction crystallization to self-assembly, this review aims to help readers be aware of the many aspects of this field.

System Integration - A Major Step toward Lab on a Chip

Microfluidics holds great promise to revolutionize various areas of biological engineering, such as single cell analysis, environmental monitoring, regenerative medicine, and point-of-care diagnostics. Despite the fact that intensive efforts have been devoted into the field in the past decades, microfluidics has not yet been adopted widely. It is increasingly realized that an effective system integration strategy that is low cost and broadly applicable to various biological engineering situations is required to fully realize the potential of microfluidics. In this article, we review several promising system integration approaches for microfluidics and discuss their advantages, limitations, and applications. Future advancements of these microfluidic strategies will lead toward translational lab-on-a-chip systems for a wide spectrum of biological engineering applications.

Droplet microfluidics for the study of artificial cells

In this review, we describe recent advances in droplet-based microfluidics technology that can be applied in studies of artificial cells. Artificial cells are simplified models of living cells and provide valuable model platforms designed to reveal the functions of biological systems. The study of artificial cells is promoted by microfluidics technologies, which provide control over tiny volumes of solutions during quantitative chemical experiments and other manipulations. Here, we focus on current and future trends in droplet microfluidics and their applications in studies of artificial cells.

Breakup of double emulsion droplets in a tapered nozzle

When double emulsion droplets flow through a tapered nozzle, the droplets may break up and cause the core to be released. We model the system on the basis of the capillary instability and show that a droplet will not break up when the tilt angle of the nozzle is larger than 9°. For smaller tilt angles, whether the droplet breaks up also depends on the diameter ratio of the core of the droplet to the orifice of the nozzle. We verified this mechanism by experiments. The ideas are useful for the design of nozzles not only to break droplets for controlled release but also to prevent the droplet from rupturing in applications requiring the reinjection of an emulsion.

Quantitative cell-based reporter gene assays using droplet-based microfluidics

We used a droplet-based microfluidic system to perform a quantitative cell-based reporter gene assay for a nuclear receptor ligand. Single Bombyx mori cells are compartmentalized in nanoliter droplets which function as microreactors with a >1000-fold smaller volume than a microtiter-plate well, together with eight or ten discrete concentrations of 20-hydroxyecdysone, generated by on-chip dilution over 3 decades and encoded by a fluorescent label. The simultaneous measurement of the expression of green fluorescent protein by the reporter gene and of the fluorescent label allows construction of the dose-response profile of the hormone at the single-cell level. Screening approximately 7500 cells per concentration provides statistically relevant data that allow precise measurement of the EC(50) (70 nM +/- 12%, alpha = 0.05), in agreement with standard methods as well as with literature data.

Dynamics of microfluidic droplets

This critical review discusses the current understanding of the formation, transport, and merging of drops in microfluidics. We focus on the physical ingredients which determine the flow of drops in microchannels and recall classical results of fluid dynamics which help explain the observed behaviour. We begin by introducing the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, namely the modifications to the flow and pressure fields that are introduced by the presence of interfacial tension. Then three practical aspects are studied in detail: (i) The formation of drops and the dominant interactions depending on the geometry in which they are formed. (ii) The transport of drops, namely the evaluation of drop velocity, the pressure-velocity relationships, and the flow field induced by the presence of the drop. (iii) The fusion of two drops, including different methods of bridging the liquid film between them which enables their merging.

Fraction collection from capillary liquid chromatography and off-line electrospray ionization mass spectrometry using oil segmented flow

Off-line analysis and characterization of samples separated by capillary liquid chromatography (LC) has been problematic using conventional approaches to fraction collection. We demonstrate collection of nanoliter fractions by forming plugs of effluent from a 75 mum inner diameter LC column segmented by an immiscible oil such as perfluorodecalin. The plugs are stored in tubing that can then be used to manipulate the samples. Off-line electrospray ionization mass spectrometry (ESI-MS) was used to characterize the samples. ESI-MS was performed by directly pumping the segmented plugs into a nanospray emitter tip. Critical parameters including the choice of oils, ESI voltage, and flow rates that allow successful direct infusion analysis were investigated. Best signals were obtained under conditions in which the oil did not form an electrospray but was siphoned away from the tip. Off-line analysis showed preservation of the chromatogram with no loss of resolution. The method was demonstrated to allow changes in flow rate during the analysis. Specifically, decreases in flow rate were used to allow extended MS analysis time on selected fractions, similar to "peak parking".

Designed pneumatic valve actuators for controlled droplet breakup and generation

The dynamic breakup of emulsion droplets was demonstrated in double-layered microfluidic devices equipped with designed pneumatic actuators. Uniform emulsion droplets, produced by shearing at a T-junction, were broken into smaller droplets when they passed downstream through constrictions formed by a pneumatically actuated valve in the upper control layer. The valve-assisted droplet breakup was significantly affected by the shape and layout of the control valves on the emulsion flow channel. Interestingly, by actuating the pneumatic valve immediately above the T-junction, the sizes of the emulsion droplets were controlled precisely in a programmatic manner that produced arrays of uniform emulsion droplets in various sizes and dynamic patterns.

Microfluidic Droplet Technique for In Vitro Directed Evolution

Increasingly over the past two decades, biotechnologists have been exploiting various molecular technologies for high-throughput screening of genes and their protein products to isolate novel functionalities with a wide range of industrial applications. One particular technology now widely used for these purposes involves directed evolution, an artificial form of evolution in which genes and proteins are evolved towards new or improved functions by imposing intense selection pressures on libraries of mutant genes generated by molecular biology techniques and expressed in heterologous systems such as Escherichia coli. Most recently, the rapid development of droplet-based microfluidics has created the potential to dramatically increase the power of directed evolution by increasing the size of the libraries and the throughput of the screening by several orders of magnitude. Here, we review the methods for generating and controlling droplets in microfluidic systems, and their applications in directed evolution. We focus on the methodologies for cell-based assays, in vitro protein expression and DNA amplification, and the prospects for using such platforms for directed evolution in next-generation biotechnologies.

Flows around confined bubbles and their importance in triggering pinch-off

We describe the breakup of a confined gas thread in a cross-flowing stream of liquid at capillary numbers Ca < 10{-2}. The breakup is initiated, not by a Plateau-Rayleigh instability, but by liquid that flows from the tip of the thread to the neck where pinch-off occurs. This flow, faster than previously estimated, is driven by different curvatures at the tip and neck and runs through large gaps between thread and channel walls. Understanding how these curvatures evolve during bubble formation leads to accurate predictions of the moment of pinch-off.

Deformation and breakup of high-viscosity droplets with symmetric microfluidic cross flows

The dynamic response of highly viscous droplets to a sharp increase in the surrounding liquid velocity is experimentally investigated in a square microchannel junction. The local injection of the continuous phase from symmetric side channels onto a train of droplets produces a large velocity contrast between the front and the rear of droplets, yielding a broad range of time-dependent deformation and breakup. In particular, due to microscale confinement, the system displays a nonlinear behavior with the initial droplet size. Deformations, relaxation times, and fragmentation processes are examined as a function of flow parameters and fluids properties with emphasis on the formation of slender viscous structures such as spoon-shaped droplets, i.e., asymmetrical droplets.

Fluorescence-activated droplet sorting (FADS): efficient microfluidic cell sorting based on enzymatic activity

We describe a highly efficient microfluidic fluorescence-activated droplet sorter (FADS) combining many of the advantages of microtitre-plate screening and traditional fluorescence-activated cell sorting (FACS). Single cells are compartmentalized in emulsion droplets, which can be sorted using dielectrophoresis in a fluorescence-activated manner (as in FACS) at rates up to 2000 droplets s(-1). To validate the system, mixtures of E. coli cells, expressing either the reporter enzyme beta-galactosidase or an inactive variant, were compartmentalized with a fluorogenic substrate and sorted at rates of approximately 300 droplets s(-1). The false positive error rate of the sorter at this throughput was <1 in 10(4) droplets. Analysis of the sorted cells revealed that the primary limit to enrichment was the co-encapsulation of E. coli cells, not sorting errors: a theoretical model based on the Poisson distribution accurately predicted the observed enrichment values using the starting cell density (cells per droplet) and the ratio of active to inactive cells. When the cells were encapsulated at low density ( approximately 1 cell for every 50 droplets), sorting was very efficient and all of the recovered cells were the active strain. In addition, single active droplets were sorted and cells were successfully recovered.

Droplet motion in microfluidic networks: Hydrodynamic interactions and pressure-drop measurements

We present experimental, numerical, and theoretical studies of droplet flows in hydrodynamic networks. Using both millifluidic and microfluidic devices, we study the partitioning of monodisperse droplets in an asymmetric loop. In both cases, we show that droplet traffic results from the hydrodynamic feedback due to the presence of droplets in the outlet channels. We develop a recently-introduced phenomenological model [W. Engl, Phys. Rev. Lett. 95, 208304 (2005)] and successfully confront its predictions to our experimental results. This approach offers a simple way to measure the excess hydrodynamic resistance of a channel filled with droplets. We discuss the traffic behavior and the variations in the corresponding hydrodynamic resistance length L_{d} and of the droplet mobility beta , as a function of droplet interdistance and confinement for channels having circular or rectangular cross sections.

Simple, robust storage of drops and fluids in a microfluidic device

We describe a single microfluidic device and two methods for the passive storage of aqueous drops in a continuous stream of oil without any external control but hydrodynamic flow. Advantages of this device are that it is simple to manufacture, robust under operation, and drops never come into contact with each other, making it unnecessary to stabilize drops against coalescence. In one method the device can be used to store drops that are created upstream from the storage zone. In the second method the same device can be used to simultaneously create and store drops from a single large continuous fluid stream without resorting to the usual flow focusing or T-junction drop generation processes. Additionally, this device stores all the fluid introduced, including the first amount, with zero waste. Transport of drops in this device depends, however, on whether or not the aqueous drops wet the device walls. Analysis of drop transport in these two cases is presented. Finally, a method for extraction of the drops from the device is also presented, which works best when drops do not wet the walls of the chip.

Formation of miscible fluid microstructures by hydrodynamic focusing in plane geometries

We experimentally investigate the flow structures formed when two miscible fluids that have large viscosity contrasts are injected and hydrodynamically focused in plane microchannels. Parallel viscous flows composed of a central stream surrounded by symmetric sheath streams are examined as a function of the flow rates, fluid viscosities, and rates of molecular diffusion. We study miscible interfacial morphologies and show a route for manipulating viscous flow-segregation processes in plane microsystems. The diffusion layer at the boundary of an ensheathed fluid grows as function of the distance downstream and depends on the Péclet number. In particular, we observe diffusion-enhanced viscous ensheathing processes. In the presence of a constriction, we investigate the formation of a lubricated viscous thread in the converging flow and also the buckling morphologies of the thread in the diverging flow. This study, relevant to multifluid flow between a "thick" material and a "thin" solvent, demonstrates the possibility to further control steady and oscillatory miscible fluid microstructures.

Pillar-induced droplet merging in microfluidic circuits

A novel method is presented for controllably merging aqueous microdroplets within segmented flow microfluidic devices. Our approach involves exploiting the difference in hydrodynamic resistance of the continuous phase and the surface tension of the discrete phase through the use of passive structures contained within a microfluidic channel. Rows of pillars separated by distances smaller than the representative droplet dimension are installed within the fluidic network and define passive merging elements or chambers. Initial experiments demonstrate that such a merging element can controllably adjust the distance between adjacent droplets. In a typical scenario, a droplet will enter the chamber, slow down and stop. It will wait and then merge with the succeeding droplets until the surface tension is overwhelmed by the hydraulic pressure. We show that such a merging process is independent of the inter-droplet separation but rather dependent on the droplet size. Moreover, the number of droplets that can be merged at any time is also dependent on the mass flow rate and volume ratio between the droplets and the merging chamber. Finally, we note that the merging of droplet interfaces occurs within both compressing and the decompressing regimes.

Droplet microfluidics

Droplet-based microfluidic systems have been shown to be compatible with many chemical and biological reagents and capable of performing a variety of "digital fluidic" operations that can be rendered programmable and reconfigurable. This platform has dimensional scaling benefits that have enabled controlled and rapid mixing of fluids in the droplet reactors, resulting in decreased reaction times. This, coupled with the precise generation and repeatability of droplet operations, has made the droplet-based microfluidic system a potent high throughput platform for biomedical research and applications. In addition to being used as microreactors ranging from the nano- to femtoliter range; droplet-based systems have also been used to directly synthesize particles and encapsulate many biological entities for biomedicine and biotechnology applications. This review will focus on the various droplet operations, as well as the numerous applications of the system. Due to advantages unique to droplet-based systems, this technology has the potential to provide novel solutions to today's biomedical engineering challenges for advanced diagnostics and therapeutics.

An optical toolbox for total control of droplet microfluidics

The use of microfluidic drops as microreactors hinges on the active control of certain fundamental operations such as droplet formation, transport, division and fusion. Recent work has demonstrated that local heating from a focused laser can apply a thermocapillary force on a liquid interface sufficient to block the advance of a droplet in a microchannel (C. N. Baroud, J.-P. Delville, F. Gallaire and R. Wunenburger, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75(4), 046302). Here, we demonstrate the generality of this optical approach by implementing the operations mentioned above, without the need for any special microfabrication or moving parts. We concentrate on the applications to droplet manipulation by implementing a wide range of building blocks, such as a droplet valve, sorter, fuser, or divider. We also show how the building blocks may be combined by implementing a valve and fuser using a single laser spot. The underlying fundamentals, namely regarding the fluid mechanical, physico-chemical and thermal aspects, will be discussed in future publications.

Microfluidic consecutive flow-focusing droplet generators

This article describes emulsification in a microfluidic double droplet generator (DDR) comprising two consecutive flow-focusing devices with locally modified surface chemistry. We generated W/O/W, O/O/W and O/W/O double emulsions with precisely controlled sizes and morphology of droplets. Secondly, by combining two mechanisms of droplet formation (the flow-focusing mechanism and the break up of liquid threads at T-junction) we produced multiple populations of droplets with varying size and/or composition. These droplets were used as the structural units for the formation of complex dynamic lattices.