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

Flow pattern maps of double emulsions transporting through bifurcation microchannels

The transportation behaviors of compound droplets in confined channels are widespread phenomena while the physical mechanisms are far from being completely unraveled. In this work, behaviors of double emulsions flowing through bifurcation microchannels are experimentally studied with the aim of building universal flow pattern maps. Three flow patterns are categorized according to different features of daughter droplets in terms of size, uniformity, and shell thickness. A detailed analysis of the dynamics of interfacial evolutions in different patterns is carried out and the coupling interaction between interfaces is found to affect the minimum tail distance during transportation. It is feasible to obtain the threshold of the occurrence of the coupling interaction, due to the different variation tendencies in the two states, which relies on three dimensionless parameters, i.e. droplet length, length ratio, and capillary number. Furthermore, a novel physical model is proposed to build the flow pattern map, with the two transition boundaries being expressed as different relationships in terms of the three identified parameters. The physical mechanisms are summarized with the aid of force analysis. An excellent agreement is shown between the model and experimental results in different liquid systems and bifurcation structures, indicating the generality of the proposed model.

Interfacing centrifugal microfluidics with linear-oriented 8-tube strips and multichannel pipettes for increased throughput of digital assays

We present a centrifugal microfluidic cartridge for the eight-fold parallel generation of monodisperse water-in-oil droplets using standard laboratory equipment. The key element is interfacing centrifugal microfluidics with its design based on polar coordinates to the linear structures of standard high-throughput laboratory automation. Centrifugal step emulsification is used to simultaneously generate droplets from eight samples directly into standard 200 μl PCR 8-tube strips. To ensure minimal manual liquid handling, the design of the inlets allows the user to load the samples and the oil via a standard multichannel pipette. Simulation-based design of the cartridge ensures that the performance is consistent in each droplet generation unit despite the varying radial positions that originate from the interface to the linear oriented PCR 8-tube strip and from the integration of linear oriented inlet holes for the multichannel pipettes. Within 10 minutes, sample volumes of 50 μl per droplet generation unit are emulsified at a fixed rotation speed of 960 rpm into 1.47 × 105 monodisperse droplets with a mean diameter of 86 μm. The overall coefficient of variation (CV) of the droplet diameter was below 4%. Feasibility is demonstrated by an exemplary digital droplet polymerase chain reaction (ddPCR) assay which showed high linearity (R2 ≥ 0.999) across all of the eight tubes of the strip.

Formation of Droplets of Shear-Thinning Non-Newtonian Fluids in Asymmetrical Parallelized Microchannels

Fluids containing polymers are frequently utilized in the chemical industry and exhibit shear-thinning characteristics. The flow distribution of non-Newtonian fluids in parallelized microchannels is a key issue to be solved during numbering-up. Numbering-up means increasing the number of parallelized microchannels. In this study, a high-speed camera is used to explore the distribution of fluid flow as well as the uniformity and stability of droplets in conceptual asymmetrical parallelized microchannels. Cyclohexane and carboxymethylcellulose sodium (CMC) aqueous solutions are used as the continuous phase and dispersed phase, respectively. The effects of fluctuation of pressure difference around the T-junction, the hydrodynamic resistance in microchannels, and the shear-thinning property of fluids on flow distribution and droplet formation are revealed. The uniformity and stability of droplets in microdevices with various cavity settings are compared, and an optimal configuration is proposed. Finally, prediction models for the flow distribution of shear-thinning fluids in asymmetrical parallelized microchannels are established.

The Phenomenon of Drug Emulsion Carriers Compaction during Their Movement in Microstructures

The greatest challenges of modern pharmacology are the design of drugs with the highest possible efficacy of an active substance and with the lowest possible invasiveness for the whole organism. A good solution features the application of a bioactive substance in different carriers. The effectiveness of such preparations is determined not only by the properties of the drug, but primarily by the dynamics of carrier movement in the body. This is the reason why studies on the dispersed systems transport in micro- and nanostructures are becoming important. This paper presents a study of emulsion systems transport in microcapillaries. A dispersed phase thickening effect was observed during the process, which resulted in a concentration increase of the flowing emulsion, in some cases up to 10 times. This phenomenon directly influences transport dynamics of such substances in microstructures and should be taken into account when designing drug parameters (concentration, release time, and action range). The effect was investigated for three different emulsions concentrations and presented quantitatively. The scales of this phenomenon occurrence at different flow conditions were investigated, and their magnitudes were modelled and described. This allows the prediction of the flow resistance in the movement of given dispersion systems, as a function of the flow rate, the emulsion parameters, and the microchannel size.

Boosting Electrically Actuated Manipulation of Water Droplets on Lubricated Surfaces through a Corona Discharge

Controllable liquid transportation is of great value in various practical applications. Here, we experimentally demonstrate a method of actuating high-speed droplet transport with large manipulation controllability on lubricated surfaces using a corona discharge generated by a simple needle-plate electrode configuration. Linear motion of droplets is realized with a maximum velocity of 30 mm/s. Factors affecting the velocity of these droplets are analyzed systematically, and the mechanism of droplet transport is explained. The lubrication film flow induced by charge deposition is shown to be the dominating factor in the droplet manipulation controllability. The new method presented here opens a new path of high-performance manipulation of liquid droplets by controlling the lubrication liquid film flow with charge deposition.

Three-dimensional visualization and analysis of flowing droplets in microchannels using real-time quantitative phase microscopy

Recent years have witnessed the development of droplet-based microfluidics as a useful and effective tool for high-throughput analysis in biological, chemical and environmental sciences. Despite the flourishing development of droplet manipulation techniques, only a few methods allow for label-free and quantitative inspection of flowing droplets in microchannels in real-time and in three dimensions (3-D). In this work, we propose and demonstrate the application of a real-time quantitative phase microscopy (RT-QPM) technique for 3-D visualization of droplets, and also for full-field and label-free measurement of analyte concentration distribution in the droplets. The phase imaging system consists of a linear-CCD-based holographic microscopy configuration and an optofluidic phase-shifting element, which can be used for retrieving quantitative phase maps of flowing objects in the microchannels with a temporal resolution only limited to the frame rate of the CCD camera. To demonstrate the capabilities of the proposed imaging technique, we have experimentally validated the 3-D image reconstruction of the droplets generated in squeezing and dripping regimes and quantitatively investigated the volumetric and morphological variation of droplets as well as droplet parameters related to the depth direction under different flow conditions. We also demonstrated the feasibility of using this technique, as a refractive index sensor, for in-line quantitative measurement of carbamide analyte concentration within the flowing droplets.

Noncontact and Nonintrusive Microwave-Microfluidic Flow Sensor for Energy and Biomedical Engineering

A novel flow sensor is presented to measure the flow rate within microchannels in a real-time, noncontact and nonintrusive manner. The microfluidic device is made of a fluidic microchannel sealed with a thin polymer layer interfacing the fluidics and microwave electronics. Deformation of the thin circular membrane alters the permittivity and conductivity over the sensitive zone of the microwave resonator device and enables high-resolution detection of flow rate in microfluidic channels using non-contact microwave as a standalone system. The flow sensor has the linear response in the range of 0-150 µl/min for the optimal sensor performance. The highest sensitivity is detected to be 0.5 µl/min for the membrane with the diameter of 3 mm and the thickness of 100 µm. The sensor is reproducible with the error of 0.1% for the flow rate of 10 µl/min. Furthermore, the sensor functioned very stable for 20 hrs performance within the cell culture incubator in 37 °C and 5% CO2 environment for detecting the flow rate of the culture medium. This sensor does not need any contact with the liquid and is highly compatible with several applications in energy and biomedical engineering, and particularly for microfluidic-based lab-on-chips, micro-bioreactors and organ-on-chips platforms.

Simulation before fabrication: a case study on the utilization of simulators for the design of droplet microfluidic networks

The functional performance of passively operated droplet microfluidics is sensitive with respect to the dimensions of the channel network, the fabrication precision as well as the applied pressure because the entire network is coupled together. Especially, the local and global hydrodynamic resistance changes caused by droplets make the task to develop a robust microfluidic design challenging as plenty of interdependencies which all affect the intended behavior have to be considered by the designer. After the design, its functionality is usually validated by fabricating a prototype and testing it with physical experiments. In case that the functionality is not implemented as desired, the designer has to go back, revise the design, and repeat the fabrication as well as experiments. This current design process based on multiple iterations of refining and testing the design produces high costs (financially as well as in terms of time). In this work, we show how a significant amount of those costs can be avoided when applying simulation before fabrication. To this end, we demonstrate how simulations on the 1D circuit analysis model can help in the design process by means of a case study. Therefore, we compare the design process with and without using simulation. As a case study, we use a microfluidic network which is capable of trapping and merging droplets with different content on demand. The case study demonstrates how simulation can help to validate the derived design by considering all local and global hydrodynamic resistance changes. Moreover, the simulations even allow further exploration of different designs which have not been considered before due to the high costs.

Simulating microfluidic networks allows to check a design even before first prototypes are realized.

A microfluidic circulatory system integrated with capillary-assisted pressure sensors

The human circulatory system comprises a complex network of blood vessels interconnecting biologically relevant organs and a heart driving blood recirculation throughout this system. Recreating this system in vitro would act as a bridge between organ-on-a-chip and "body-on-a-chip" and advance the development of in vitro models. Here, we present a microfluidic circulatory system integrated with an on-chip pressure sensor to closely mimic human systemic circulation in vitro. A cardiac-like on-chip pumping system is incorporated in the device. It consists of four pumping units and passive check valves, which mimic the four heart chambers and heart valves, respectively. Each pumping unit is independently controlled with adjustable pressure and pump rate, enabling users to control the mimicked blood pressure and heartbeat rate within the device. A check valve is located downstream of each pumping unit to prevent backward leakage. Pulsatile and unidirectional flow can be generated to recirculate within the device by programming the four pumping units. We also report an on-chip capillary-assisted pressure sensor to monitor the pressure inside the device. One end of the capillary was placed in the measurement region, while the other end was sealed. Time-dependent pressure changes were measured by recording the movement of the liquid-gas interface in the capillary and calculating the pressure using the ideal gas law. The sensor covered the physiologically relevant blood pressure range found in humans (0-142.5 mmHg) and could respond to 0.2 s actuation time. With the aid of the sensor, the pressure inside the device could be adjusted to the desired range. As a proof of concept, human normal left ventricular and arterial pressure profiles were mimicked inside this device. Human umbilical vein endothelial cells (HUVECs) were cultured on chip and cells can respond to mechanical forces generated by arterial-like flow patterns.

Measurement of the hydrodynamic resistance of microdroplets

Here, we demonstrate a novel method of measurement which determines precisely the hydrodynamic resistance of a droplet flowing through a channel. The obtained results show that the hydrodynamic resistance of a droplet in a microchannel achieves its maximum for lengths of the droplet ranging from 3w to 4w and that interactions between beads in a train exist.

On-chip pressure sensor using single-layer concentric chambers

A vision-based on-chip sensor for sensing local pressure inside a microfluidic device is proposed and evaluated in this paper. The local pressure is determined from the change of color intensity in the sensing chamber which is pre-filled with colored fluid. The working principle of the sensor is based on polydimethylsiloxane deformation. The pressure at the point of interest is guided into a deformation chamber, where the structural stiffness is softened by chamber geometry, and thus, the chamber deforms as a result of pressure changes. Such deformation is transmitted to the sensing chamber, a same-layer concentric inside the deformation chamber. The deformation in the sensing chamber causes the colored fluid flowing in or out the chamber and leads to different color intensity from the top view through a microscope. Experimental evaluations on static and dynamic responses by regulated input pressures were conducted. The correlation in static response is 0.97 while the dynamic responses are successfully observed up to 16 Hz. The greatest advantage is that the local pressure can be directly seen without any additional hardware or electricity. The whole sensor is on a single-layer microfluidic design, so that the fabrication is simple, consistent, and low-cost. The single-layer design also provides the convenience of easy integration for existing microfluidic systems.

Dense bubble traffic in microfluidic loops: Selection rules and clogging

We study the repartition of monodisperse bubbles at the inlet node of an asymmetric microfluidic loop for low to high bubble densities. In large loops, we evidence a new regime. Contrary to the classical belief, we point out that bubbles are directed not towards the arm having the higher total flow rate but towards the arm with the higher water flow rate at low and moderate relative gas flow rates. At higher rates, they enter the longer arm when they reach close packing in the shorter arm. In small loops, we evidence a clogging regime at high relative gas flow rates. Collisions between bubbles coming from the two arms at the outlet clog the longer arm. We propose a comprehensive analysis allowing us to explain these results.

Investigation of droplet coalescence in nanoparticle suspensions by a microfluidic collision experiment

Understanding the phenomenon of droplet coalescence in nanoparticle suspensions is extremely important for the preparation of Pickering emulsions. A microfluidic platform, which can provide compulsive droplet collisions, was developed to imitate the droplet coalescence process in the early stages of emulsification. Microscope videos showed the variations in the droplet coalescence percentage, droplet contact time, and liquid film drainage time in different working systems containing 158-306 nm polystyrene (PS) particles in the continuous oil phase. The intersections of the half and total droplet contact times as well as the liquid film drainage time indicated the transitions of coalescence percentage. The additional hydrodynamic resistance in the liquid film between the approaching interfaces caused by the embedded hydrophobic nanoparticles was understood to be the main reason for reduced droplet coalescence, whereas hydrophilic particles were found to promote coalescence. As a novel method, the microfluidic collision experiment provided accurate and quantitative data for analyzing the formation of Pickering emulsions.

Droplet migration characteristics in confined oscillatory microflows

We analyze the migration characteristics of a droplet in an oscillatory flow field in a parallel plate microconfinement. Using phase field formalism, we capture the dynamical evolution of the droplet over a wide range of the frequency of the imposed oscillation in the flow field, drop size relative to the channel gap, and the capillary number. The latter two factors imply the contribution of droplet deformability, commonly considered in the study of droplet migration under steady shear flow conditions. We show that the imposed oscillation brings an additional time complexity in the droplet movement, realized through temporally varying drop shape, flow direction, and the inertial response of the droplet. As a consequence, we observe a spatially complicated pathway of the droplet along the transverse direction, in sharp contrast to the smooth migration under a similar yet steady shear flow condition. Intuitively, the longitudinal component of the droplet movement is in tandem with the flow continuity and evolves with time at the same frequency as that of the imposed oscillation, although with an amplitude decreasing with the frequency. The time complexity of the transverse component of the movement pattern, however, cannot be rationalized through such intuitive arguments. Towards bringing out the underlying physics, we further endeavor in a reciprocal identity based analysis. Following this approach, we unveil the time complexities of the droplet movement, which appear to be sufficient to rationalize the complex movement patterns observed through the comprehensive simulation studies. These results can be of profound importance in designing droplet based microfluidic systems in an oscillatory flow environment.

A microfluidic device with focusing and spacing control for resistance-based sorting of droplets and cells

This paper reports a novel hydrodynamic technique for sorting of droplets and cells based on size and deformability. The device comprises two modules: a focusing and spacing control module and a sorting module. The focusing and spacing control module enables focusing of objects present in a sample onto one of the side walls of a channel with controlled spacing between them using a sheath fluid. A 3D analytical model is developed to predict the sheath-to-sample flow rate ratio required to facilitate single-file focusing and maintain the required spacing between a pair of adjacent objects. Experiments are performed to demonstrate focusing and spacing control of droplets (size 5-40 μm) and cells (HL60, size 10-25 μm). The model predictions compare well with experimental data in terms of focusing and spacing control within 9%. In the sorting module, the main channel splits into two branch channels (straight and side branches) with the flow into these two channels separated by a "dividing streamline". A sensing channel and a bypass channel control the shifting of the dividing streamline depending on the object size and deformability. While resistance offered by individual droplets of different sizes has been studied in our previous work (P. Sajeesh, M. Doble and A. K. Sen, Biomicrofluidics, 2014, 8, 1-23), here we present resistance of individual cells (HL60) as a function of size. A theoretical model is developed and used for the design of the sorter. Experiments are performed for size-based sorting of droplets (sizes 25 and 40 μm, 10 and 15 μm) and HL60 cells (sizes 11 μm and 19 μm) and deformability-based sorting of droplets (size 10 ± 1.0 μm) and polystyrene microbeads (size 10 ± 0.2 μm). The performance of the device for size- and deformability-based sorting is characterized in terms of sorting efficiency. The proposed device could be potentially used as a diagnostic tool for sorting of larger tumour cells from smaller leukocytes.

Control of the breakup process of viscous droplets by an external electric field inside a microfluidic device

Droplet-based microfluidic devices have received extensive attention in the fields of chemical synthesis, biochemical analysis, lab-on-chip devices, etc. Conventional passive microfluidic hydrodynamic flow-focusing devices (HFFDs) control the droplet breakup process by manipulating the flow ratios of the continuous phase to the dispersed phase. They confront difficulties in controlling droplet sizes in the dripping regime especially when the dispersed phase has a large viscosity. Previous studies have reported that an external electric field can be utilized as an additional tool to control the droplet breakup process in microfluidic devices. In this computational fluid dynamics (CFD) study, we have investigated the effect of an external static electric field on the droplet breakup process using the conservative level-set method coupled with the electrostatic model. The numerical simulations have demonstrated that the interaction of the electric field and the electric charges on the fluid interface induces the electric force, which plays a significant role in controlling the droplet formation dynamics. If the microfluidic system is applied with the electric field of varying strength, the droplet breakup process experiences three distinct regimes. In Regime 1, where low electric voltages are applied, the droplet size decreases almost linearly with the increase of voltage. Then the droplet size increases with the applied voltages in Regime 2, where the electric field has moderate strength. In Regime 3, where very large voltages are applied, the droplet size decreases with the applied voltage again. These interesting variations in the droplet breakup processes are explained by using transient pressure profiles in the dispersed phase and the continuous phase. The droplet breakup processes regulated by an external electric field that are revealed in this study can provide useful guidance on the design and operations of such droplet-based systems.

Analytical relations for long-droplet breakup in asymmetric T junctions

We develop accurate analytical relations for the droplet volume ratio, droplet length during breakup process, and pressure drop of asymmetric T junctions with a valve in each of the branches for producing unequal-sized droplets. An important advantage of this system is that after manufacturing the system, the size of the generated droplets can be changed simply by adjusting the valves. The results indicate that if the valve ratio is smaller than 0.65, the system enters a nonbreakup regime. Also the pressure drop does not depend on the time and decreases by increasing the valve ratio, namely, opening the degree of valve 1 to valve 2. In addition, the results reveal that by decreasing (increasing) the valve ratio, the droplet length of branch 1 decreases (increases) and the droplet length of branch 2 increases (decreases) linearly while the whole length of the droplet remains unchanged.

Cooperative breakups induced by drop-to-drop interactions in one-dimensional flows of drops against micro-obstacles

Depending on the capillary number at play and the parameters of the flow geometry, a drop may or may not break when colliding with an obstacle in a microdevice. Modeling the flow of one-dimensional trains of monodisperse drops impacting a micro-obstacle, we show numerically that complex dynamics may arise through drop-to-drop hydrodynamic interactions: we observe sequences of breakup events in which the size of the daughter drops created upon breaking mother ones becomes a periodic function of time. We demonstrate the existence of numerous bifurcations between periodic breakup regimes and we establish diagrams mapping the possible breakup dynamics as a function of the governing (physicochemical, hydrodynamic, and geometric) parameters. Microfluidic experiments validate our model as they concur very well with predictions.

Millifluidics as a simple tool to optimize droplet networks: Case study on drop traffic in a bifurcated loop

We report that modular millifluidic networks are simpler, more cost-effective alternatives to traditional microfluidic networks, and they can be rapidly generated and altered to optimize designs. Droplet traffic can also be studied more conveniently and inexpensively at the millimeter scale, as droplets are readily visible to the naked eye. Bifurcated loops, ladder networks, and parking networks were made using only Tygon(®) tubing and plastic T-junction fittings and visualized using an iPod(®) camera. As a case study, droplet traffic experiments through a millifluidic bifurcated loop were conducted, and the periodicity of drop spacing at the outlet was mapped over a wide range of inlet drop spacing. We observed periodic, intermittent, and aperiodic behaviors depending on the inlet drop spacing. The experimentally observed periodic behaviors were in good agreement with numerical simulations based on the simple network model. Our experiments further identified three main sources of intermittency between different periodic and/or aperiodic behaviors: (1) simultaneous entering and exiting events, (2) channel defects, and (3) equal or nearly equal hydrodynamic resistances in both sides of the bifurcated loop. In cases of simultaneous events and/or channel defects, the range of input spacings where intermittent behaviors are observed depends on the degree of inherent variation in input spacing. Finally, using a time scale analysis of syringe pump fluctuations and experiment observation times, we find that in most cases, more consistent results can be generated in experiments conducted at the millimeter scale than those conducted at the micrometer scale. Thus, millifluidic networks offer a simple means to probe collective interactions due to drop traffic and optimize network geometry to engineer passive devices for biological and material analysis.

Hydrodynamic resistance and mobility of deformable objects in microfluidic channels

This work reports experimental and theoretical studies of hydrodynamic behaviour of deformable objects such as droplets and cells in a microchannel. Effects of mechanical properties including size and viscosity of these objects on their deformability, mobility, and induced hydrodynamic resistance are investigated. The experimental results revealed that the deformability of droplets, which is quantified in terms of deformability index (D.I.), depends on the droplet-to-channel size ratio [Formula: see text] and droplet-to-medium viscosity ratio [Formula: see text]. Using a large set of experimental data, for the first time, we provide a mathematical formula that correlates induced hydrodynamic resistance of a single droplet [Formula: see text] with the droplet size [Formula: see text] and viscosity [Formula: see text]. A simple theoretical model is developed to obtain closed form expressions for droplet mobility [Formula: see text] and [Formula: see text]. The predictions of the theoretical model successfully confront the experimental results in terms of the droplet mobility [Formula: see text] and induced hydrodynamic resistance [Formula: see text]. Numerical simulations are carried out using volume-of-fluid model to predict droplet generation and deformation of droplets of different size ratio [Formula: see text] and viscosity ratio [Formula: see text], which compare well with that obtained from the experiments. In a novel effort, we performed experiments to measure the bulk induced hydrodynamic resistance [Formula: see text] of different biological cells (yeast, L6, and HEK 293). The results reveal that the bulk induced hydrodynamic resistance [Formula: see text] is related to the cell concentration and apparent viscosity of the cells.

Bioinspired micro-/nanostructure fibers with a water collecting property

We review the recent research on structure-induced water collecting properties of spider silk and bioinspired fibers. Since the capture silks of cribellate spiders have a unique wet-rebuilt structure with spindle-knots and joints for directional water collection, we were inspired to fabricate a series of artificial gradient micro-/nanostructure fibers. These fibers display excellent functions, such as driving tiny water drops in certain directions, water capturing, multi-gradient cooperation effect, and wet-response to environmental humidity. This review is helpful to the design of novel smart functional materials that can be extended to develop devices or systems for water collection, sensors, fluid-control, filters and others.

Origin of periodic and chaotic dynamics due to drops moving in a microfluidic loop device

Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We observe that the periodic behavior is an outcome of carrier phase mass conservation principle, which translates into a droplet spacing quantization rule. This rule implies that the summation of exit spacing is equal to an integral multiple of inlet spacing. This principle also enables identification of periodicity in experimental systems with input scatter. We find that the origin of chaotic behavior is through intermittency, which arises when drops enter and leave the junctions at the same time. We derive an analytical expression to estimate the occurrence of these chaotic regions as a function of system parameters. We provide experimental, simulation, and analytical results to validate the origin of periodic and chaotic behavior.

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.

A micro-rheological method for determination of blood type

The measurement of time and distance can be used for determining agglutination in small (nL) samples of liquid. We demonstrate the use of this new scheme of detection in typing and subtyping blood in a simple microfluidic system that monitors the speed of flow of microdroplets. The system (i) accepts small samples of liquids deposited directly onto the chip, (ii) forms droplets on demand from these samples, (iii) merges the droplets, and (iv) measures their speed in a microchannel. A sequence of measurements on different combinations of blood and antibodies can thus be used to determine blood type with the estimated probability of mistyping being less than 1 in a million tests. In addition, in the agglutinated samples, red blood cells concentrate at the rear of the droplets yielding an additional vista for detection and suggesting a possible mechanism for separations.

Droplet sorting in a loop of flat microfluidic channels

Motivated by recent experiments, we numerically study the droplet traffic in microfluidic channels forming an asymmetric loop with a long and a short arm. The loop is connected to an inlet and an outlet channel by two right angled T-junctions. Assuming flat channels, we employ the boundary element method (BEM) to numerically solve the two-dimensional Darcy equation that governs two phase flow in the Hele-Shaw limit. The occurrence of different sorting regimes is summarized in sorting diagrams in terms of droplet size, distance between consecutive droplets in the inlet channel, and loop asymmetry for mobility ratios of the liquid phases larger and smaller than one. For large droplet distances, the traffic is regulated by the ratio of the total hydraulic resistances of the long and short arms. At high droplet densities and below a critical droplet size, droplet-droplet collisions are observed for both mobility ratios.

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.

Bistability in droplet traffic at asymmetric microfluidic junctions

We present the first experimental demonstration of confined microfluidic droplets acting as discrete negative resistors, wherein the effective hydrodynamic resistance to flow in a microchannel is reduced by the presence of a droplet. The implications of this hitherto unexplored regime in the traffic of droplets in microfluidic networks are highlighted by demonstrating bistable filtering into either arm of symmetric and asymmetric microfluidic loops, and programming oscillatory droplet routing therein.

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.

Discontinuous transition in a laminar fluid flow: a change of flow topology inside a droplet moving in a micron-size channel

Even at moderate values of Reynolds number [e.g., Re=O(1)] a curved interface between liquids can induce an abrupt transition between topologically different configurations of laminar flow. Here we show for the first time direct evidence of a sharp transition in the speed of flow of a droplet upon a small increase of the value of the capillary number above a threshold and the associated change of topology of flow. The quantitative results on the dependence of the threshold capillary number on the contrast of viscosities and on the direction of transition cannot be explained by any of the existing theories and call for a new description.

Filtering microfluidic bubble trains at a symmetric junction

We report how a nominally symmetric microfluidic junction can be used to sort all bubbles of an incoming train exclusively into one of its arms. The existence of this "filter" regime is unexpected, given that the junction is symmetric. We analyze this behavior by quantifying how bubbles modulate the hydrodynamic resistance in microchannels and show how speeding up a bubble train whilst preserving its spatial periodicity can lead to filtering at a nominally symmetric junction. We further show how such an asymmetric traffic of bubble trains can be triggered in symmetric geometries by identifying conditions wherein the resistance to flow decreases with an increase in the number of bubbles in the microchannel and derive an exact criterion to predict the same.

Design of pressure-driven microfluidic networks using electric circuit analogy

This article reviews the application of electric circuit methods for the analysis of pressure-driven microfluidic networks with an emphasis on concentration- and flow-dependent systems. The application of circuit methods to microfluidics is based on the analogous behaviour of hydraulic and electric circuits with correlations of pressure to voltage, volumetric flow rate to current, and hydraulic to electric resistance. Circuit analysis enables rapid predictions of pressure-driven laminar flow in microchannels and is very useful for designing complex microfluidic networks in advance of fabrication. This article provides a comprehensive overview of the physics of pressure-driven laminar flow, the formal analogy between electric and hydraulic circuits, applications of circuit theory to microfluidic network-based devices, recent development and applications of concentration- and flow-dependent microfluidic networks, and promising future applications. The lab-on-a-chip (LOC) and microfluidics community will gain insightful ideas and practical design strategies for developing unique microfluidic network-based devices to address a broad range of biological, chemical, pharmaceutical, and other scientific and technical challenges.

Hamiltonian traffic dynamics in microfluidic-loop networks

Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain poorly understood. In this Letter, we focus on the transport of a finite number of particles in one-dimensional loop networks. By combining numerical, theoretical, and experimental efforts, we evidence that this collective process offers a unique example of Hamiltonian dynamics for hydrodynamically interacting particles. In addition, we show that the asymptotic trajectories are necessarily reciprocal despite the microscopic traffic rules explicitly break the time-reversal symmetry. We exploit these two remarkable properties to account for the salient features of the effective three-particle interaction induced by the exploration of fluidic loops.

Bubbles navigating through networks of microchannels

This paper describes the behavior of bubbles suspended in a carrier liquid and moving within microfluidic networks of different connectivities. A single-phase continuum fluid, when flowing in a network of channels, partitions itself among all possible paths connecting the inlet and outlet. The flow rates along different paths are determined by the interaction between the fluid and the global structure of the network. That is, the distribution of flows depends on the fluidic resistances of all channels of the network. The movement of bubbles of gas, or droplets of liquid, suspended in a liquid can be quite different from the movement of a single-phase liquid, especially when they have sizes slightly larger than the channels, so that the bubbles (or droplets) contribute to the fluidic resistance of a channel when they are transiting it. This paper examines bubbles in this size range; in the size range examined, the bubbles are discrete and do not divide at junctions. As a consequence, a single bubble traverses only one of the possible paths through the network, and makes a sequence of binary choices ("left" or "right") at each branching intersection it encounters. We designed networks so that, at each junction, a bubble enters the channel into which the volumetric flow rate of the carrier liquid is highest. When there is only a single bubble inside a network at a time, the path taken by the bubble is, counter-intuitively, not necessarily the shortest or the fastest connecting the inlet and outlet. When a small number of bubbles move simultaneously through a network, they interact with one another by modifying fluidic resistances and flows in a time dependent manner; such groups of bubbles show very complex behaviors. When a large number of bubbles (sufficiently large that the volume of the bubbles occupies a significant fraction of the volume of the network) flow simultaneously through a network, however, the collective behavior of bubbles-the fluxes of bubbles through different paths of the network-can resemble the distribution of flows of a single-phase fluid.

Speed of flow of individual droplets in microfluidic channels as a function of the capillary number, volume of droplets and contrast of viscosities

Droplet microfluidic techniques offer an attractive compromise between the throughput (of i.e. reactions per second) and the number of input/output controls needed to control them. Reduction of the number of controls follows from the confinement to essentially one-dimensional flow of slugs in channels which--in turn--relies heavily on the speed of flow of droplets. This speed is a complicated function of numerous parameters, including the volume of droplets (or length L of slugs), their viscosity μ(d), viscosity μ(c) and rate of flow of the continuous phase, interfacial tension and geometry of the cross-section of the channel. Systematic screens of the impact of these parameters on the speed of droplets remain an open challenge. Here we detail an automated system that screens the speeds of individual droplets at a rate of up to 2000 experiments per hour, with high precision and without human intervention. The results of measurements in channels of square cross-section (of width w = 360 μm) for four different values of the contrast of viscosities λ = μ(d)/μ(c) = 0.3, 1, 3, and 33, wide ranges of values of the capillary number Ca ∈ (10(-4), 10(-1)), and wide ranges of lengths of droplets l = L/w∈ (0.8, 30) show that the speed of droplets depends significantly both on l and on λ. The dependence on Ca is very strong for λ > 1, while it is less important both for λ ≤ 1 and for λ ≫ 1.

Transport of resistance through a long microfluidic channel

We introduce a continuous analytical model of propagation of resistance in pressure-driven flow of two-phase fluid in a single channel. This model can be used to predict and interpret experimental results in droplet microfluidics where the hydrodynamic resistance of a capillary comprises a constant part, specific to the channel and the viscosity of the continuous fluid, and a variable part, related to the presence and distribution of droplets. The continuous model is a convenient generalization of the discrete models as demonstrated via comparisons with discrete simulations and with experiments.

Complex dynamics of droplet traffic in a bifurcating microfluidic channel: periodicity, multistability, and selection rules

The binary path selection of droplets reaching a T junction is regulated by time-delayed feedback and nonlinear couplings. Such mechanisms result in complex dynamics of droplet partitioning: numerous discrete bifurcations between periodic regimes are observed. We introduce a model based on an approximation that makes this problem tractable. This allows us to derive analytical formulae that predict the occurrence of the bifurcations between consecutive regimes, establish selection rules for the period of a regime, and describe the evolutions of the period and complexity of droplet pattern in a cycle with the key parameters of the system. We discuss the validity and limitations of our model which describes semiquantitatively both numerical simulations and microfluidic experiments.

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.