This work has explored interface evolution and pinch-off mechanism of the droplet formation in two-phase flow through cross-flow microfluidic device. The two-dimensional mathematical model equations have been solved using the finite element method under the squeezing regime ($Ca_c < 10^{-2}$) for wide range of flow rates ($Qr = 0.1 - 10$) and fixed contact angle ($θ=135^o$). The droplet formation process has been classified into various instantaneous stages as initial, filling, squeezing, pinch-off and stable droplet through microscopic visualization of interface evolution in phase profiles. The dynamics of interface, and point pressure in both phases is further gained and discussed. Maximum pressure in the continuous phase varied linearly with Qr. The droplet pinch-off mechanism has been thoroughly elucidated by determining the local radius of the curvature ($R_{c,min}$) and neck width (2r) during the squeezing and pinch-off stages. At the pinch-off point, both $R_{c,min}$ and 2r are non-linearly related to Qr. Further, the topological dynamics of interface has been explored by analyzing the Laplace pressure ($p_{\text{L}}$), acting on the interface curvature, evaluated using (a) pressure sensors in both phases, (b) local radius of curvature, and (c) minimum radius of curvature. The insights obtained from the present work can reliably be used in designing the model and prototypes of microfluidic devices for generating monodispersed droplets in emulsions, and the droplet breakup mechanism would help accurate prediction of the pinch-off moment. The proposed knowledge provides detailed insights of the interface evolution and droplet pinch-off to a precision of 10 $μ$s and resolution of 10 $μ$m, equivalent to experimental flow visualization with a high-speed ($10^{5}$ fps) and high-resolution (10 $μ$m pixel size) camera.
Controlling fluid droplets efficiently in the microscale is of great interest both from a basic science and a technology perspective. We have designed and developed a general-purpose, highly scalable microfluidic control strategy through a single global clock signal that enables synchronous control of arbitrary number of droplets in a planar geometry. A rotating precessive magnetic field provides a global clock signal, enabling simultaneous control of droplet position, velocity and trajectories. Here, in this fluid dynamics video, we explain the main physics of this new microfluidic concept. V…
Various microfluidic systems, such as chemical and biological lab-on-a-chip devices, involve motion of multiple droplets within an immersing fluid in shallow micro-channels. Modeling the dynamics of such systems requires calculation of the forces of interaction between the moving droplets. These forces are commonly approximated by superposition of dipoles solutions, which requires an assumption of sufficiently large distance between the droplets. In this work we obtain exact solutions (in the Hele-Shaw limit) for two moving droplets, and a droplet within a droplet, located within a moving imme…
Pinch-off and satellite droplets formation during breakup of near-inviscid liquid bridge sandwiched between two given equal and coaxial circular plates have been investigated. The breakup always results in the formation of a spindle shape which is the precursor of the satellite droplet at the moment of pinch-off. Interestingly, the slenderness of this spindle is always bigger than 2π and always results in the formation of only one satellite droplet regardless of the surface tension and the slenderness of the liquid bridge. We predict the cone angle of this spindle formed during the pinch-off o…
In this work we show that in a microfluidic network and in low Reynolds numbers a system can be irreversible because of hysteresis effects.The network, which is employed in our simulations, is taken from recent experiments. The network consists of one loop connected to input and output pipes. A train of droplets enter the system at a uniform rate, but they may leave it in different patterns, e.g. periodic or even chaotic. The out put pattern depends on the time interval among the incoming droplets as well as the network geometry and for some parameters the system is not reversible.
On-demand microfluidic droplet pinching and splitting under local confinement gradients
Gulliver CNRS UMR 7083, PSL Research University, ESPCI Paris（高勒弗实验室，PSL研究大学，巴黎高等物理化工学院）；Department of Mathematics, University of Pennsylvania（宾夕法尼亚大学数学系）；Institut Curie, CNRS UMR168, Laboratoire Physico Chimie Curie, Institut Pierre-Gilles de Gennes, PSL Research University（居里研究所，法国国家科学研究中心联合研究实验室168，居里物理化学实验室，皮埃尔-吉勒·德热纳研究所，PSL研究大学）；Université Rennes, CNRS, IPR (Institut de Physique de Rennes) - UMR 6251（雷恩大学，法国国家科学研究中心，雷恩物理研究所）
We study microfluidic self digitization in Hele-Shaw cells using pancake droplets anchored to surface tension traps. We show that above a critical flow rate, large anchored droplets break up to form two daughter droplets, one of which remains in the anchor. Below the critical flow velocity for breakup the shape of the anchored drop is given by an elastica equation that depends on the capillary number of the outer fluid. As the velocity crosses the critical value, the equation stops admitting a solution that satisfies the boundary conditions; the drop breaks up in spite of the neck still having…
Here, we trap and control the position of droplets to study their dynamics using hydrodynamic forces alone without an external field. The hydrodynamic trap is adapted from a previously implemented Stokes trap by incorporating a drop-on-demand system to generate droplets at a T-junction geometry on the same microfluidic chip. We then study confined droplet dynamics in response to perturbation by applying a millisecond-pressure pulse to deform trapped droplets. Droplet shape relaxation after cessation of the pressure pulse follows an exponential decay. The characteristic droplet shape relaxation…
We used volume-of-fluid (VOF) method to perform three-dimensional numerical simulations of droplet formation of Newtonian fluids in microfluidic T-junction devices. To evaluate the performance of the VOF method we examined the regimes of drop formation and determined droplet size as a function of system parameters. Comparison of the simulation results with four sets of experimental data from the literature showed good agreement, validating the VOF method. Motivated by the lack of adequate studies investigating the influence of viscosity ratio (λ) on the generated droplet size, we mapped the de…
The present study looks into the pinch-off dynamics of a compound droplet, which is suspended in another fluid in a parallel plate microchannel. The droplet is subjected to a transverse electric field in the presence of an imposed pressure driven flow. For the present study, a leaky dielectric model have been taken into consideration. When a concentric compound droplet migrates in a pressure driven flow, the inner droplet shifts from the concentric position and forms a eccentric configuration that finally leads to the rupture of the outer shell. The present investigation have uncovered that th…
High speed microfluidic jets can be generated by a thermocavitation process: from the evaporation of the liquid inside a microfluidic channel, a rapidly expanding bubble is formed and generates a jet through a flow focusing effect. Here, we study the impact and traversing of such jets on a pendant liquid droplet. Upon impact, an expanding cavity is created, and, above a critical impact velocity, the jet traverses the entire droplet. We predict the critical traversing velocity (i) from a simple energy balance and (ii) by comparing the Young-Laplace and dynamic pressures in the cavity that is cr…
Solvent shifting is a process in which a non-solvent is added to a solvent/solute mixture and extracts the solvent. The solvent and the non-solvent are miscible. Because of solution supersaturation a portion of the solute transforms to droplets. In this paper, based on this process, we present an investigation on droplet formation and their radial motion in a microfluidic device in which a jet is injected in a co-flowing liquid stream. Thanks to the laminar flow, the microfluidic setup enables studying diffusion mass transfer in radial direction and obtaining well-defined concentration distrib…
The influence of drop formation due to micro rib-like structures, viz., the Junction Gutters (JGs) within a standard microfluidic T-junction, is numerically investigated. Hydrodynamic conditions that lead to various flow regimes are identified characterized by the Capillary number (Ca) and velocity ratios of the dispersed and continuous phases (q) within a standard T-junction. Subsequently, under such conditions, a range of gutter configurations is introduced in the standard channel. The results predict that the introduction of JGs can favourably alter the formation frequency and morphology of…
The migration characteristics of a suspended deformable droplet in a parallel plate microchannel is studied, both analytically and numerically, under the combined influence of a constant temperature gradient in the transverse direction and an imposed pressure driven flow. Any predefined transverse position in the micro channel can be attained by the droplet depending on the applied temperature gradient in the cross-stream direction or how small the droplet is with respect to the channel width. For the analytical solution, an asymptotic approach is used, where we neglect any effect of inertia o…
The hydrodynamics of droplets is significant in wide-ranging applications involving immiscible fluids and emulsions in food and pharmaceutical. The control and manipulation of droplets are primarily a function of flow governing and geometrical parameters. The finite element and level set approaches are used in this work to explore the influences of capillary number (Ca) and flow rate ratio (Qr) of dispersed and continuous phases on hydrodynamics of droplet generation in two-phase flow through T-junction cross-flow microfluidic device. A mathematical model based on a mass continuity, Navier-Sto…
The so-called "Kelvin water dropper" is a simple experiment demonstrating the spontaneous appearance of induced free charge in droplets emitted through a tube. As Lord Kelvin explained, water droplets spontaneously acquire a net charge during detachment from a faucet due to the presence of electrical fields in their surrounding created by any metallic object. In his experiment, two streams of droplets are allowed to drip from separated nozzles into separated buckets, which are at the same time interconnected through the dripping needles. In this paper we build a microfluidic water dropper and …
Droplets are natural candidates for use as microfluidic reactors, if active control of their formation and transport can be achieved. We show here that localized heating from a laser can block the motion of a water-oil interface, acting as a microfluidic valve for two-phase flows. A theoretical model is developed to explain the forces acting on a drop due to thermocapillary flow, predicting a scaling law which favors miniaturization. Finally, we show how the laser forcing can be applied to sorting drops, thus demonstrating how it may be integrated in complex droplet microfluidic systems.
Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We propose that the periodic behavior is an outcome of a dispersed phase conservation principle. This conservation principle translates into a droplet spacing conservation equation. Additionally, we define a simple technique to identify periodicity in experimental systems with input scatter. Aperiodic behavior is observed in the transition regions between different periodic behaviors. We propose that the cause for aperiodicity is the synchronization of timing between th…
This study has numerically investigated the effect of surface wettability on two-phase immiscible flow and dynamics of droplet pinch-off in a T-junction microchannel using finite element method. A conservative level set method (CLSM) has been adopted to capture the interface topology in squeezing regime ($Ca_c <10^{-2}$) for wide flow rate ratio ($1/10 \leq Q_r \leq 10$) and contact angle ($120^{\circ} \leq θ\leq 180^{\circ}$). Based on the instantaneous phase profiles, droplet formation stages are classified as initial, filling, squeezing, pinch-off and stable droplet. Wettability effects are…
In the present study, the role of surfactants on the cross-stream migration of droplets is investigated both experimentally and theoretically. For experimental analysis, sunflower oil is used as the carrier phase and DI water as the dispersed phase which is intermixed with Triton X-100 that acts as the surfactant. A T-junction is used in the microchannel for the purpose of droplet generation. Presence of an imposed pressure driven flow induces droplet deformation and disturbs the equilibrium that results in subsequent surfactant-redistribution along the interface. This further induces a gradie…
Andrew J. deMello is professor of Biochemical Engineering in the Department of Chemistry and Applied Biosciences at ETH Zürich. In this contribution he describes the efforts that his lab has undertaken in developing novel microfluidic systems for molecular and nanomaterial synthesis, droplet-based systems for ultra-high-throughput experimentation and novel optical techniques for sensitive and rapid analysis in small volume environments.
Ultrasound-controlled stream splitting in a microfluidic coflow
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Indian Institute of Technology Guwahati（印度古瓦哈提理工学院）；Indian Institute of Technology Gandhinagar（印度甘地纳加尔理工学院）
We present a computational investigation of the mechanism governing size-based particle separation in microfluidic pinched flow fractionation. We study the behavior of particles moving through a pinching gap (i.e., a constriction in the aperture of a channel) in the Stokes regime as a function of particle size. The constriction aperture is created by a plane wall and spherical obstacle, and emulates the pinching segment in pinched flow fractionation devices. The simulation results show that the distance of closest approach between the particle and obstacle surfaces (along a trajectory) decreas…
This fluid dynamics video showcases how optically induced electrowetting can be used to manipulate liquid droplets in open space and particulate phases inside the droplet. A photoconductive layer is added to a conventional electrowetting-on-dielectric (EWOD) structure to generate light enabled virtual electrodes, hence resulting in an eletrowetting action. Coplanar electrodes deployed alternately on a substrate enable open droplet manipulations differentiating from a sandwiched configuration. An integration with an optoelectric method shows dynamic and rapid particle handling by strong micro f…
Motion in a one-dimensional (1D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row, and due to their hydrodynamic interactions spacing between these droplets oscillates with a wave-like motion that is longitudinal or transverse. The simulation yields wave spectra that agree well with experiment. The wave-like motion has an instability which is confirmed to arise from nonlinearities in the interaction potential. The instability's growth is spatially localized. By selecting an appropriate correlation function, the interaction between the longit…
Coalescence of micrometer-scale droplets is impacted by several parameters, including droplet size, viscosities of the two phases, droplet velocity and angle of approach, as well as interfacial tension and surfactant coverage. The dynamics and thinning of films between coalescing droplets can be particularly complex in the presence of surfactants, due to the generation of Marangoni stresses and reduced film mobility. In this work, a microfluidic hydrodynamic Stokes trap is used to gently steer and trap surfactant-laden micrometer-sized droplets at the center of a cross-slot. Incoming droplets …
The present study deals with the dynamics of a double emulsion confined in a microchannel under the presence of a uniform electric field. Towards investigating the non-trivial electrohydrodynamics of a compound droplet, confined in between two parallel plate electrodes, a phase field approach has been adopted. Under the assumption of negligible fluid inertia and small shape deformation, an asymptotic model is also developed to predict the transient as well as the steady state droplet dynamics in the limiting case of an unbounded suspending medium. The phases involved are either assumed to be p…
Based on mesoscale lattice Boltzmann (LB) numerical simulations, we investigate the effects of viscoelasticity on the break-up of liquid threads in microfluidic cross-junctions, where droplets are formed by focusing a liquid thread of a dispersed (d) phase into another co-flowing continuous (c) immiscible phase. Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) to droplet formation downstream of the cross-junction (DC) (Liu $\&$ Zhang, ${\it Phys. ~Fluids.}$ ${\bf 23}$, 082101 (2011)). We …
Bacteria biodegradation of immiscible oil requires cell-droplet encounters, surface attachment, and hydrocarbon metabolism. Chemical dispersants are applied to oil spills to reduce the mean dispersed droplet size, thereby increasing the available surface area for attachment, in attempts to facilitate bacterial biodegradation. However, their effectiveness remains contentious as studies have shown that dispersants can inhibit, enhance, or have no effect on biodegradation. Therefore, questions remain on whether dispersants affect surface attachment or cell viability. Here, using microfluidics and…
The impact of droplets on a liquid pool is ubiquitous in nature and important in many industrial applications. A droplet impacting on a liquid pool can result in the pinch-off of a regular bubble or entrap a large bubble under certain impact conditions. In this study, the cavity deformation and the bubble entrapment during the impact of droplets on a liquid pool are studied by combined experimental measurements and numerical simulations. The time evolution of the free surface profile obtained in the numerical simulation is in good agreement with the experimental results. The cavity created by …
The complexity of droplet microfluidics grows by implementing parallel processes and multiple functionalities on a single device. This poses a challenge to the engineer designing the microfluidic networks. In today's design processes, the engineer relies on calculations, assumptions, simplifications, as well as his/her experiences and intuitions. In order to validate the obtained specification of the microfluidic network, usually a prototype is fabricated and physical experiments are conducted thus far. In case the design does not implement the desired functionality, this prototyping iteration…
Microfluidic techniques have been extensively developed to realize micro-total analysis systems in a small chip. For microanalysis, electro-magnetic forces have generally been utilized for the trapping of objects, but hydrodynamics has been little explored despite its relevance to pattern formation. Here, we report that water-in-oil (W/O) droplets can be transported in the grid of an array of other large W/O droplets. As each droplet approaches an interspace of the large droplet array, while exhibiting persistent back-and-forth motion, it is conveyed at a velocity equal to the droplet array. W…
The simplest microfluidic network (a loop) comprises two parallel channels with a common inlet and a common outlet. Recent studies, that assumed constant cross-section of the channels along their length, have shown that the sequence of droplets entering left (L) or right (R) arm of the loop can present either a uniform distribution of choices (e.g. RLRLRL...) or long sequences of repeated choices (RRR...LLL), with all the intermediate permutations being dynamically equivalent and virtually equally probable to be observed. We use experiments and computer simulations to show that even small vari…
We report on experiments that consist in deforming a collection of monodisperse droplets produced by a microfluidic chip through a flow-focusing device. We show that a proper numerical modelling of the flow is necessary to access the stress applied by the latter on the droplet along its trajectory through the chip. This crucial step enables the full integration of the differential equation governing the dynamical deformation, and consequently the robust measurement of the interfacial tension by fitting the experiments with the calculated deformation. Our study thus demonstrates the feasibility…
When a droplet is generated, the ligament connecting the drop to the nozzle thins down and eventually pinches off. Adding solid particles to the liquid phase leads to a more complex dynamic, notably by increasing the shear viscosity. Moreover, it introduces an additional length scale to the system, the diameter of the particles, which eventually becomes comparable to the diameter of the ligament. In this paper, we experimentally investigate the thinning and pinch-off of drops of suspensions with two different sizes of particles. We characterize the thinning for different particle size ratios a…
We present a droplet-based surface acoustic wave (SAW) system designed to viably detach biological cells from a surface and sort cell types based on differences in adhesion strength (adhesion contrast), without the need to label cells with molecular markers. The system uses modulated SAW to generate pulsatile flows in the droplets and efficiently detach the cells, thereby minimizing SAW excitation power and exposure time. As a proof-of-principle, the system is shown to efficiently sort HEK 293 from A7r5 cells based on adhesion contrast. Results are obtained in minutes with sorting purity and e…
We present a regularized version of the color gradient lattice Boltzmann (LB) scheme for the simulation of droplet formation in microfluidic devices of experimental relevance. The regularized version is shown to provide computationally efficient access to Capillary number regimes relevant to droplet generation via microfluidic devices, such as flow-focusers and the more recent microfluidic step emulsifier devices.
The multiphase flow of droplets is widespread, both at the industrial and the microscale, for both biological and non-biological applications alike. But the ensemble interactions of such systems are inherently nonlinear and complex, compounded by interfacial effects, making it a difficult many-body problem for theory. In comparison, the self-assembly dynamics of solid particles in flow have long been described and successfully exploited in the field of inertial microfluidics, where particle crystals can be realized from inertial forces and hydrodynamic interactions. Here, we report novel self-…
We propose a simple model to analyze the traffic of droplets in microfluidic ``dual networks''. Such functional networks which consist of two types of channels, namely those accessible or forbidden to droplets, often display a complex behavior characteristic of dynamical systems. By focusing on three recently proposed configurations, we offer an explanation for their remarkable behavior. Additionally, the model allows us to predict the behavior in different parameter regimes. A verification will clarify fundamental issues, such as the network symmetry, the role of the driving conditions, and o…
We present a mesoscale representation of near-contact interactions between colliding droplets which permits to reach up to the scale of full microfluidic devices, where such droplets are produced. The method is demonstrated for the case of colliding droplets and the formation of soft flowing crystals in flow-focussing microfluidic devices. This model may open up the possibility of multiscale simulation of microfluidic devices for the production of new droplet/bubble-based mesoscale porous materials.
A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it does not describe breakup. However, the observed steepening of the profile corresponds to experiments and simulations with fluids at low viscosity. The singularity has similarity form, which we compute analytically. The result agrees well with numerical simulations of the model equations.
We investigate imbibition of a monodisperse emulsion into a low-aspect ratio microfluidic channel with the height h comparable to the droplet diameter d. For confinement ratio d/h = 1.2, the tightly confined disk-like droplets in the channel move more slowly compared to the average suspension velocity. Behind the meniscus that drives the imbibition, there is a droplet-free region, separated from the suspension region by a sharp concentration front. The suspension exhibits strong droplet density and velocity fluctuations, but on average, the suspension domain remains uniform. For weaker confine…
Microfluidic chips provide unparalleled control over droplets and jets, which have advanced all natural sciences. However, microfluidic applications could be vastly expanded by increasing the per-channel throughput and directly exploiting the output of chips for rapid additive manufacturing. We unlock these features with in-air microfluidics, a new chip-free platform to manipulate microscale liquid streams in the air. By controlling the composition and in-air impact of liquid microjets by surface tension-driven encapsulation, we fabricate monodisperse emulsions, particles, and fibers with diam…
Droplets confined in a microfluidic channel often exhibit intriguing shapes, primarily attributable to complex hydrodynamic interactions over small scales. We show that effect of varied substrate wettability conditions may further complicate these interactions remarkably, and often non-trivially. Our studies reveal that the combined influence of substrate wettability and fluidic confinement eventually culminates towards influencing the droplet transients, distortion of the local shear flow field, as well as drop stabilization against breakup or detachment, allowing one to develop different reg…
