Bubbling in unbounded coflowing liquids

Nip the bubble in the bud: a guide to avoid gas nucleation in microfluidics

Gas bubbles are almost a routine occurrence encountered by researchers working in the field of microfluidics. The spontaneous and unexpected nature of gas bubbles represents a major challenge for experimentalists and a stumbling block for the translation of microfluidic concepts to commercial products. This is a startling example of successful scientific results in the field overshadowing the practical hurdles of day-to-day usage. We however believe such hurdles can be overcome with a sound understanding of the underlying conditions that lead to bubble formation. In this tutorial, we focus on the two main conditions that result in bubble nucleation: surface nuclei and gas supersaturation in liquids. Key theoretical concepts such as Henry's law, Laplace pressure, the role of surface properties, nanobubbles and surfactants are presented along with a view of practical implementations that serve as preventive and curative measures. These considerations include not only microfluidic chip design and bubble traps but also often-overlooked conditions that regulate bubble formation, such as gas saturation under pressure or temperature gradients. Scenarios involving electrolysis, laser and acoustic cavitation or T-junction/co-flow geometries are also explored to provide the reader with a broader understanding on the topic. Interestingly, despite their often-disruptive nature, gas bubbles have also been cleverly utilized for certain practical applications, which we briefly review. We hope this tutorial will provide a reference guide in helping to deal with a familiar foe, the "bubble".

The science of foaming

The generation of liquid foams is at the heart of numerous natural, technical or scientific processes. Even though the subject of foam generation has a long-standing history, many recent progresses have been made in an attempt to elucidate the fundamental processes at play. We review the subject by providing an overview of the relevant key mechanisms of bubble generation within a coherent hydrodynamic context; and we discuss different foaming techniques which exploit these mechanisms.

Production of microbubbles from axisymmetric flow focusing in the jetting regime for moderate Reynolds numbers

We analyze both experimentally and numerically the formation of microbubbles in the jetting regime reached when a moderately viscous liquid stream focuses a gaseous meniscus inside a converging micronozzle. If the total (stagnation) pressure of the injected gas current is fixed upstream, then there are certain conditions on which a quasisteady gas meniscus forms. The meniscus tip is sharpened by the liquid stream down to the gas molecular scale. On the other side, monodisperse collections of microbubbles can be steadily produced in the jetting regime if the feeding capillary is appropriately located inside the nozzle. In this case, the microbubble size depends on the feeding capillary position. The numerical simulations for an imposed gas flow rate show that a recirculation cell appears in the gaseous meniscus for low enough values of that parameter. The experiments allow one to conclude that the bubble pinch-off comprises two phases: (i) a stretching motion of the precursor jet where the neck radius versus the time before the pinch essentially follows a potential law, and (ii) a final stage where a very thin and slender gaseous thread forms and eventually breaks apart into a number of micron-sized bubbles. Because of the difference between the free surface and core velocities, the gaseous jet breakage differs substantially from that of liquid capillary jets and gives rise to bubbles with diameters much larger than those expected from the Rayleigh-type capillary instability. The dependency of the bubble diameter upon the flow-rate ratio agrees with the scaling law derived by A. M. Gañán-Calvo [Phys. Rev. E 69, 027301 (2004)], although a slight influence of the Reynolds number can be observed in our experiments.

Building functional materials for health care and pharmacy from microfluidic principles and Flow Focusing

In this review, we aim at establishing a relationship between the fundamentals of the microfluidics technologies used in the Pharmacy field, and the achievements accomplished by those technologies. We describe the main methods for manufacturing micrometer drops, bubbles, and capsules, as well as the corresponding underlying physical mechanisms. In this regard, the review is intended to show non-specialist readers the dynamical processes which determine the success of microfluidics techniques. Flow focusing (FF) is a droplet-based method widely used to produce different types of fluid entities on a continuous basis by applying an extensional co-flow. We take this technique as an example to illustrate how microfluidics technologies for drug delivery are progressing from a deep understanding of the physics of fluids involved. Specifically, we describe the limitations of FF, and review novel methods which enhance its stability and robustness. In the last part of this paper, we review some of the accomplishments of microfluidics when it comes to drug manufacturing and delivery. Special attention is paid to the production of the microencapsulated form because this fluidic structure gathers the main functionalities sought for in Pharmacy. We also show how FF has been adapted to satisfy an ample variety of pharmaceutical requirements to date.

Theoretical investigation of a technique to produce microbubbles by a microfluidic T junction

A microfluidic technique is proposed to produce microbubbles. A gaseous stream is injected through a T junction into a channel transporting a liquid current. The gas adheres to a hydrophobic strip printed on the channel surface. When the gas and liquid flow rates are set appropriately, a gaseous rivulet flows over that strip. The rivulet breaks up downstream due to a capillary pearling instability, which leads to a monodisperse collection of microbubbles that can be much smaller than the channel size. The physics of the process is theoretically investigated, using both full numerical simulation of the Navier-Stokes equations and a linear stability analysis of an infinite gaseous rivulet driven by a coflowing liquid stream. This stability analysis allows one to determine a necessary condition to get this effect in a T junction device. It also provides reasonably good predictions for the size of the produced microbubbles as obtained from numerical experiments.

Mastering a double emulsion in a simple co-flow microfluidic to generate complex polymersomes

We show that the production and the geometrical shape of complex polymersomes can be predicted by varying the flow rates of a simple microdevice using an empirical law which predicts the droplet size. This device is constituted of fused silica capillaries associated with adjusted tubing sleeves and T-junctions. Studying the effect of several experimental parameters, double emulsions containing a controlled number of droplets were fabricated. First, this study examines the stability of a jet in a simple confined microfluidic system, probing the conditions required for droplets production. Then, multicompartmental polymersomes were formed, controlling flow velocities. In this work, poly(dimethylsiloxane)-graft-poly(ethylene oxide) (PDMS-g-PEO) and poly(butadiene)-block-poly(ethyleneoxide) (PBut-b-PEO) amphiphilic copolymers were used and dissolved in chloroform/cyclohexane mixture. The ratio of these two solvents was adjusted in order to stabilize the double emulsion formation. The aqueous suspension contained poly(vinyl alcohol) (PVA), limiting the coalescence of the droplets. This work constitutes major progress in the control of double emulsion formation in microfluidic devices and shows that complex structures can be obtained using such a process.

Systematic investigation of droplet generation at T-junctions

Droplet microfluidics has attracted much attention in recent years. For many droplet-based applications, researchers want to predict the size of the droplets in a certain experimental condition. To meet this need, van Steijn and colleagues proposed an elegant theoretical model that predicts the volume of droplets generated in a common channel configuration for forming a steady-state, continuous stream of droplets, the T-junction geometry. To determine the accuracy of this model in predicting droplet volume, we performed a systematic experimental study over two orders of magnitude in capillary number. We found that this model, albeit elegant, has a limited range of interfacial tension over which it can predict accurately the droplet volume. Our experimental results, together with fluid dynamic simulations, allowed us to highlight the importance of physical fluid properties when employing theoretical models.

Global stability of the focusing effect of fluid jet flows

The global stability of the steady jetting mode of liquid jets focused by coaxial gas streams is analyzed both theoretically and experimentally. Numerical simulations allow one to identify the physical mechanisms responsible for instability in the low viscosity and very viscous regimes of the focused liquid. The characteristic flow rates for which global instability takes place are estimated by a simple scaling analysis. These flow rates do not depend on the pressure drop (energy) applied to the system to produce the microjet. Their dependencies on the liquid viscosity are opposite for the two extremes studied: the characteristic flow rate increases (decreases) with viscosity for very low (high) viscosity liquids. Experiments confirmed the validity of these conclusions. The minimum flow rates below which the liquid meniscus becomes unstable are practically independent of the applied pressure drop for sufficiently large values of this quantity. For all the liquids analyzed, there exists an optimum value of the capillary-to-orifice distance for which the minimum flow rate attains a limiting value. That limiting value represents the lowest flow rate attainable with a given experimental configuration in the steady jetting regime. A two-dimensional stability map with a high degree of validity is plotted on the plane defined by the Reynolds and capillary numbers based on the limiting flow rate.

Spatiotemporal instability of a confined capillary jet

Recent experimental studies on the instability of capillary jets have revealed the suitability of a linear spatiotemporal instability analysis to ascertain the parametrical conditions for specific flow regimes such as steady jetting or dripping. In this work, an extensive analytical, numerical, and experimental description of confined capillary jets is provided, leading to an integrated picture both in terms of data and interpretation. We propose an extended, accurate analytic model in the low Reynolds number limit, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show remarkable accuracy when compared with the extensive experimental mapping.

Liquid flow focused by a gas: jetting, dripping, and recirculation

The liquid cone-jet mode can be produced upon stimulation by a coflowing gas sheath. Most applications deal with the jet breakup, leading to either of two droplet generation regimes: Jetting and dripping. The cone-jet flow pattern is explored by direct axisymmetric volume of fluid (VOF) numerical simulation; its evolution is studied as the liquid flow rate is increased around the jetting-dripping transition. As observed in other focused flows such as electrospraying cones upon steady thread emission, the flow displays a strong recirculating pattern within the conical meniscus; it is shown to play a role on the stability of the system, being a precursor to the onset of dripping. Close to the minimum liquid flow rate for steady jetting, the recirculation cell penetrates into the feed tube. Both the jet diameter and the size of the cell are accurately estimated by a simple theoretical model. In addition, the transition from jetting to dripping is numerically analyzed in detail in some illustrative cases, and compared, to good agreement, with a set of experiments.

Unconditional jetting

Capillary jetting of a fluid dispersed into another immiscible phase is usually limited by a critical capillary number, a function of the Reynolds number and the fluid property ratios. Critical conditions are set when the minimum spreading velocity of small perturbations v_{-};{*} along the jet (marginal stability velocity) is zero. Here we identify and describe parametric regions of high technological relevance, where v_{-};{*}>0 and the jet flow is always supercritical independently of the dispersed liquid flow rate; within these relatively broad regions, the jet does not undergo the usual dripping-jetting transition, so that either the jet can be made arbitrarily thin (yielding droplets of any imaginably small size), or the issuing flow rate can be made arbitrarily small. In this work, we provide illustrative analytical studies of asymptotic cases for both negligible and dominant inertia forces. In this latter case, requiring a nonzero jet surface velocity, axisymmetric perturbation waves "surf" downstream for all given wave numbers, while the liquid bulk can remain static. In the former case (implying small Reynolds flow) we found that the jet profile small slope is limited by a critical value; different published experiments support our predictions.

Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries

We adress the question of the stability of a confined coflowing jet at low Reynolds number in various geometries. Our study is motivated by recent experiments in microfluidic devices. When immiscible fluids flow in microchannels, either monodisperse droplets or parallel flows are obtained depending upon the flow rate of the aqueous phase and the oil phase. In these experiments, the confining and the shape of the geometry play a fundamental role. In a previous paper [Guillot, Phys. Rev. Lett 99, 104502 (2007)], we analyzed the stability of the jet in the framework of the lubrication approximation at low Reynolds number in a cylindrical geometry, and we related the transition between the droplets regime and the jet regime to the absolute-convective transition of the Rayleigh plateau instability. In this work, the effect of the channel geometry and the jet position within the microfluidic device are discussed. New flow patterns are pointed out. Bidimensional jets are encountered in square and rectangular geometry. Contrary to jets occuring in circular geometry, these two-dimensional jets are absolutely stable. Focusing on situations where the inner fluid is more viscous than the outer one, we evidence a range of parameters where droplets are produced through a blocking and pinching mechanism. In this particular case, the flow is unstable, the growing perturbations are convected upstream. This induces the clogging of the channel by the internal phase and its pinching by the external one. In a future presentation we will give a comparison between this model and experimental data.

Stability of coflowing capillary jets under nonaxisymmetric perturbations

In this paper, linear hydrodynamic stability analysis is used to study the response of a capillary jet and a coflowing fluid to both axisymmetric and nonaxisymmetric perturbations. The temporal analysis revealed that nonaxisymmetric perturbations were damped (or overdamped) within the region of parameter space explored, which involved equal velocities for the jet and focusing fluid. It is explained how an extension to a spatiotemporal analysis implies that those perturbations can yield no transition from convective (jetting) to absolute (whipping) instability for that parameter region. This result provides a theoretical explanation for the absence of that kind of transition in most experimental results in the literature.

Role of the channel geometry on the bubble pinch-off in flow-focusing devices

The formation of bubbles by flow focusing of a gas and a liquid in a rectangular channel is shown to depend strongly on the channel aspect ratio. Bubble breakup consists in a slow linear 2D collapse of the gas thread, ending in a fast 3D pinch-off. The 2D collapse is predicted to be stable against perturbations of the gas-liquid interface, whereas the 3D pinch-off is unstable, causing bubble polydispersity. During 3D pinch-off, a scaling w_(m) approximately tau(1/3) between the neck width w_(m) and the time tau before breakup indicates that breakup is driven by the inertia of both gas and liquid, not by capillarity.

Stability of a jet in confined pressure-driven biphasic flows at low reynolds numbers

Motivated by its importance for microfluidic applications, we study the stability of jets formed by pressure-driven concentric biphasic flows in cylindrical capillaries. The specificity of this variant of the classical Rayleigh-Plateau instability is the role of the geometry which imposes confinement and Poiseuille flow profiles. We experimentally evidence a transition between situations where the flow takes the form of a jet and regimes where drops are produced. We describe this as the transition from convective to absolute instability, within a simple linear analysis using lubrication theory for flows at low Reynolds number, and reach remarkable agreement with the data.

Aerodynamically assisted jet processing of viscous single- and multi-phase media

This paper reports a robust approach for jet-processing viscous media in both the single- and multi-phase. The multi-phase medium (a nanosuspension) has nanosized SiO (5 nm) particulate material at a loading of ∼10 wt% in suspension. Aerodynamically assisted jetting has previously not been applied to the processing of particulate-based high viscosity nanosuspensions. Our investigations demonstrate that it is possible to generate jets, from which droplets are initiated by jet fragmentation, to the drawing of continuous threads in the micrometer range from the processing of particulate suspensions. The study presents an operational guide of applied pressure-flow rate; demarcations identify regions within the map where droplets and threads are generated, together with their respective operational parameters. The effect of applied pressure and flow rate on the jetting process to the generation of droplets to threads together with transmission electron micrographs of the droplet residues forms the discussion in this paper. These investigations into this jetting approach both elucidate and welcome aerodynamically assisted jetting into the micro- and nano-fabrication arena.

Absolute instability of a viscous hollow jet

An investigation of the spatiotemporal stability of hollow jets in unbounded coflowing liquids, using a general dispersion relation previously derived, shows them to be absolutely unstable for all physical values of the Reynolds and Weber numbers. The roots of the symmetry breakdown with respect to the liquid jet case, and the validity of asymptotic models are here studied in detail. Asymptotic analyses for low and high Reynolds numbers are provided, showing that old and well-established limiting dispersion relations [J. W. S. Rayleigh, The Theory of Sound (Dover, New York, 1945); S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961)] should be used with caution. In the creeping flow limit, the analysis shows that, if the hollow jet is filled with any finite density and viscosity fluid, a steady jet could be made arbitrarily small (compatible with the continuum hypothesis) if the coflowing liquid moves faster than a critical velocity.