Droplet formation in microfluidic T-junction generators operating in the transitional regime. II. Modeling

Microfluidic Fabrication of Gelatin-Nano Hydroxyapatite Scaffolds for Enhanced Control of Pore Size Distribution and Osteogenic Differentiation of Dental Pulp Stem Cells

The combination of gelatin and hydroxyapatite (HA) has emerged as a promising strategy in dental tissue engineering due to its favorable biocompatibility, mechanical properties, and ability to support cellular activities essential for tissue regeneration, rendering them ideal components for hard tissue applications. Besides, precise control over interconnecting porosity is of paramount importance for tissue engineering materials. Conventional methods for creating porous scaffolds frequently encounter difficulties in regulating pore size distribution. This study demonstrates the fabrication of gelatin-nano HA scaffolds with uniform porosity using a T-type junction microfluidic device in a single-step process. Significant improvements in control over the pore size distribution are achieved by regulating the flow parameters, resulting in effective and time-efficient manufacturing comparable in quality to the innovative 3D bioprinting techniques. The overall porosity of the scaffolds exceeded 60%, with a remarkably narrow size distribution. The incorporation of nano-HAinto 3D porous gelatin scaffolds successfully induced osteogenic differentiation in stem cells at both the protein and gene levels, as evidenced by the significant increase in osteocalcin (OCN), an important marker of osteogenic differentiation. The OCN levels are 26 and 43 times higher for gelatin and gelatin-HA scaffolds, respectively, compared to the control group.

Studying surfactant mass transport through dynamic interfacial tension measurements: A review of the models, experiments, and the contribution of microfluidics

Surfactant mass transport towards an interface plays a critical role during formation of emulsions, foams and in industrial processes where two immiscible phases coexist. The understanding of these mechanisms as experimentally observed by dynamic interfacial tension measurements, is crucial. In this review, theoretical models describing both equilibrated systems and surfactant kinetics are covered. Experimental results from the literature are analysed based on the nature of surfactants and the tensiometry methods used. The innovative microfluidic techniques that have become available to study both diffusion and adsorption mechanisms during surfactant mass transport are discussed and compared with classical methods. This review focuses on surfactant transport during formation of droplets or bubbles; stabilisation of dispersed systems is not discussed here.

Microfluidic-assisted synthesis and modeling of stimuli-responsive monodispersed chitosan microgels for drug delivery applications

Droplet microfluidic has been established to synthesize and functionalize micro/nanoparticles for drug delivery and screening, biosensing, cell/tissue engineering, lab-on-a-chip, and organ-on-a-chip have attracted much attention in chemical and biomedical engineering. Chitosan (CS) has been suggested for different biomedical applications due to its unique characteristics, such as antibacterial bioactivities, immune-enhancing influences, and anticancer bioactivities. The simulation results exhibited an alternative for attaining visions in this complex method. In this regard, the role of the flow rate ratio on the CS droplet features, including the generation rate and droplet size, were thoroughly described. Based on the results, an appropriate protocol was advanced for controlling the CS droplet properties for comparing their properties, such as the rate and size of the CS droplets in the microchip. Also, a level set (LS) laminar two-phase flow system was utilized to study the CS droplet-breaking process in the Flow Focused-based microchip. The outcomes demonstrated that different sizes and geometries of CS droplets could be established via varying the several parameters that validated addressing the different challenges for several purposes like drug delivery (the droplets with smaller sizes), tissue engineering, and cell encapsulation (the droplets with larger sizes), lab-on-a-chip, organ-on-a-chip, biosensing and bioimaging (the droplets with different sizes). An experimental study was added to confirm the simulation results. A drug delivery application was established to verify the claim.

Droplet formation of biological non-Newtonian fluid in T-junction generators. II. Model for final droplet volume prediction

This work represents the second part of a two-part series on the dynamics of droplet formation in a T-junction generator under the squeezing regime when using solutions of red blood cells as the dispersed phase. Solutions containing red blood cells are non-Newtonian; however, these solutions do not behave in the same way as other non-Newtonian fluids currently described in the literature. Hence, available models do not capture nor predict important features useful for the design of T-junction microfluidic systems, including droplet volume. The formation of a red blood cell-containing droplet consists of three stages: a lag stage, a filling stage, and a necking stage, with the lag stage only observed in narrow dispersed phase channel setups. Unlike other shear-thinning fluids, thread elongation into the main channel at the end of the necking stage is not observed for red blood cell solutions. In this work, a model that predicts the final droplet volume of a red blood cell containing droplets in T-junction generators is presented. The model combines a detailed analysis of the geometrical shape of the droplet during the formation process, with force and Laplace pressure balances to obtain the penetration depth (b_{fill}^{*}) and the critical neck thickness (2r_{pinch}^{*}) of the droplet. The performance of the model was validated by comparing the operational parameters (droplet volume, the spacing between the droplet, and the generation frequency) with the experimental data across a range of the dimensionless parameters (flow rate ratios, continuous phase viscosities, and channel geometries).

Phase synchronization of fluid-fluid interfaces as hydrodynamically coupled oscillators

Hydrodynamic interactions play a role in synchronized motions of coupled oscillators in fluids, and understanding the mechanism will facilitate development of applications in fluid mechanics. For example, synchronization phenomenon in two-phase flow will benefit the design of future microfluidic devices, allowing spatiotemporal control of microdroplet generation without additional integration of control elements. In this work, utilizing a characteristic oscillation of adjacent interfaces between two immiscible fluids in a microfluidic platform, we discover that the system can act as a coupled oscillator, notably showing spontaneous in-phase synchronization of droplet breakup. With this observation of in-phase synchronization, the coupled droplet generator exhibits a complete set of modes of coupled oscillators, including out-of-phase synchronization and nonsynchronous modes. We present a theoretical model to elucidate how a negative feedback mechanism, tied to the distance between the interfaces, induces the in-phase synchronization. We also identify the criterion for the transition from in-phase to out-of-phase oscillations.

The robust production of droplets by microfluidic T-junctions is a well-established technique. Um et al. demonstrate how the mutual interaction between droplets can be used to achieve additional control including the simultaneous release of droplets caused by synchronization phenomena.

Accounting for corner flow unifies the understanding of droplet formation in microfluidic channels

While shear emulsification is a well understood industrial process, geometrical confinement in microfluidic systems introduces fascinating complexity, so far prohibiting complete understanding of droplet formation. The size of confined droplets is controlled by the ratio between shear and capillary forces when both are of the same order, in a regime known as jetting, while being surprisingly insensitive to this ratio when shear is orders of magnitude smaller than capillary forces, in a regime known as squeezing. Here, we reveal that further reduction of—already negligibly small—shear unexpectedly re-introduces the dependence of droplet size on shear/capillary-force ratio. For the first time we formally account for the flow around forming droplets, to predict and discover experimentally an additional regime—leaking. Our model predicts droplet size and characterizes the transitions from leaking into squeezing and from squeezing into jetting, unifying the description for confined droplet generation, and offering a practical guide for applications.

T-junctions are a tool for droplet generation; they are well-described by models that distinguish for squeezing and jetting regimes for different capillary numbers. By considering the usually neglected corner flow, the authors identify an additional leaking regime for very low capillary numbers.

Advances in the Use of Microfluidics to Study Crystallization Fundamentals

This review compares droplet-based microfluidic systems used to study crystallization fundamentals in chemistry and biology. An original high-throughput droplet-based microfluidic platform is presented. It uses nanoliter droplets, generates a chemical library, and directly solubilizes powder, thus economizing both material and time. It is compatible with all solvents without the need for surfactant. Its flexibility permits phase diagram determination and crystallization studies (screening and optimizing experiments) and makes it easy to use for nonspecialists in microfluidics. Moreover, it allows concentration measurement via ultraviolet spectroscopy and solid characterization via X-ray diffraction analysis.

Mixing Efficiency Analysis on Droplet Formation Process in Microchannels by Numerical Methods

Liquid–liquid two-phase flow in microchannels has attracted much attention, due to the superiority of mass transfer enhancement. One of the biggest unresolved challenges is the low mixing efficiency at the microscale. Suitable mixing efficiency is important to promote the mass transfer of two-phase flow in microchannels. In this paper, the mixing efficiency in three junction configurations, including a cross-shaped junction, a cross-shaped T-junction, and a T-junction, is investigated by the volume of fluid (VOF) method coupled with user-defined scalar (UDS) model. All three junction configurations are designed with the same hydraulic diameter of 100 μm. Mixing components are distributed in the front and back parts of the droplet. The mixing efficiency in the droplet forming stage and the droplet moving stage are compared quantitatively. Results show that different junction configurations create very different mixing efficiencies, and the cross-shaped T-junction performs best, with relatively lower disperse phase fractions. However, with an increase of the disperse phase fraction, the cross-shaped junction is superior.

Examining the Effect of Flow Rate Ratio on Droplet Generation and Regime Transition in a Microfluidic T-Junction at Constant Capillary Numbers

The focus of this work is to examine the effect of flow rate ratio (quotient of the dispersed phase flow rate over the continuous phase flow rate) on a regime transition from squeezing to dripping at constant capillary numbers. The effect of the flow rate ratio on the volume of droplets generated in a microfluidic T-junction is discussed, and a new scaling law to estimate their volume is proposed. Existing work on a regime transition reported by several researchers focuses on the effect of the capillary number on regime transition, and the results that are presented in this paper advance the current understanding by indicating that the flow rate ratio is another parameter that dictates regime transition. In this paper, the transition between squeezing and dripping regimes is reported at constant capillary numbers, with a transition region identified between squeezing and dripping regimes. Dripping is observed at lower flow rate ratios and squeezing at higher flow rate ratios, with a transition region between the two regimes at flow rate ratios between 1 and 2. This is presented in a flow regime map that is constructed based on the observed mechanism. A scaling model is proposed to characterise droplet volume in terms of flow rate ratio and capillary number. The effect of flow rate ratio on the non-dimensional droplet volume is presented, and lastly, the droplet volume is expressed in terms of a range of parameters, such as the viscosity ratio between the dispersed and the continuous phase, capillary number, and the geometrical characteristics of the channels.

Label-Free Sensing in Microdroplet-Based Microfluidic Systems

Droplet microfluidic systems have evolved as fluidic platforms that use much less sample volume and provide high throughput for biochemical analysis compared to conventional microfluidic devices. The variety of droplet fluidic applications triggered several detection techniques to be applied for analysis of droplets. In this review, we focus on label-free droplet detection techniques that were adapted to various droplet microfluidic platforms. We provide a classification of most commonly used droplet platform technologies. Then we discuss the examples of various label-free droplet detection schemes implemented for these platforms. While providing the research landscape for label-free droplet detection methods, we aim to highlight the strengths and shortcomings of each droplet platform so that a more targeted approach can be taken by researchers when selecting a droplet platform and a detection scheme for any given application.

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 Chip for Liquid Metal Droplet Generation and Sorting

A liquid metal based microfluidic system was proposed and demonstrated for the generation and sorting of liquid metal droplets. This micro system utilized silicon oil as the continuous phase and Ga₆₆In_20.5Sn_13.5 (66.0 wt % Ga, 20.5 wt % In, 13.5 wt % Sn, melting point: 10.6 °C) as the dispersed phase to generate liquid metal droplets on a three-channel F-junction generator. The F-junction is an updated design similar to the classical T-junction, which has a special branch channel added to a T-junction for the supplement of 30 wt % aqueous NaOH solution. To perform active sorting of liquid metal droplets by dielectrophoresis (DEP), the micro system utilized liquid-metal-filled microchannels as noncontact electrodes to induce electrical fields through the droplet channel. The electrode channels were symmetrically located on both sides of the droplet channel in the same horizontal level. According to the results, the micro system can generate uniformly spherical liquid metal droplets, and control the flow direction of the liquid metal droplets. To better understand the control mechanism, a numerical simulation of the electrical field was performed in detail in this work.

Passive and active droplet generation with microfluidics: a review

Precise and effective control of droplet generation is critical for applications of droplet microfluidics ranging from materials synthesis to lab-on-a-chip systems. Methods for droplet generation can be either passive or active, where the former generates droplets without external actuation, and the latter makes use of additional energy input in promoting interfacial instabilities for droplet generation. A unified physical understanding of both passive and active droplet generation is beneficial for effectively developing new techniques meeting various demands arising from applications. Our review of passive approaches focuses on the characteristics and mechanisms of breakup modes of droplet generation occurring in microfluidic cross-flow, co-flow, flow-focusing, and step emulsification configurations. The review of active approaches covers the state-of-the-art techniques employing either external forces from electrical, magnetic and centrifugal fields or methods of modifying intrinsic properties of flows or fluids such as velocity, viscosity, interfacial tension, channel wettability, and fluid density, with a focus on their implementations and actuation mechanisms. Also included in this review is the contrast among different approaches of either passive or active nature.

Lattice Boltzmann simulations of droplet formation in confined channels with thermocapillary flows

Based on mesoscale lattice Boltzmann simulations with the "Shan-Chen" model, we explore the influence of thermocapillarity on the breakup properties of fluid threads in a microfluidic T-junction, where a dispersed phase is injected perpendicularly into a main channel containing a continuous phase, and the latter induces periodic breakup of droplets due to the cross-flowing. Temperature effects are investigated by switching on-off both positive-negative temperature gradients along the main channel direction, thus promoting a different thread dynamics with anticipated-delayed breakup. Numerical simulations are performed at changing the flow rates of both the continuous and dispersed phases, as well as the relative importance of viscous forces, surface tension forces, and thermocapillary stresses. The range of parameters is broad enough to characterize the effects of thermocapillarity on different mechanisms of breakup in the confined T-junction, including the so-called "squeezing" and "dripping" regimes, previously identified in the literature. Some simple scaling arguments are proposed to rationalize the observed behavior, and to provide quantitative guidelines on how to predict the droplet size after breakup.

Effects of viscoelasticity on droplet dynamics and break-up in microfluidic T-Junctions: a lattice Boltzmann study

The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number (Ca), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to Ca ≈ 3×10(-2). A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of Ca which is broad enough to characterize all the three characteristic mechanisms of break-up in the confined T-junction, i.e. squeezing, dripping and jetting regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time τP and the finite extensibility parameter L2, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with Droplet Viscoelasticity (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with Matrix Viscoelasticity (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios Q ≈ O(1) of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.

Programmable active droplet generation enabled by integrated pneumatic micropumps

In this work we have investigated the integrated diaphragm micropump as an active fluidic control approach for the on-demand generation of droplets with precisely defined size, frequency and timing. In contrast to valve-actuated devices that only modulate the flow of the dispersed phase being continuously injected, this integrated micropump allows the combination of fluidic transport and modulation to achieve active control of droplet generation. A distinct characteristic of this method compared to the valve modulated droplet formation processes is that it enables independent control of droplet generation frequency by adjusting the pumping frequency and droplet size by flow conditions. We also demonstrated the generation of complex droplet patterns through programming the pumping configurations and the application to multi-volume digital PCR for precise and quantitative detection of genetic targets. Overall, our results suggest that the pump-based droplet microfluidics provide a robust platform for programmable active droplet generation which could facilitate the development of high-performance chemical and biological assays.

Droplet formation in microfluidic T-junction generators operating in the transitional regime. III. Dynamic surfactant effects

This study extends our previous work on droplet generation in microfluidic T-junction generators to include dynamic interfacial tension effects created by the presence of surfactants. In Paper I [T. Glawdel, C. Elbuken, and C. L. Ren, Phys. Rev. E 85, 016322 (2012)], we presented experimental findings regarding the formation process in the squeezing-to-transition regime, and in Paper II [T. Glawdel, C. Elbuken, and C. L. Ren, Phys. Rev. E 85, 016323 (2012)] we developed a theoretical model that describes the performance of T-junction generators without surfactants. Here we study dynamic interfacial tension effects for two surfactants, one with a small molecular weight that adsorbs quickly, and the other with a large molecular weight that adsorbs slowly. Using the force balance developed in Paper II we extract the dynamic interfacial tension from high speed videos obtained during experiments. We then develop a theoretical model to predict the dynamic interfacial tension in microfluidic T-junction generators as a function of the surfactant properties, flow conditions, and generator design. This model is then incorporated into the overall model for generator performance to effectively predict the size of droplets produced when surfactants are present.

Droplet formation in microfluidic T-junction generators operating in the transitional regime. I. Experimental observations

This is the first part of a two-part study on the generation of droplets at a microfluidic T-junction operating in the transition regime where confinement of the droplet creates a large squeezing pressure that influences droplet formation. In this regime, the operation of the T-junction depends on the geometry of the intersection (height-to-width ratio, inlet width ratio), capillary number, flow ratio, and viscosity ratio of the two phases. Here in paper I we presented our experimental observations through the analysis of high-speed videos of the droplet formation process. Various parameters are tracked during the formation cycle such as the shape of the droplet (penetration depth and neck), interdroplet spacing, production rate, and flow of both phases across several T-junction designs and flow conditions. Generally, the formation process is defined by a two-stage model consisting of an initial filling stage followed by a necking stage. However, video evidence suggests the inclusion of a third stage, which we term the lag stage, at the beginning of the formation process that accounts for the retraction of the interface back into the injection channel after detachment. Based on the observations made in this paper, a model is developed to describe the formation process in paper II, which can be used to understand the design and operation of T-junction generators in the transition regime.