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

Parallelization of Microfluidic Droplet Junctions for Ultraviscous Fluids

The parallelization of multiple microfluidic droplet junctions has been successfully achieved so that the production throughput of the uniform microemulsions/particles has witnessed considerable progress. However, these advancements have been observed only in the case of a low viscous fluid (viscosity of 10^-2 -10^-3 Pa s). This study designs and fabricates a microfluidic device, enabling a uniform micro-emulsification of an ultraviscous fluid (viscosity of 3.5 Pa s) with a throughput of ≈330 000 droplets per hour. Multiple T-junctions of a dispersed oil phase, split from a single inlet, are connected into the single post-crossflow channel of a continuous water phase. In the proposed device, the continuous water phase undergoes a series circuit, wherein the resistances are continuously accumulated. The independent corrugations of the dispersed oil phase channel, under the theoretical guidance, compromise such increased resistances; the ratio of water to oil flow rates at each junction becomes consistent across T-junctions. Owing to the design being based on a fully 2D interconnection, single-step soft lithography is sufficient for developing the full device. This easy-to-craft architecture contrasts with the previous approach, wherein complicated 3D interconnections of the multiple junctions are involved, thereby facilitating the rapid uptake of high throughput droplet microfluidics for experts and newcomers alike.

Breakup Dynamics of Droplets in Symmetric Y-Junction Microchannels

The experimental method is used to study the droplet breaking characteristics of an immiscible liquid–liquid t8wo-phase fluid in symmetric Y-junction microchannels. Silicone oil is used as the dispersed phase and distilled water containing 0.5% SDS is used as the continuous phase. Three breakup behaviors were observed: breakup with permanent obstruction, breakup with gaps, and no breakup. Two stages of the change of the neck width of the sub-droplet during the breakup process were discovered: a rapid breakup stage and a thread breakup stage. The effect of the breakup behavior on the flow pattern was investigated and it was found that the breakup behavior of the droplets made the slug flow area smaller; further, a new flow pattern was observed, being droplet flow. The length of the sub-droplet increases with an increase of the volume flow rate of the dispersed phase and the ratio of the volume flow rate of the dispersed phase to the continuous phase, while decreasing with an increase of the volume flow rate and the capillary number of the continuous phase. Based on the influence of the two-phase flow parameters on the length of the sub-droplet, a correlation formula for the length of the sub-droplet with good predictive performance is proposed.

Magnetic-field- and thermal-radiation-induced entropy generation in a multiphase nonisothermal plane Poiseuille flow

The effect of radiative heat transfer on the entropy generation in a two-phase nonisothermal fluid flow between two infinite horizontal parallel plates under the influence of a constant pressure gradient and transverse noninvasive magnetic field have been explored. Both fluids are considered to be viscous, incompressible, immiscible, Newtonian, and electrically conducting. The governing equations in Cartesian coordinates are solved analytically with appropriate boundary conditions to obtain the velocity and temperature profile inside the channel. Application of a transverse magnetic field is found to reduce the throughput and the temperature distribution of the fluids in a pressure-driven flow. The temperature and fluid flow inside the channel can also be noninvasively altered by tuning the magnetic field intensity, temperature difference between the channel walls and the fluids, and several intrinsic fluid properties. The entropy generation due to the heat transfer, magnetic field, and fluid flow irreversibilities can be controlled by altering the Hartmann number, radiation parameter, Brinkmann number, filling ratio, and ratios of fluid viscosities and thermal and electrical conductivities. The surfaces of the channel wall are found to act as a strong source of entropy generation and heat transfer irreversibility. The rate of heat transfer at the channel walls can also be tweaked by the magnetic field intensity, temperature differences, and fluid properties. The proposed strategies in the present study can be of significance in the design and development of next-generation microscale reactors, micro-heat exchangers, and energy-harvesting devices.

Self-Similar Relaxation of Confined Microfluidic Droplets

We report an experimental study concerning the capillary relaxation of a confined liquid droplet in a microscopic channel with a rectangular cross section. The confinement leads to a droplet that is extended along the direction normal to the cross section. These droplets, found in numerous microfluidic applications, are pinched into a peanutlike shape thanks to a localized, reversible deformation of the channel. Once the channel deformation is released, the droplet relaxes back to a pluglike shape. During this relaxation, the liquid contained in the central pocket drains towards the extremities of the droplet. Modeling such viscocapillary droplet relaxation requires considering the problem as 3D due to confinement. This 3D consideration yields a scaling model incorporating dominant dissipation within the droplet menisci. As such, the self-similar droplet dynamics is fully captured.

Droplet Breakup Dynamics in Bi-Layer Bifurcating Microchannel

Breakup of droplets at bi-layer bifurcating junction in polydimethylsiloxane (PDMS) microchannel has been investigated by experiments and numerical simulation. The pressure drop in bi-layer bifurcating channel was investigated and compared with single-layer bifurcating channel. Daughter droplet size variation generated in bi-layer bifurcating microchannel was analyzed. The correlation was proposed to predict the transition between breakup and non-breakup conditions of droplets in bi-layer bifurcating channel using a phase diagram. In the non-breakup regime, droplets exiting port can be switched via tuning flow resistance by controlling radius of curvature, and or channel height ratio. Compared with single-layer bifurcating junction, 3-D cutting in diagonal direction from bi-layer bifurcating junction induces asymmetric fission to form daughter droplets with distinct sizes while each size has good monodispersity. Lower pressure drop is required in the new microsystem. The understanding of the droplet fission in the novel microstructure will enable more versatile control over the emulsion formation, fission and sorting. The model system can be developed to investigate the encapsulation and release kinetics of emulsion templated particles such as drug encapsulated microcapsules as they flow through complex porous media structures, such as blood capillaries or the porous tissue structures, which feature with bifurcating junctions.

Numerical simulation and scaling of droplet deformation in a hyperbolic flow

Motivated by a recent experiment (C. Ulloa et al., Phys. Rev. E 89, 033004 (2014)), droplet deformation in a flat microfluidic channel having a cross intersection with two inlet channels and two outlet channels, i.e. hyperbolic flow, is numerically investigated. Employing the boundary element method (BEM), we numerically solve the Darcy equation in the two dimensions and investigate droplet motion and droplet deformation as the droplet enters the cross intersection. We numerically find that the maximum deformation of droplet depends on droplet size, capillary number, viscosity ratio and flow rate ratio of the two inlets. Our numerical scaling is in good agreement with the experimental scaling report.

Numerical simulation of high inertial liquid-in-gas droplet in a T-junction microchannel

Two new flow regimes named unstable dripping and unstable jetting are identified in aqueous droplet generation within high inertial air flow inside a T-Junction microchannel.

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.

Rapid and continuous magnetic separation in droplet microfluidic devices

We present a droplet microfluidic method to extract molecules of interest from a droplet in a rapid and continuous fashion. We accomplish this by first marginalizing functionalized super-paramagnetic beads within the droplet using a magnetic field, and then splitting the droplet into one droplet containing the majority of magnetic beads and one droplet containing the minority fraction. We quantitatively analysed the factors which affect the efficiency of marginalization and droplet splitting to optimize the enrichment of magnetic beads. We first characterized the interplay between the droplet velocity and the strength of the magnetic field and its effect on marginalization. We found that marginalization is optimal at the midline of the magnet and that marginalization is a good predictor of bead enrichment through splitting at low to moderate droplet velocities. Finally, we focused our efforts on manipulating the splitting profile to improve the enrichment provided by asymmetric splitting. We designed asymmetric splitting forks that employ capillary effects to preferentially extract the bead-rich regions of the droplets. Our strategy represents a framework to optimize magnetic bead enrichment methods tailored to the requirements of specific droplet-based applications. We anticipate that our separation technology is well suited for applications in single-cell genomics and proteomics. In particular, our method could be used to separate mRNA bound to poly-dT functionalized magnetic microparticles from single cell lysates to prepare single-cell cDNA libraries.

Effect of confinement on the deformation of microfluidic drops

We study the deformation of drops squeezed between the floor and ceiling of a microchannel and subjected to a hyperbolic flow. We observe that the maximum deformation of drops depends on both the drop size and the rate of strain of the external flow and can be described with power laws with exponents 2.59±0.28 and 0.91±0.05, respectively. We develop a theoretical model to describe the deformation of squeezed drops based on the Darcy approximation for shallow geometries and the use of complex potentials. The model describes the steady-state deformation of the drops as a function of a nondimensional parameter Caδ2, where Ca is the capillary number (proportional to the strain rate and the drop size) and δ is a confinement parameter equal to the drop size divided by the channel height. For small deformations, the theoretical model predicts a linear relationship between the deformation of drops and this parameter, in good agreement with the experimental observations.

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.

Automated generation of libraries of nL droplets

We demonstrate an integrated system for rapid and automated generation of multiple, chemically distinct populations of ~10(3)-10(4) sub-nanoliter droplets. Generation of these 'libraries of droplets' proceeds in the following automated steps: i) generation of a sequence of micro-liter droplets of individually predetermined composition, ii) injection of these 'parental' droplets onto a chip, iii) transition from a mm- to a μm-scale of the channels and splitting each of the parental drops with a flow-focusing module into thousands of tightly monodisperse daughter drops and iv) separation of such formed homogeneous populations with plugs of a third immiscible fluid. This method is compatible both with aspiration of microliter portions of liquid from a 96-well plate with a robotic station and with automated microfluidic systems that generate (~μL) droplets of preprogrammed compositions. The system that we present bridges the techniques that provide elasticity of protocols executed on microliter droplets with the techniques for high-throughput screening of small (~pL, ~nL) droplet libraries. The method that we describe can be useful in exploiting the synergy between the ability to rapidly screen distinct chemical environments and to perform high-throughput studies of single cells or molecules and in digital droplet PCR systems.

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.

Droplet based microfluidics

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

Dissolution of carbon dioxide bubbles and microfluidic multiphase flows

We experimentally study the dissolution of carbon dioxide bubbles into common liquids (water, ethanol, and methanol) using microfluidic devices. Elongated bubbles are individually produced using a hydrodynamic focusing section into a compact microchannel. The initial bubble size is determined based on the fluid volumetric flow rates of injection and the channel geometry. By contrast, the bubble dissolution rate is found to depend on the inlet gas pressure and the fluid pair composition. For short periods of time after the fluids initial contact, the bubble length decreases linearly with time. We show that the initial rate of bubble shrinkage is proportional to the ratio of the diffusion coefficient and the Henry's law constant associated with each fluid pair. Our study shows the possibility to rapidly impregnate liquids with CO(2) over short distances using microfluidic technology.