Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping

In this work, we have systematically analyzed the scaling law of droplet formation by cross-flow shear method in T-junction microfluidic devices. The droplet formation mechanisms can be distinguished by the capillary number for the continuous phase (Ca_c), which are the squeezing regime (Ca_c < 0.002), dripping regime (0.01 < Ca_c < 0.3), and the transient regime (0.002 < Ca_c< 0.01). Three corresponding correlations have been suggested in the different range of Ca_c. In the dripping regime, we developed a modified capillary number for the continuous phase (Ca_c′) by considering the influence of growing droplet size on the continuous phase flow rate. And the modified model could predict droplet diameter more accurately. In the squeezing regime, the final plug length was contributed by the growth and ‘squeeze’ stages based on the observation of dynamic break-up process. In the transient regime, we firstly suggested a mathematical model by considering the influences of the above two mechanisms. The correlations should be very useful for the application of controlling droplet size in T-junction microfluidic devices.     

Droplet generation in a microchannel with a controllable deformable wall

We report the droplet generation behavior of a microfluidic droplet generator with a controllable deformable membrane wall using experiments and analytical model. The confinement at the droplet generation junction is controlled by using external pressure, which acts on the membrane, to generate droplets smaller than junction size (with other parameters fixed) and stable and monodispersed droplets even at higher capillary numbers. A non-dimensional parameter, i.e., controlling parameter K _p, is used to represent the membrane deformation characteristics due to the external pressure. We investigate the effect of the controlled membrane deformation (in terms of K _p), viscosity ratio λ and flow rate ratio r on the droplet size and mobility. A correlation is developed to predict droplet size in the controllable deformable microchannel in terms of the controlling parameter K _p, viscosity ratio λ and flow rate ratio r. Due to the deflection of the membrane wall, we demonstrate that the transition from the stable dripping regime to the unstable jetting regime is delayed to a higher capillary number Ca (as compared to rigid droplet generators), thus pushing the high throughput limit. The droplet generator also enables generation of droplets of sizes smaller than the junction size by adjusting the controlling parameter.     

Generation of droplets in the T-junction with a constriction microchannel

Droplet microfluidics plays an essential role in science and technology with various applications such as chemical engineering, environment, energy and other fields. T-junction with a constriction microchannel is designed for the controlled production of monodisperse microdroplets, which could produce droplets with the same size under a lower flow resistance. The influence of the microchannel structure, operating conditions, and physical properties on the dispersion rules is systematically investigated by combinations of micro-particle image velocimetry (Micro-PIV), high-speed camera and numerical simulation. Compared to the traditional T-junction channel, the T-junction with a constriction microchannel can generate smaller droplets whose size conforms to the size prediction formula of the traditional T-junction channel. It is found that the velocity vector of the T-junction with a constriction microchannel is faster than that in the T-junction channel at each stage of droplet generation. The droplet size is mainly based on the Ca number, the flow rate ratio and viscosity ratio of the continuous phases in our channel, and the range of the index of Ca with the droplet size is found. The constriction width has a significant influence on the dispersion rule, as there is a decreasing tendency for the droplet size with reducing constriction width.     

Micro-droplet formation in non-Newtonian fluid in a microchannel

Micro-droplet formation from an aperture with a diameter of micrometers is numerically investigated under the cross-flow conditions of an experimental microchannel emulsification process. The process involves dispersing an oil phase into continuous phase fluid through a microchannel wall made of apertured substrate. Cross-flow in the microchannel is of non-Newtonian nature, which is included in the simulations. Micro-droplets of diameter 0.76–30 μm are obtained from the simulations for the apertures of diameter 0.1–10.0 μm. The simulation results show that rheology of the bulk liquid flow greatly affects the formation and size of droplets and that dispersed micro-droplets are formed by two different breakup mechanisms: in dripping regime and in jetting regime characterized by capillary number Ca. Relations between droplet size, aperture opening size, interfacial tension, bulk flow rheology, and disperse phase flow rate are discussed based on the simulation and the experimental results. Data and models from literature on membrane emulsification and T-junction droplet formation processes are discussed and compared with the present results. Detailed force balance models are discussed. Scaling factor for predicting droplet size is suggested.     

Effect of operating conditions and liquid physical properties on the size of monodisperse microbubbles produced in a capillary embedded T-junction device

The aim of this study was to investigate the effect of operating parameters such as liquid flow rate, gas inlet pressure, and capillary diameter as well as the influence of the physical properties of the liquid, in particular viscosity, on the generation of monodisperse microbubbles in a circular cross section T-junction device. Aqueous glycerol solutions with viscosities ranging from 1- to 100 mPa s were used in the experiments. The bubble diameter generated was studied for systematically varied combinations of gas inlet pressure, liquid flow rate, and liquid viscosity with a fixed capillary inner diameter of 150 μm for the liquid and gas inlet channels as well as the outlet channel. In addition, the effect of channel geometry on bubble size was studied using capillaries with inner diameters of first 100 and then 200 μm. In all the experiments the distance between the coaxial capillaries at the junction was set to be 200 μm. All the microbubbles produced in this study were highly monodisperse (polydispersity index <1 %) and it was found, as expected, that bubble formation and size were influenced by the ratio of liquid to gas flow rate, capillary size, and liquid viscosity. The experimental data were then compared with empirical scaling laws derived for rectangular cross-section junctions. In contrast with these previous studies, which have found bubble size to be dependent on either the flow rate ratio (the squeezing regime) or capillary number (the dripping regime), in this experimental study bubble size was found to depend on both capillary number and flow ratio.     

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

The spontaneous capillary-driven filling of microchannels is important for a wide range of applications. These channels are often rectangular in cross-section, can be closed or open, and horizontal or vertically orientated. In this work, we develop the theory for capillary imbibition and rise in channels of rectangular cross-section, taking into account rigidified and non-rigidified boundary conditions for the liquid–air interfaces and the effects of surface topography assuming Wenzel or Cassie-Baxter states. We provide simple interpolation formulae for the viscous friction associated with flow through rectangular cross-section channels as a function of aspect ratio. We derive a dimensionless cross-over time, T _c, below which the exact numerical solution can be approximated by the Bousanquet solution and above which by the visco-gravitational solution. For capillary rise heights significantly below the equilibrium height, this cross-over time is T _c ≈ (3X _e/2)^2/3 and has an associated dimensionless cross-over rise height X _c ≈ (3X _e/2)^1/3, where X _e = 1/G is the dimensionless equilibrium rise height and G is a dimensionless form of the acceleration due to gravity. We also show from wetting considerations that for rectangular channels, fingers of a wetting liquid can be expected to imbibe in advance of the main meniscus along the corners of the channel walls. We test the theory via capillary rise experiments using polydimethylsiloxane oils of viscosity 96.0, 48.0, 19.2 and 4.8 mPa s within a range of closed square tubes and open rectangular cross-section channels with SU-8 walls. We show that the capillary rise heights can be fitted using the exact numerical solution and that these are similar to fits using the analytical visco-gravitational solution. The viscous friction contribution was found to be slightly higher than predicted by theory assuming a non-rigidified liquid–air boundary, but far below that for a rigidified boundary, which was recently reported for imbibition into horizontally mounted open microchannels. In these experiments we also observed fingers of liquid spreading along the internal edges of the channels in advance of the main body of liquid consistent with wetting expectations. We briefly discuss the implications of these observations for the design of microfluidic systems.     

Engineering droplet navigation through tertiary-junction microchannels

We present an experimental and in silico investigation of path selection by a single droplet inside a tertiary-junction microchannel using oil-in-water as a model system. The droplet was generated at a T-junction inside a microfluidic chip, and its flow behavior as a function of droplet size, streamline position, viscosity, and Reynolds number (Re) of the continuous phase was studied downstream at a tertiary junction having perpendicular channels of uniform square cross section and internal fluidic resistance proportional to their lengths. Numerical studies were performed using the multicomponent lattice Boltzmann method. Both the experimental and numerical results showed good agreement and suggested that at higher Re equal to 3, the flow was dominated by inertial forces resulting in the droplets choosing a path based on their center position in the flow streamline. At lower Re of 0.3, the streamline-assisted path selection became viscous force-assisted above a critical droplet size. As the Re was further reduced to 0.03, or when the viscosity of the dispersed phase was increased, the critical droplet size for transition also decreased. This multivariate approach can in future be used to engineer sorting of cells, e.g., circulating tumor cells (CTCs) allowing early-stage detection of life-threatening diseases.     

Reliable addition of reagents into microfluidic droplets

This article reports a design that reliably adds reagents into droplets by exploiting the physics of fluid flow at a T-junction in the microchannel. An expanded section right after the T-junction enhances merging of a stream with a droplet, eliminates the drawbacks such as extra droplet formation and long mixing time. The expanded section reduces the pressure buildup at the T-junction and minimizes the tendency to form extra droplets; plays the role in creating low Laplace pressure jump across the interface of the droplet forming from the T-junction which reduces the probability of forming extra droplet in the merging process; provides space for droplet coalescence if there is an extra droplet due to droplet break-up before merging. In this design, after merging, the reactants are in axial arrangement inside the droplets which lead to faster mixing. Reliable addition of reagent to the droplets happens for the combination of flow rates in a broad range from 25 to 250 μl/h, for both DI water (Q _DI) and fluorescent (Q _fluo) streams.     

Microdroplet formation of water and nanofluids in heat-induced microfluidic T-junction

This paper reports experimental investigations on the droplet formation and size manipulation of deionized water (DIW) and nanofluids in a microfluidic T-junction at different temperatures. Investigations of the effect of microchannel depths on the droplet formation process showed that the smaller the depth of the channel the larger the increase of droplet size with temperature. Sample nanofluids were prepared by dispersing 0.1 volume percentage of titanium dioxide (TiO₂) nanoparticles of 15 nm and 10 nm × 40 nm in DIW for their droplet formation experiments. The heater temperature also affects the droplet formation process. Present results demonstrate that nanofluids exhibit different characteristics in droplet formation with the temperature. Addition of spherical-shaped TiO₂ (15 nm) nanoparticles in DIW results in much smaller droplet size compared to the cylindrical-shaped TiO₂ (10 nm × 40 nm) nanoparticles. Besides changing the interfacial properties of based fluid, nanoparticles can influence the droplet formation of nanofluids by introducing interfacial slip at the interface. Other than nanofluid with cylindrical-shaped nanoparticles, the droplet size was found to increase with increasing temperature.     

Flow of CO<Subscript>2</Subscript>–ethanol and of CO<Subscript>2</Subscript>–methanol in a non-adiabatic microfluidic T-junction at high pressures

In this work, an experimental investigation of the single- and multiphase flows of two sets of fluids, CO₂–ethanol and CO₂–methanol, in a non-adiabatic microfluidic T-junction is presented. The operating conditions ranged from 7 to 18 MPa, and from 294 to 474 K. The feed mass fraction of CO₂ in the mixtures was 0.95 and 0.87, respectively. Under these operating conditions, CO₂ was either in liquid, gas or supercritical state; and the mixtures experienced a miscible single phase or a vapour–liquid equilibrium (VLE), with two separated phases. Taylor, annular and wavy were the two-phase flow regimes obtained in the VLE region. In the single phase region, the observed flows were classified into standard single-phase flows, “pseudo” two-phase flows and local phenomena in the T-junction. Flow regime maps were generated, based on temperature and pressure conditions. Two-phase flow void fractions and several parameters of Taylor flow were analysed. They showed a clear dependency on temperature, but were mostly insensitive to pressure. A continuous accumulation of liquid, either in the CO₂ channel or at the CO₂-side wall after the T-junction, disturbed most of the experiments in VLE conditions by randomly generating liquid plugs. This phenomenon is analysed, and capillary and wetting effects due to local Marangoni stresses are suggested as possible causes.     

Effect of viscosities of dispersed and continuous phases in microchannel oil-in-water emulsification

Although many aspects of microchannel emulsification have been covered in literature, one major uncharted area is the effect of viscosity of both phases on droplet size in the stable droplet generation regime. It is expected that for droplet formation to take place, the inflow of the continuous phase should be sufficiently fast compared to the outflow of the liquid that is forming the droplet. The ratio of the viscosities was therefore varied by using a range of continuous and dispersed phases, both experimentally and computationally. At high viscosity ratio (η _d/η _c), the droplet size is constant; the inflow of the continuous phase is fast compared to the outflow of the dispersed phase. At lower ratios, the droplet diameter increases, until a viscosity ratio is reached at which droplet formation is no longer possible (the minimal ratio). This was confirmed and elucidated through CFD simulations. The limiting value is shown to be a function of the microchannel design, and this should be adapted to the viscosity of the two fluids that need to be emulsified.     

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.     

Droplet generation in micro-sieve dispersion device

Microfluidic devices with micro-sieve plate as the dispersion medium have been widely used for the mass production of emulsions. While unfortunately, few studies have so far been made for the droplet generation rules in those devices. In this work, the droplet generation processes in micro-sieve dispersion devices are investigated with specially designed micro-sieve pore arrays. The effects of channel structure, pore arrangement, and feeding method of dispersed phase on the average size and distribution of droplets are studied carefully. It is found the dimensionless average droplet diameters (d _av/d _e) in micro-sieve dispersion devices can be represented by a linear relation with Ca^−1/4 of continuous phase, the same as the scaling law in T-junction microchannels. The flow distribution among pores and the steric hindrance between droplets affect the diameter distribution of generated droplet very much. Monodispersed droplets with polydispersity index less than 5% can be made at Ca number larger than 0.01 and phase ratio (Q _D/Q _C) less than 1/6 in the present investigation.     

Micro-PIV investigation of the internal flow transitions inside droplets traveling in a rectangular microchannel

This paper discusses the studies on the internal flow field of droplets traveling in a rectangular microchannel by means of microparticle image velocimetry, specifically concentrating on the effects of capillary number, viscosity ratio and interfacial tension. The flow topology is predominantly dependent on the capillary number. It shows that the evident transitions from three pairs of recirculation zones at lower capillary numbers to one pair of recirculation zones near the sidewalls with low velocity in the central area at intermediate capillary numbers, then to a pair of recirculation zones closest to the axial centerline with high velocity in the central area at higher capillary numbers. There are two critical capillary numbers increasing with viscosity ratio in the evolution of flow features. Droplet size only influences two velocity components values other than the flow topology within intervals separated by the critical values. The equilibrium mechanism of viscous friction force and Marangoni stress dominate the internal topological transition in a surfactant added system. The obtained internal fluid phenomena inside droplets are beneficial to provide a guideline for screening of biochemical reaction conditions in the device.     

Dynamics of capillary flow in an open superoleophilic microchannel and its application to sensing of oil

We report the dynamics of capillary flow of oil in an open superoleophilic channel. The superoleophilic surface is fabricated by spin coating a layer of PDMS?+?n-hexane followed by candle sooting. The occurrence of various flow regimes, including the inertial, visco-inertial, and Lucas–Washburn regimes, are studied using analytical modelling as well as experiments. In case of a superoleophilic channel, much shorter inertial regime is observed as compared to that in an oleophilic channel due to the wicking of oil into the micro-roughness grooves ahead to moving bulk liquid meniscus. The study of the effect of channel aspect ratio \(\varepsilon\) on the mobility parameter \(k~\)showed that the mobility parameter \(k\) is maximum for an aspect ratio of \(\varepsilon =1.6\), which is attributed to the balance between the capillary and viscous forces. Finally, we demonstrate the application of the superoleophilic channel integrated with electrodes for impedance-based sensing of oil from an oil–water emulsion.     

Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows

The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to simulations of the deformation and breakup of a particle-cluster aggregate in shear flows. In the simulations, the solid particle is modeled by a droplet with strong interfacial tension and large viscosity. The van der Waals attraction force is taken into account for the interaction between the particles. The ratio of the hydrodynamic drag force to cohesive force, I, is introduced, and the effect of I on the aggregate deformation and breakup in shear flows is investigated. It is found that the aggregate is easier to deform and to be dispersed when I is over 100.     

Inkjet droplet deposition dynamics into square microcavities for OLEDs manufacturing

The dynamics of inkjet deposition in square microcavities are investigated utilizing a three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann (LB) model with large density ratios. A geometric scheme is considered within the pseudopotential LBM framework to obtain the desired contact angles. The effects of wettability, density ratios, droplet viscosity and impact velocity are explored to reveal the droplet–microcavity interactions. With the contact angles of microcavity increasing, the physical outcomes including the crown-like shape with a small round dot, circular hollow core, uniform film and convex film are identified and analyzed. At a lower density ratio ρ_r?=?11.6, the surrounding denser gas resists the droplet recoiling flow resulting in an increasing hollow core. The appropriate higher droplet viscosity and decreasing impact velocity are preferred which could eliminate the hollow core in the recoiling phase and accelerate the inkjet deposition process straightforward. The revelation of droplet-microcavity dynamics is beneficial for optimizing inkjet deposition process and fabricating uniform OLEDs panels.     

Holdup characteristics of two-phase parallel microflows

Two-phase parallel microflows, i.e., stratified flow and core-annular flow, have many applications in lab-on-chip devices. These include transport and reaction processes, such as liquid–liquid extraction and phase transfer catalysis. The phase holdup (fraction of the microchannel volume occupied by a specified phase) is a key parameter of these flow systems. In this work, mathematical models based on fundamental principles are used to predict the phase holdup in stratified flow and core-annular flow. For stratified flow, a two-dimensional model of flow in a rectangular channel of arbitrary aspect ratio is considered. A simpler one-dimensional model of stratified flow between infinite parallel plates is also analyzed. In the case of core-annular flow, axisymmetry is assumed in the model. The results of the models agree well with published experimental results. The dependence of phase holdup on the flow-rate fraction (the primary operating variable which can be controlled experimentally) is studied in detail. The nature of this relationship varies with the ratio of fluid viscosities and the channel’s aspect ratio (in the case of stratified flow). In the literature, the holdup is sometimes erroneously assumed to be identical to the flow-rate fraction. It is shown that this is not possible in the case of core-annular flow, while in stratified flow it is true only for a unique critical flow-rate. This critical flow-rate is viscosity dependent. The aspect ratio of the channel is found to have a considerable influence on the holdup in stratified flow when the fluids have different viscosities. However, even in such cases, there exists a point of geometric invariance at which the holdup is independent of the aspect ratio. At this point, the simple one-dimensional model of stratified flow can predict the holdup with complete accuracy.     

Liquid–liquid micro-dispersion in a double-pore T-shaped microfluidic device

For further understanding the dispersion process in the T-shaped microfluidic device, a double-pore T-shaped microchannel was designed and tested with octane/water system to form monodispersed plugs and droplets in this work. The liquid–liquid two-phase flow patterns were investigated and it was found that only short plugs, relative length L/w < 1.4, were produced. Additionally, the droplets flow was realized at phase ratios (F _C /F _D) just higher than 0.5, which is much smaller than that in the single-pore T-shaped microchannels. A repulsed effect between the initial droplets was observed in the droplet formation process and the periodic fluctuation flow of the dispersed phase was discussed by analyzing the resistances. Besides, the effect of the two-phase flow rates on the plug length and the droplet diameter was investigated. Considering the mutual effect of the initial droplets and the equilibrium between the shearing force with the interfacial tension, phase ratio and Ca number were introduced into the semi-empirical models to present the plug and droplet sizes at different operating conditions.     

Generating gas/liquid/liquid three-phase microdispersed systems in double T-junctions microfluidic device

This article describes the generation of microdispersed bubbles and droplets in a double T-junctions microfluidic device to form immiscible gas/liquid/liquid three-phase flowing systems. Segmented gas plugs are controllably prepared in water at the first T-junction to form gas/liquid two-phase fluid with the perpendicular flow cutting method. Then using this two-phase fluid as the cross-shearing fluid for the oil phase at the second T-junction, the gas/liquid/liquid three-phase flowing systems are prepared. Interestingly, it is found that the break-up of the oil droplets is mainly dominated by the cutting effect of the gas/liquid interface or the pressure drop across the emerging droplet, but independent with the viscous shearing effect of the continuous phase, even at the capillary number (Ca = u _wμ_w/γ_ow) higher than 0.01. The size laws and the distributions of the bubbles and droplets are investigated carefully, and a mathematical model has been developed to relating the operating conditions with the dispersed sizes.