Microfluidic breakups of confined droplets against a linear obstacle: The importance of the viscosity contrast

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.

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.

Lamella Division in a Foam Flowing through a Two-Dimensional Porous Medium: A Model Fragmentation Process

We flow a 2D foam through a model 2D porous medium and study experimentally and numerically how the bubble size distribution evolves along the medium. The dominant mechanism of bubble creation is a fragmentation process occurring when bubbles pinched against obstacles are split in two smaller bubbles. We infer the statistics of these individual and local fragmentation events from the experimental data and propose a fragmentation equation to relate that statistics to the evolution of the global size distribution. The predicted evolution shows very good agreement with direct experimental measurements of the bubble size distribution.

Geometrical instability in the imbibition of a sphere

We study the imbibition of a spherical porous aggregate. When the difference in pressure between the inside and the outside of the aggregate is large enough, the imbibition front becomes unstable. This instability leads to the acceleration of the imbibition process. In more complex geometries with non-constant curvatures, the imbibition becomes locally unstable in the regions with the highest curvatures, leading to spatially heterogeneous front velocities.

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.

Microfluidic cell fragmentation for mechanical phenotyping of cancer cells

Circulating tumor cells (CTCs) shed from the primary tumor undergo significant fragmentation in the microvasculature, and very few escape to instigate metastases. Inspired by this in vivo behavior of CTCs, we report a microfluidic method to phenotype cancer cells based on their ability to arrest and fragment at a micropillar-based bifurcation. We find that in addition to cancer cell size, mechanical properties determine fragmentability. We observe that highly metastatic prostate cancer cells are more resistant to fragmentation than weakly metastatic cells, providing the first indication that metastatic CTCs can escape rupture and potentially initiate secondary tumors. Our method may thus be useful in identifying phenotypes that succumb to or escape mechanical trauma in microcirculation.

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.

Millifluidics as a simple tool to optimize droplet networks: Case study on drop traffic in a bifurcated loop

We report that modular millifluidic networks are simpler, more cost-effective alternatives to traditional microfluidic networks, and they can be rapidly generated and altered to optimize designs. Droplet traffic can also be studied more conveniently and inexpensively at the millimeter scale, as droplets are readily visible to the naked eye. Bifurcated loops, ladder networks, and parking networks were made using only Tygon(®) tubing and plastic T-junction fittings and visualized using an iPod(®) camera. As a case study, droplet traffic experiments through a millifluidic bifurcated loop were conducted, and the periodicity of drop spacing at the outlet was mapped over a wide range of inlet drop spacing. We observed periodic, intermittent, and aperiodic behaviors depending on the inlet drop spacing. The experimentally observed periodic behaviors were in good agreement with numerical simulations based on the simple network model. Our experiments further identified three main sources of intermittency between different periodic and/or aperiodic behaviors: (1) simultaneous entering and exiting events, (2) channel defects, and (3) equal or nearly equal hydrodynamic resistances in both sides of the bifurcated loop. In cases of simultaneous events and/or channel defects, the range of input spacings where intermittent behaviors are observed depends on the degree of inherent variation in input spacing. Finally, using a time scale analysis of syringe pump fluctuations and experiment observation times, we find that in most cases, more consistent results can be generated in experiments conducted at the millimeter scale than those conducted at the micrometer scale. Thus, millifluidic networks offer a simple means to probe collective interactions due to drop traffic and optimize network geometry to engineer passive devices for biological and material analysis.

Deformation and breakup of a liquid droplet past a solid circular cylinder: a lattice Boltzmann study

In this paper, we present a numerical study on the deformation and breakup behavior of liquid droplet past a solid circular cylinder by using an improved interparticle-potential lattice Boltzmann method. The effects of the eccentric ratio β, viscosity ratio λ between the droplet and the surrounding fluid, surface wettability, and Bond number (Bo) on the dynamic behavior of the liquid droplet are considered. The parameter β represents the degree that the solid cylinder deviates from the center line, and Bo is the ratio between the inertial force and capillary force. Numerical results show that there are two typical patterns, i.e., breakup and no breakup, which are greatly influenced by the aforementioned parameters. When β increases to a critical value βc, the droplet can pass the circular cylinder without a breakup, otherwise, the breakup phenomenon occurs. The critical eccentric ratio βc increases significantly with increasing Bo for case with λ>1, while for the case with λ<1, the viscosity effects on the βc is not obvious when Bo is large. For the breakup case, the amount of deposited liquid on the tip of the circular cylinder is almost unaffected by β. In addition, the results also show that the viscosity ratio and wettability affect the deformation and breakup process of the droplet. For case with λ<1, the viscosity ratio plays a minor role in the thickness variations of the deposited liquid, which decreases to a nonzero constant eventually; while for λ>1, the increase of the viscosity ratio significantly accelerates the decrease of the deposited liquid, and finally no fluid deposits on the cylinder. In term of the wettability, there occurs continuous gas phase trapped by the wetting droplet, but this does not happen for nonwetting droplet. Besides, for λ<1, the time required to pass the cylinder (tp) decreases monotonically with decreasing contact angle, while a nonmonotonic decrease appears for λ>1. It is also found that tp decreases monotonically with increasing Bo and is less sensitive to λ at a large Bo.

Hydrodynamic interaction of two deformable drops in confined shear flow

We investigate hydrodynamic interaction between two neutrally buoyant circular drops in a confined shear flow based on a computational fluid dynamics simulation using the volume-of-fluid method. The rheological behaviors of interactive drops and the flow regimes are explored with a focus on elucidation of underlying physical mechanisms. We find that two types of drop behaviors during interaction occur, including passing-over motion and reversing motion, which are governed by the competition between the drag of passing flow and the entrainment of reversing flow in matrix fluid. With the increasing confinement, the drop behavior transits from the passing-over motion to reversing motion, because the entrainment of the reversing-flow matrix fluid turns to play the dominant role. The drag of the ambient passing flow is increased by enlarging the initial lateral separation due to the departure of the drop from the reversing flow in matrix fluid, resulting in the emergence of passing-over motion. In particular, a corresponding phase diagram is plotted to quantitatively illustrate the dependence of drop morphologies during interaction on confinement and initial lateral separation.

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.

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.

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.