Study of flow behaviors of droplet merging and splitting in microchannels using Micro-PIV measurement

Droplet merging and splitting are important droplet manipulations in droplet-based microfluidics. However, the fundamental flow behaviors of droplets were not systematically studied. Hence, we designed two different microstructures to achieve droplet merging and splitting respectively, and quantitatively compared different flow dynamics in different microstructures for droplet merging and splitting via micro-particle image velocimetry (micro-PIV) experiments. Some flow phenomena of droplets different from previous studies were observed during merging and splitting using a high-speed microscope. It was also found the obtained instantaneous velocity vector fields of droplets have significant influence on the droplets merging and splitting. For droplet merging, the probability of droplets coalescence (η) in a microgroove is higher (50% < η < 92%) than that in a T-junction microchannel (15% < η < 50%), and the highest coalescence efficiency (η = 92%) comes at the two-phase flow ratio e of 0.42 in the microgroove. Moreover, compared with a cylinder obstacle, Y-junction bifurcation can split droplets more effectively and the droplet flow during splitting is steadier. The results can provide better understanding of droplet behaviors and are useful for the design and applications of droplet-based microfluidics.     

Microchannel geometry design for rapid and uniform reagent distribution

Rapid and uniform reagent distribution is critical to the performance of a high-throughput microfluidic system, and its geometric design of the microchannels dominates the accuracy and distribution uniformity of the daughter droplets. This research’s purpose is to optimize the geometry of the T-junction to achieve a uniform distribution of two daughter droplets from a single liquid droplet. Models of gas–liquid flow were realized in the transient numerical simulations to investigate the geometry-dependent pressure distributions and the flowing velocities inside the droplet during the splitting process that leads to an improved design of the T-junction that can increase the stability of the droplet splitting process. To validate that increasing the stability of the splitting process can help improve the distribution uniformity of the daughter droplets, microfluidic devices were manufactured on poly(methyl methacrylate) substrates with micromilling and thermal bonding for experiments. In the multiple experiments, 2 μl of reagent was loaded into the microfluidic device and a uniform pneumatic pressure was applied to push the droplet into the T-junction for splitting. The experimental results, after statistical analysis, show that the improved T-junction can achieve better distribution uniformity of the daughter droplets with a higher reliability and a less reagent loss during the splitting process.     

Modeling and characterization of an industrial inkjet head for micro-patterning on printed circuit boards

A conceptual design using computational fluid dynamics (CFD) and micro-electro-mechanical systems (MEMS) fabrication has been performed to develop an industrial inkjet head for micro-patterning on printed circuit boards. The printhead has been fabricated with silicon and silicon on insulator (SOI) wafers by MEMS process and silicon to silicon bonding method. The measured displacement waveform from a piezoelectric actuator by laser doppler vibrometer (LDV) was used as input data for the three-dimensional flow solver to simulate the droplet formation. The mechanism of droplet ejection from piezoelectric-type inkjet heads was investigated by simulating two-phase flows of the air and metal inks. As a preliminary approach, liquid metal jetting phenomena are identified by simulating droplet ejection and droplet formation in a consequent manner. Parametric studies are followed by the design optimization process to deduce key factors to inkjet head performance: nozzle geometry, droplet size, ejecting speed, pulse amplitude, and ink viscosity. The present design tool, based on a two-phase flow solver and experimental measurements, has shown its promising applicability to various concept designs of industrial inkjet system for micro-patterning on electronic chips and boards.     

Centrifugal generation and manipulation of droplet emulsions

This work for the first time describes a centrifugal technique for the production and manipulation of highly monodisperse water droplets (CV of droplet diameter below 2%) immersed in a continuous flow of immiscible oil. Within a given working range, droplet volumes (5–22 nL) and their mutual spacing is governed by the channel geometry and the frequency of rotation. Different regimes of liquid–liquid flows are presented. We also demonstrate capabilities like droplet splitting and sedimentation as well as the production of two colored droplets, thus setting the stage for a novel centrifugal platform for multiphase flows.     

Droplet formation by squeezing in a microfluidic cross-junction

In microfluidics, flow focusing is widely used to produce water-in-oil droplets in microchannels at high frequency. We here report an experimental study of droplet formation in a microfluidic cross-junction with a minimum number of geometrical parameters. We mostly focus on the squeezing regime, which is composed of two distinct steps: filling and pinching. The duration of each step (and corresponding volumes of each liquid phase) is analyzed. They vary according to both water and oil flow rates. These variations provide several insights about the fluid flows in both phases. We propose several scaling laws to relate the droplet volume and frequency to the flow rate of both phases. We also discuss the influence of surfactant and channel compliance on droplet formation.     

Control of serial microfluidic droplet size gradient by step-wise ramping of flow rates

This paper describes a method to control and detect droplet size gradient by step-wise flow rate ramping of water-in-oil droplets in a microfluidic device. The droplets are generated in a cross channel device with two oil inlets and a water inlet. The droplet images are captured and analyzed in a time sequence in order to quantify the droplet generation frequency. It is demonstrated that by controlling the ramping of the oil flow rates it is possible to manipulate the ramping of droplet sizes. Increasing or decreasing of droplet sizes is achieved for a step-wise triangular ramping profile of the oil flow rate. The dynamic behavior of droplets due to the step-wise flow pulses is investigated. Uniform linear size ramping of water-in-oil droplets from 73 to 83 μm in diameter is generated with an oil flow ramping range from 1 to 11 μL/min in a minimum of five steps while water flow rate is held constant at 2 μL/min.     

A study of capillary flow from a pendant droplet

Surface tension driven capillary flow from a pendant droplet into a horizontal glass capillary is investigated in this paper. Effect of the droplet surface on dynamic behavior of such capillary flow is examined and compared with surface tension driven capillary flow from an infinite reservoir. In the experiment, capillaries of 300–700 μm in diameter were used with glycerol–DI water mixture solutions having viscosities ranging from 80 to 934 mPa s. It is observed that compared to the capillary flow from an infinite reservoir, the capillary flow from a droplet exhibits higher rates of meniscus displacement. This is due to an additional driving force resulted from change in droplet surface area (or curvature). The two main parameters influencing the flow are the dimensionless droplet geometry parameter (k) and the dynamic contact angle (θ _D). The molecular kinetics theory of Blake and De Coninck’s model [Adv Colloid Interface Sci 96(1–3):21–36, 2002] is used to interpret the dynamic contact angle. This theory considers a molecular friction coefficient (ζ) at the liquid front flowing over a solid surface. Moreover, three models are proposed to describe the shape of the pendant droplet during capillary action. It is found that the egg-shaped model provides a more realistic model to compute the shape of the pendant droplet deformed during the capillary action. Thus the predictions by the egg-shaped model are in good agreement with the experimental data.     

Critical conditions and breakup of non-squashed microconfined droplets: effects of fluid viscoelasticity

Droplet breakup in systems with either a viscoelastic matrix or a viscoelastic droplet is studied microscopically in bulk and confined shear flow, using a parallel plate counter rotating shear flow cell. The ratio of droplet diameter to gap spacing is systematically varied between 0.1 and 0.85. In bulk shear flow, the effects of matrix and droplet viscoelasticity on the critical capillary number for breakup are very moderate under the studied conditions. However, in confined conditions a profoundly different behaviour is observed: the critical capillary numbers of a viscoelastic droplet are similar to those of a Newtonian droplet, whereas matrix viscoelasticity causes breakup at a much lower capillary number. The critical capillary numbers are compared with the predictions of a phenomenological model by Minale et al. (Langmuir 26:126–132, 2010); the model results are in qualitative disagreement with the experimental data. It is also found that the critical dimensionless droplet length, the critical capillary number, and the dimensionless droplet length at breakup show a similar dependency on confinement ratio. As a result, confined droplets in a viscoelastic matrix have a smaller dimensionless length at breakup than droplets in a Newtonian matrix, which affects the breakup mode. Whereas confined droplets in a Newtonian matrix can break up into multiple parts, only two daughter droplets are obtained after breakup in a viscoelastic matrix, up to very large confinement ratios.     

Design optimization of supersonic jet pumps using high fidelity flow analysis

Supersonic jet pumps are simple devices with no moving parts, where a high velocity (primary) flow is used to pump a second fluid. In this paper, Computational Fluid Dynamics (CFD) is combined with an optimization framework in order to develop a tool for the rapid generation of jet pump designs. A key feature of the problem formulation is the transformation of the jet pump design parameters in terms of geometric ratios. This approach dramatically reduces the number of unrealistic designs covered by the Design of Experiments. Optimal Latin Hypercubes for surrogate model building and model validation points are constructed using a permutation genetic algorithm and design points are evaluated using CFD. Surrogate models of primary and entrained flow rates are built using a Moving Least Squares approach. A series of optimizations for various pump sizes are performed using a genetic algorithm and Sequential Quadratic Programming, with responses calculated from the surrogates. This approach results in a set of optimized designs, from which pumps for a wide range of flow rates can be interpolated.     

Microfluidic sorting of droplets by size

Droplet sorting by size was achieved in microfluidic channels through controlling the bifurcating junction geometry and the flow rates of the daughter channels. The sorting designs separated droplets with a radius difference of as little as 4 μm. The developed droplet channel design can be potentially used in combination with other particle sorting system to improve the sorting efficiency without the control of electrodes or fluidic valves.     

Scale-up and control of droplet production in coupled microfluidic flow-focusing geometries

A single microfluidic chip consisting of six microfluidic flow-focusing devices operating in parallel was developed to investigate the feasibility of scaling microfluidic droplet generation up to production rates of hundreds of milliliters per hour. The design utilizes a single inlet channel for both the dispersed aqueous phase and the continuous oil phase from which the fluids were distributed to all six flow-focusing devices. The exit tubing for each of the six flow-focusing devices is separate and individually plumbed to each device. Within each flow-focusing device, the droplet size was monodisperse, but some droplet size variations were observed across devices. We show that by modifying the flow resistance in the outlet channel of an individual flow-focusing device it is possible to control both the droplet size and frequency of droplet production. This can be achieved through the use of valves or, as is done in this study, by changing the length of the exit tubing plumbed to the outlet of the each device. Longer exit tubing and larger flow resistance is found to lead to larger droplets and higher production frequencies. The devices can thus be individually tuned to create a monodisperse emulsion or an emulsion with a specific drop size distribution.     

Generation of uniform-size droplets by multistep hydrodynamic droplet division in microfluidic circuits

A microfluidic system is presented to generate multiple daughter droplets from a mother droplet, by the multistep hydrodynamic division of the mother droplet at multiple branch points in a microchannel. A microchannel network designed based on the resistive circuit model enables us to control the distribution ratio of the flow rate, which dominates the division ratios of the mother droplets. We successfully generated up to 15 daughter droplets from a mother droplet with a variation in diameter of less than 2%. In addition, we examined factors affecting the division ratio, including the average fluid velocity, interfacial tension, fluid viscosity, and the distribution ratio of volumetric flow rates at a branch point. Additionally, we actively controlled the volume of the mother droplets and examined its influence on the size of the daughter droplets, demonstrating that the size of the daughter droplets was not significantly influenced by the volume of the mother droplet when the distribution ratio was properly controlled. The presented system for controlling droplet division would be available as an innovative means for preparing monodisperse emulsions from polydisperse emulsions, as well as a technique for making a microfluidic dispenser for digital microfluidics to analyze the droplet compositions.     

Microparticle Concentration and Separation by Traveling-Wave Dielectrophoresis (twDEP) for Digital Microfluidics

This paper describes highly efficient in-droplet particle concentration and separation where particles are concentrated and separated into droplets by traveling-wave dielectrophoresis (DEP) and subsequent electrowetting-on-dielectric droplet splitting. A successful concentration for 5-mum aldehyde sulfate (AS) latex particles was experimentally achieved using microfabricated devices, showing that 98% of the total particles were concentrated into a split daughter droplet. In addition, in-droplet particle separation was successfully achieved using the following two different cases of particle mixtures: case 1) a mixture of 5-mum AS latex beads and 8-mum glass beads; and case 2) a mixture of ground pine (GP) spores and 8-mum glass beads. In case 1), 97% of the total AS beads were separated into one split droplet and 77% of the total glass beads into the other split droplet. In case 2), over 92% of the GP spores were separated into a split daughter droplet, whereas 86% of the glass beads were separated into the other split daughter droplet. In all these concentration and separation experiments, the applied frequency and the conductivity medium are key parameters influencing the concentration and separation performance, which have been optimally determined by measuring the DEP and electrorotation spectra of the used particles prior to the concentration and separation experiments. This integrated in-droplet separation and concentration method may provide an additional functionality to digital microfluidics.     

Electrokinetic motion of an electrically induced Janus droplet in microchannels

The electrokinetic motion of an electrically induced Janus oil droplet with one side covered with an aluminum oxide nanoparticle film in a circular microchannel was numerically simulated in this paper. The Janus oil droplet is electrically anisotropic as the nanoparticle-covered area carries positive charges and the rest oil–water surface area carries negative charges. A theoretical model was constructed to calculate the electrokinetic velocity of the Janus droplet by considering the force balance on the surface of the Janus droplet at steady state. In the model, the effects of the electric double layer and surface charges on the motion at the oil–water interface are considered. The effects of five parameters on the electrokinetic motion of the Janus droplets were studied: the electric field, the zeta potential ratio of the positively charged side to the negatively charged side of the Janus droplet, the viscosity ratio of the oil phase to the water phase, the nanoparticle coverage of the Janus droplet, and the size ratio of the diameter of the Janus droplet to the diameter of the cylindrical microchannel. The simulation results indicate that the increase in the electrical field, the zeta potential ratio, the viscosity ratio or the nanoparticle coverage leads to faster electrokinetic motion of the Janus droplet. On the other hand, with the increase in size ratio, the electrokinetic velocity of Janus droplet first decreases gradually then increases sharply. The simulated results were compared with the experimental results and good agreement was found.     

Numerical modeling of electrowetting processes in digital microfluidic devices

We use a three-dimensional multiphase lattice-Boltzmann model to study basic operations such as transport, merging and splitting of nanoliter water droplets actuated by electrowetting in digital microfluidic devices. In a first step, numerical and analytical predictions for the droplet transport velocity are compared and very good agreement is obtained for a wide range of contact angles. The same algorithm is employed then to study the dynamics of the splitting processes at different contact angles and different geometries of the cell. The configuration of the liquid droplet involved in a splitting process and the dependence of the splitting time on the transport velocity are also investigated and phenomenological laws describing these processes are also proposed.     

Electrowetting droplet microfluidics on a single planar surface

Electrowetting refers to an electrostatically induced reduction in the contact angle of an electrically conductive liquid droplet on a surface. Most designs ground the droplet by either sandwiching the droplet with a grounding plate on top or by inserting a wire into the droplet. Washizu and others have developed systems capable of generating droplet motion without a top plate while allowing the droplet potential to float. In contrast to these designs, we demonstrate an electrowetting system in which the droplet can be electrically grounded from below using thin conductive lines on top of the dielectric layer. This alternative method of electrically grounding the droplet, which we refer to as grounding-from-below, enables more robust droplet translation without requiring a top plate or wire. We present a concise electrical-energy analysis that accurately describes the distinction between grounded and non-grounded designs, the improvements in droplet motion, and the simplified control strategy associated with grounding-from-below designs. Electrowetting on a single planar surface offers flexibility for interfacing to liquid-handling instruments, utilizing droplet inertial dynamics to achieve enhanced mixing of two droplets upon coalescence, and increasing droplet translation speeds. In this paper, we present experimental results and a number of design issues associated with the grounding-from-below approach.     

Multi-helical micro-channels for rapid generation of drops of water in oil

High throughput generation of microscopic mono-dispersed droplets of one liquid into the continuous flow of another is important for large number of engineering and biomedical applications. However, meeting conflicting demands of both uniformity of size and high rate of droplet generation have been a difficult task to be accomplished in conventional systems. We have attempted to address this problem by designing a novel multi-helical micro-channel which we have used to generate water droplets in a continuous flow of oil. The channel consists of three or more helical flow paths joined along their contour length forming a single channel with inherently asymmetric geometry. Helix angle and radius are found to be two additional geometric parameters which influence different drop break-up regimes. We have shown that both time period of generation of drops and the droplet size can be minimized by suitably altering the helix angle. A scaling law has been derived to rationalize these results.     

Behavior of microdroplets in diffuser/nozzle structures

This paper investigates the behavior of microdroplets flowing in microchannels with a series of diffuser/nozzle structures. Depending on the imposed flow direction, the serial structures can act either as a series of diffusers or nozzles. Different serial diffuser/nozzle microchannels with opening angles ranging from 15° to 45° were considered. A 2D numerical model was employed to study the dynamics of the microdroplet during its passage through the diffuser/nozzle structures. The deformation of the microdroplet was captured using a level set method. On the experimental front, test devices were fabricated in polydimethylsiloxane using soft lithography. T-junctions for droplet formation, diffuser/nozzle structures and pressure ports were integrated in a single device. Mineral oil with 2% w/w surfactant span 80 and de-ionized water with fluorescent worked as the carrier phase and the dispersed phase, respectively. The deformation of the water droplet and the corresponding pressure drop across the diffuser/nozzle structures were measured in both diffuser and nozzle configurations at a fixed flow rate ratio between oil and water of 30. The results show a linear relationship between the pressure drop and the flow rate. Furthermore, the rectification effect was observed in all tested devices. The pressure drop in the diffuser configuration is higher than that of the nozzle configuration. Finally, the pressure measured results with droplet and without droplet were analyzed and compared.     

A scaling model for electrowetting-on-dielectric microfluidic actuators

A hydrodynamic scaling model of droplet actuation in an electrowetting-on-dielectric (EWD) actuator is presented that takes into account the effects of contact angle hysteresis, drag from the filler fluid, drag from the solid walls, and change in the actuation force while a droplet traverses a neighboring electrode. Based on this model, the threshold voltage, V _T, for droplet actuation is estimated as a function of the filler medium of a scaled device. It is shown that scaling models of droplet splitting and liquid dispensing all show a similar scaling dependence on [t/ε_r(d/L)]^1/2, where t is insulator thickness and d/L is the aspect ratio of the device. It is also determined that reliable operation of a EWD actuator is possible as long as the device is operated within the limits of the Lippmann–Young equation. The upper limit on applied voltage, V _sat, corresponds to contact-angle saturation. The minimum 3-electrode splitting voltages as a function of aspect ratio d/L < 1 for an oil medium are less than V _sat. However, for an air medium the minimum voltage for 3-electrode droplet splitting exceeds V _sat for d/L ≥ 0.4. EWD actuators were fabricated to operate with droplets down to 35pl. Reasonable scaling results were achieved.