Dripping, jetting and tip streaming.

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. First, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results of the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming in open systems. Second, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

Electrospray cone-jet mode for weakly viscoelastic liquids.

We study theoretically the influence of viscoelasticity on the steady cone-jet mode of electrospray for small stress relaxation times. For this purpose, we numerically integrate the leaky-dielectric model together with the Oldroyd-B constitutive relationship and calculate both the base flow and linear eigenmodes characterizing its stability as a function of the governing parameters. We describe the effect of the polymeric stresses on both the cone-jet mode and the minimum flow rate stability limit. There are considerable differences between the Newtonian and viscoelastic electrospray realizations even for relatively small stress relaxation times due to the intense extensional deformation suffered by the fluid particles in the cone-jet transition region The axial polymeric stress shrinks the liquid meniscus and stabilizes it by pushing the fluid particle in the cone-to-jet transition region.

Aerodynamically stabilized Taylor cone jets.

We introduce a way to stabilize steady micro/nanoliquid jets issuing from Taylor cones together with coflowing gas streams. We study the dripping-jetting transition of this configuration theoretically through a global stability analysis as a function of the governing parameters involved. A balance between the local radial acceleration to the surface tension gradient, the mass conservation, and the energy balance equations enable us to derive two coupled scaling laws that predict both the minimum jet diameter and its maximum velocity. The theoretical prediction provides a single curve that describes not only the numerical computations but also experimental data from the literature for cone jets assisted with gas coflow. Additionally, we performed a set of experiments to verify what parameters influence the jet length. We adopt a very recent model for capillary jet length to our configuration by combining electrohydrodynamic effects with the gas flow through an equivalent liquid pressure. Due to diameters below 1 µm and high speeds attainable in excess of 100 m/s, this concept has the potential to be utilized for structural biology analyses with x-ray free-electron lasers at megahertz repetition rates as well as other applications.

Synthesis of lidocaine-loaded PLGA microparticles by flow focusing. Effects on drug loading and release properties.

In the present work, two methods for the preparation of lidocaine-loaded PLGA microparticles are compared. The differences between the polymeric particles obtained by solvent evaporation (SEVM) or flow focusing (FF) were studied by means of scanning electron microscopy and surface thermodynamics determinations. A detailed investigation of the capabilities of the polymer particles to load this drug is described. The physical state of the drug in the polymeric particles and the existence of interactions between both entities were studied by differential scanning calorimetry. The main factors determining the lidocaine incorporation and the release kinetics were the synthesis procedure followed, the amount of drug dissolved in the organic phase during the synthesis routine, the type of polymer (molecular weight and end chemical groups) and the size and the hydrophobic/hydrophilic properties of the particles. The FF technology allowed higher drug incorporations and slower release kinetics. The release studies showed a biphasic profile probably due to diffusion-cum-degradation mediated processes.

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.

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.

Straightforward production of encoded microbeads by Flow Focusing: potential applications for biomolecule detection.

Fluorescently encoded polymeric microparticles are acquiring great importance in the development of simultaneous multianalyte screening assays. We have developed a very versatile and straightforward method for the production of dye-labeled microparticles with a very reproducible size distribution and freely-chosen and discernible fluorescent properties. Our method combines Flow Focusing technology with a solvent evaporation/extraction procedure in a single step, yielding spherical, non-aggregate and non-porous particles. We have designed a multi-coloured bead array which includes the possibility of modifying the surface properties of the microparticles, which offer excellent properties for covalent attachment of biomolecules such as peptides, oligonucleotides, proteins, etc. We also show the potential of the fluorescently labeled microspheres for the detection of biomolecule (peptides and oligonucelotides) interactions using flow cytometry.

Monosized dripping mode of axisymmetric flow focusing.

We identify and analyze the perfectly regular dripping mode of flow focusing. This mode occurs within narrow intervals of injected flow rates and applied pressure drops and leads to homogeneous-size droplets with diameters similar to or smaller than that of the discharge orifice. The balance between the local acceleration of the fluid particle and the applied pressure drop yields the scaling law for the droplet diameter. This scaling law is validated experimentally with excellent accord.

The onset of electrospray: the universal scaling laws of the first ejection.

The disintegration of liquid drops with low electrical conductivity and subject to an electric field is investigated both theoretically and experimentally. This disintegration takes place through the development of a conical cusp that eventually ejects an ultrathin liquid ligament. A first tiny drop is emitted from the end of this ligament. Due to its exceptionally small size and large electric charge per unit volume, that drop has been the object of relevant recent studies. In this paper, universal scaling laws for the diameter and electric charge of the first issued droplet are proposed and validated both numerically and experimentally. Our analysis shows how charge relaxation is the mechanism that differentiates the onset of electrospray, including the first droplet ejection, from the classical steady cone-jet mode. In this way, our study identifies when and where charge relaxation and electrokinetic phenomena come into play in electrospray, a subject of live controversy in the field.

Convective-to-absolute instability transition in a viscoelastic capillary jet subject to unrelaxed axial elastic tension.

The convective-to-absolute instability transition in an Oldroyd-B capillary jet subject to unrelaxed axial stress is examined theoretically. There is a critical Weber number below which the jet is absolutely unstable under axisymmetric perturbations. We analyze the dependence of this critical parameter with respect to the Reynolds and Deborah numbers, as well as the unrelaxed axial stress. For small Deborah numbers, the unrelaxed stress destabilizes the viscoelastic jet, increasing the critical Weber number for which the convective-to-absolute instability transition takes place. If the Deborah number takes higher values, then the transitional Weber number decreases as the unrelaxed stress increases until two solution branches cross each other. The dominant branch for large axial stress leads to a threshold of this quantity above which the viscoelastic jet becomes absolutely unstable independently of the Weber number. The threshold depends on neither the Reynolds nor the Deborah number for sufficiently large values of these parameters.

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.

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.

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.

Numerical simulation of electrospray in the cone-jet mode.

We present a robust and computationally efficient numerical scheme for simulating steady electrohydrodynamic atomization processes (electrospray). The main simplification assumed in this scheme is that all the free electrical charges are distributed over the interface. A comparison of the results with those calculated with a volume-of-fluid method showed that the numerical scheme presented here accurately describes the flow pattern within the entire liquid domain. Experiments were performed to partially validate the numerical predictions. The simulations reproduced accurately the experimental shape of the liquid cone jet, providing correct values of the emitted electric current even for configurations very close to the cone-jet stability limit.

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.

Perfectly monodisperse microbubbling by capillary flow focusing.

Here we report a simple microfluidics phenomenon which allows the efficient mass production of micron size gas bubbles with a perfectly monodisperse and controllable diameter. It resorts on a self-excited breakup phenomenon (which locks at a certain frequency) of a short gas microligament coflowing in a focused liquid stream. In this work, we describe the physics of the phenomenon and obtain closed expressions for the bubble diameter as a function of the liquid and gas properties, geometry, and flow parameters, from a large set of experimental results.

Micro/nano encapsulation via electrified coaxial liquid jets.

We report a method to generate steady coaxial jets of immiscible liquids with diameters in the range of micrometer/nanometer size. This compound jet is generated by the action of electro-hydrodynamic (EHD) forces with a diameter that ranges from tens of nanometers to tens of micrometers. The eventual jet breakup results in an aerosol of monodisperse compound droplets with the outer liquid surrounding or encapsulating the inner one. Following this approach, we have produced monodisperse capsules with diameters varying between 10 and 0.15 micrometers, depending on the running parameters.