Passive breakups of isolated drops and one-dimensional assemblies of drops in microfluidic geometries: experiments and models

Interfacial Dynamics in Dual Channels: Inspired by Cuttlebone

The cuttlebone, a chambered gas-filled structure found in cuttlefish, serves a crucial role in buoyancy control for the animal. This study investigates the motion of liquid-gas interfaces within cuttlebone-inspired artificial channels. The cuttlebone's unique microstructure, characterized by chambers divided by vertical pillars, exhibits interesting fluid dynamics at small scales while pumping water in and out. Various channels were fabricated with distinct geometries, mimicking cuttlebone features, and subjected to different pressure drops. The behavior of the liquid-gas interface was explored, revealing that channels with pronounced waviness facilitated more non-uniform air-water interfaces. Here, Lyapunov exponents were employed to characterize interface separation, and they indicated more differential motions with increased pressure drops. Channels with greater waviness and amplitude exhibited higher Lyapunov exponents, while straighter channels exhibited slower separation. This is potentially aligned with cuttlefish's natural adaptation to efficient water transport near the membrane, where more straight channels are observed in real cuttlebone.

Droplet-based microfluidics in biomedical applications

Droplet-based microfluidic systems have been employed to manipulate discrete fluid volumes with immiscible phases. Creating the fluid droplets at microscale has led to a paradigm shift in mixing, sorting, encapsulation, sensing, and designing high throughput devices for biomedical applications. Droplet microfluidics has opened many opportunities in microparticle synthesis, molecular detection, diagnostics, drug delivery, and cell biology. In the present review, we first introduce standard methods for droplet generation (i.e., passive and active methods) and discuss the latest examples of emulsification and particle synthesis approaches enabled by microfluidic platforms. Then, the applications of droplet-based microfluidics in different biomedical applications are detailed. Finally, a general overview of the latest trends along with the perspectives and future potentials in the field are provided.

Dynamics of partially obstructed breakup of bubbles in microfluidic Y-junctions

For revealing the dynamics of partially obstructed breakup of bubbles in microfluidic Y-junctions, the combination of dimensionless power-law and geometric model was applied to study the effects of capillary number, bubble length, and channel angle on the bubble rupture process. In the squeezing process, the gas-liquid interface curve follows the parabolic model. For the evolution of the bubble neck during breakup, the increase of the bubble length, the channel angle, and the capillary number leads to the decrease of the focus distance α. The chord m increases with the increase of the capillary number and the decrease of the bubble length, and it would reach the maximum value when the channel angle is 90°. In the fast pinch-off stage during bubble breakup, the bubble's neck curve no longer conforms to the parabolic model so the focus and chord no longer exist. For the evolution of the bubble head during breakup, the value of γ approaches 1 with the increase of the capillary number and the bubble length, and with the close of the channel angle to 90°. It is found that the quadrilateral model can be applied for the partially obstructed rupture of bubbles in the symmetrical microfluidic Y-junction.

Direct Observation of Splitting in Oil-In-Water-In-Oil Emulsion Droplets via a Microchannel Mimicking Membrane Pores

Direct observation of double emulsion droplet permeation through a microchannel that mimicked 100 μm membrane pores with a porosity of 66.7% provided insights regarding splitting mechanisms in porous membranes. The microchannel was fabricated by standard soft lithography, and the oil-in-water-in-oil double emulsion droplets were prepared with a glass capillary device. By changing the flow rate from 0.5 to 5.0 × 10^-2 m s^-1, three characteristic behaviors were observed: (a) passage into one channel without splitting; (b) division into two smaller components; and (c) stripping of the middle water phase of the double emulsion droplets into a smaller double emulsion droplet and a smaller water-in-oil single emulsion droplet. The mechanisms are discussed with respect to the balance of viscous forces and interfacial tension, the contact point with the tip of the channel, and the relative position of the innermost droplet within the middle droplet.

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.

Particle-bubble interaction inside a Hele-Shaw cell

Hydrodynamic interactions between air bubbles and particles have wide applications in multiphase separation and reaction processes. In the present work, we explore the fundamental mechanism of such complex processes by studying the collision of a single bubble with a fixed solid particle inside a Hele-Shaw cell. Physical experiments show that an air bubble either splits or slides around the particle depending on the initial transverse distance between the bubble and particle centroids. An air bubble splits into two daughter bubbles at small transverse distances, and slides around the particle at large distances. In order to predict the critical transverse distance that separates these two behaviors, we also develop a theoretical model by estimating the rate of the bubble volume transfer from one side of the particle to the other based on Darcy's law, which is in good agreement with experiments.

Magnetofluidic control of the breakup of ferrofluid droplets in a microfluidic Y-junction

Breakup of the ferrofluid droplets at the Y-junction divergence under various flow rate ratios.

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.

Gas-liquid-liquid three-phase flow pattern and pressure drop in a microfluidic chip: similarities with gas-liquid/liquid-liquid flows

We report a three-phase slug flow and a parallel-slug flow as two major flow patterns found under the nitrogen-decane-water flow through a glass microfluidic chip which features a long microchannel with a hydraulic diameter of 98 μm connected to a cross-flow mixer. The three-phase slug flow pattern is characterized by a flow of decane droplets containing single elongated nitrogen bubbles, which are separated by water slugs. This flow pattern was observed at a superficial velocity of decane (in the range of about 0.6 to 10 mm s(-1)) typically lower than that of water for a given superficial gas velocity in the range of 30 to 91 mm s(-1). The parallel-slug flow pattern is characterized by a continuous water flow in one part of the channel cross section and a parallel flow of decane with dispersed nitrogen bubbles in the adjacent part of the channel cross section, which was observed at a superficial velocity of decane (in the range of about 2.5 to 40 mm s(-1)) typically higher than that of water for each given superficial gas velocity. The three-phase slug flow can be seen as a superimposition of both decane-water and nitrogen-decane slug flows observed in the chip when the flow of the third phase (viz. nitrogen or water, respectively) was set at zero. The parallel-slug flow can be seen as a superimposition of the decane-water parallel flow and the nitrogen-decane slug flow observed in the chip under the corresponding two-phase flow conditions. In case of small capillary numbers (Ca ≪ 0.1) and Weber numbers (We ≪ 1), the developed two-phase pressure drop model under a slug flow has been extended to obtain a three-phase slug flow model in which the 'nitrogen-in-decane' droplet is assumed as a pseudo-homogeneous droplet with an effective viscosity. The parallel flow and slug flow pressure drop models have been combined to obtain a parallel-slug flow model. The obtained models describe the experimental pressure drop with standard deviations of 8% and 12% for the three-phase slug flow and parallel-slug flow, respectively. An example is given to illustrate the model uses in designing bifurcated microchannels that split the three-phase slug flow for high-throughput processing.

Electrostatic potential wells for on-demand drop manipulation in microchannels

Precise control and manipulation of individual drops are crucial in many lab-on-a-chip applications. We present a novel hybrid concept for channel-based discrete microfluidics with integrated electrowetting functionality by incorporating co-planar electrodes (separated by a narrow gap) in one of the microchannel walls. By combining the high throughput of channel-based microfluidics with the individual drop control achieved using electrical actuation, we acquire the strengths of both worlds. The tunable strength of the electrostatic forces enables a wide range of drop manipulations, such as on-demand trapping and release, guiding, and sorting of drops in the microchannel. In each of these scenarios, the retaining electrostatic force competes with the hydrodynamic drag force. The conditions for trapping can be predicted using a simple model that balances these forces.

Path selection rules for droplet trains in single-lane microfluidic networks

We investigate the transport of periodic trains of droplets through microfluidic networks having one inlet, one outlet, and nodes consisting of T junctions. Variations of the dilution of the trains, i.e., the distance between drops, reveal the existence of various hydrodynamic regimes characterized by the number of preferential paths taken by the drops. As the dilution increases, this number continuously decreases until only one path remains explored. Building on a continuous approach used to treat droplet traffic through a single asymmetric loop, we determine selection rules for the paths taken by the drops and we predict the variations of the fraction of droplets taking these paths with the parameters at play including the dilution. Our results show that as dilution decreases, the paths are selected according to the ascending order of their hydrodynamic resistance in the absence of droplets. The dynamics of these systems controlled by time-delayed feedback is complex: We observe a succession of periodic regimes separated by a wealth of bifurcations as the dilution is varied. In contrast to droplet traffic in single asymmetric loops, the dynamical behavior in networks of loops is sensitive to initial conditions because of extra degrees of freedom.