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.

Making use of experimental and theoretical considerations, in this Letter we deduce a criterion to determine the critical velocity for which a drop impacting a smooth dry surface either spreads over the substrate or disintegrates into smaller droplets. The derived equation, which expresses the splash threshold velocity as a function of the material properties of the two fluids involved, the drop radius, and the mean free path of the molecules composing the surrounding gaseous atmosphere, has been thoroughly validated experimentally at normal atmospheric conditions using eight different liquids with viscosities ranging from μ=3×10(-4) to μ=10(-2)  Pa s, and interfacial tension coefficients varying between σ=17 and σ=72  mN m(-1). Our predictions are also in fair agreement with the measured critical speed of drops impacting in different gases at reduced pressures given by Xu et al. [Phys. Rev. Lett. 94, 184505 (2005).

Here we provide a theoretical framework describing the generation of the fast jet ejected vertically out of a liquid when a bubble, resting on a liquid–gas interface, bursts. The self-consistent physical mechanism presented here explains the emergence of the liquid jet as a consequence of the collapse of the gas cavity driven by the low capillary pressures that appear suddenly around its base when the cap, the thin film separating the bubble from the ambient gas, pinches. The resulting pressure gradient deforms the bubble which, at the moment of jet ejection, adopts the shape of a truncated cone. The dynamics near the lower base of the cone, and thus the jet ejection process, is determined by the wavelength $\unicode[STIX]{x1D706}^{\ast }$ of the smallest capillary wave created during the coalescence of the bubble with the atmosphere which is not attenuated by viscosity. The minimum radius at the lower base of the cone decreases, and hence the capillary suction and the associated radial velocities increase, with the wavelength $\unicode[STIX]{x1D706}^{\ast }$. We show that $\unicode[STIX]{x1D706}^{\ast }$ increases with viscosity as $\unicode[STIX]{x1D706}^{\ast }\propto Oh^{1/2}$ for $Oh\lesssim O(0.01)$, with $Oh=\unicode[STIX]{x1D707}/\sqrt{\unicode[STIX]{x1D70C}R\unicode[STIX]{x1D70E}}$ the Ohnesorge number, $R$ the bubble radius and $\unicode[STIX]{x1D70C}$, $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D70E}$ indicating respectively the liquid density, viscosity and interfacial tension coefficient. The velocity of the extremely fast and thin jet can be calculated as the flow generated by a continuous line of sinks extending along the axis of symmetry a distance proportional to $\unicode[STIX]{x1D706}^{\ast }$. We find that the jet velocity increases with the Ohnesorge number and reaches a maximum for $Oh=Oh_{c}$, the value for which the crest of the capillary wave reaches the vertex of the cone, and which depends on the Bond number $Bo=\unicode[STIX]{x1D70C}gR^{2}/\unicode[STIX]{x1D70E}$. For $Oh>Oh_{c}$, the jet is ejected after a bubble is pinched off; in this regime, viscosity delays the formation of the jet, which is thereafter emitted at a velocity which is inversely proportional to the liquid viscosity.

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a rn proportional to tau1/3 power law. These findings are verified experimentally.

Cylindrical liquid jets are inherently unstable and eventually break into drops due to the Rayleigh-Plateau instability, characterized by the growth of disturbances that are either convective or absolute in nature. Convective instabilities grow in amplitude as they are swept along by the flow, while absolute instabilities are disturbances that grow at a fixed spatial location. Liquid jets are nearly always convectively unstable. Here we show that two-phase jets can breakup due to an absolute instability that depends on the capillary number of the outer liquid, provided the Weber number of the inner liquid is >O(1). We verify our experimental observations with a linear stability analysis.

A new regime of operation of PDMS-based flow-focusing microfluidic devices is presented. We show that monodisperse microbubbles with diameters below one-tenth of the channel width (here w = 50 μm) can be produced in low viscosity liquids thanks to a strong pressure gradient in the entrance region of the channel. In this new regime bubbles are generated at the tip of a long and stable gas ligament whose diameter, which can be varied by tuning appropriately the gas and liquid flow rates, is substantially smaller than the channel width. Through this procedure the volume of the bubbles formed at the tip of the gas ligament can be varied by more than two orders of magnitude. The experimental results for the bubble diameter d(b) as function of the control parameters are accounted for by a scaling theory, which predicts d(b)/w ∝ (μ(g)/μ(l))(1/12)(Q(g)/Q(l))(5/12), where μ(g) and μ(l) indicate, respectively, the gas and liquid viscosities and Q(g) and Q(l) are the gas and liquid flow rates. As a particularly important application of our results we produce monodisperse bubbles with the appropriate diameter for therapeutic applications (d(b) ≃ 5 μm) and a production rate exceeding 10(5) Hz.

We provide a comprehensive and systematic description of the diverse microbubble generation methods recently developed to satisfy emerging technological, pharmaceutical, and medical demands. We first introduce a theoretical framework unifying the physics of bubble formation in the wide variety of existing types of generators. These devices are then classified according to the way the bubbling process is controlled: outer liquid flows (e.g., coflows, cross flows, and flow-focusing flows), acoustic forcing, and electric fields. We also address modern techniques developed to produce bubbles coated with surfactants and liquid shells. The stringent requirements to precisely control the bubbling frequency, the bubble size, and the properties of the coating make microfluidics the natural choice to implement such techniques.

A solid object impacting on liquid creates a liquid jet due to the collapse of the impact cavity. Using visualization experiments with smoke particles and multiscale simulations we show that in addition a high-speed air-jet is pushed out of the cavity. Despite an impact velocity of only 1 m/s, this air-jet attains supersonic speeds already when the cavity is slightly larger than 1 mm in diameter. The structure of the air flow resembles closely that of compressible flow through a nozzle -with the key difference that here the "nozzle" is a liquid cavity shrinking rapidly in time.PACS numbers: 47.55. 47.60.Kz, 47.11.St, 47.80.Jk Taking a stone and throwing it onto the quiescent surface of a lake triggers a spectacular series of events which has been the subject of scientists' interest for more than a century [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]: upon impact a thin sheet of liquid (the "crown splash") is thrown upwards along the rim of the impacting object while below the water surface a large cavity forms in the wake of the impactor. Due to the hydrostatic pressure of the surrounding liquid this cavity immediately starts to collapse and eventually closes in a single point ejecting a thin, almost needle-like liquid jet. Just prior to the ejection of the liquid jet the cavity possesses a characteristic elongated "hourglass" shape with a large radius at its bottom, a thin neck region in the center, and a widening exit towards the atmosphere.This shape is very reminiscent of the convergingdiverging ("de Laval") nozzles known from aerodynamics as the paradigmatic picture of compressible gas flow through, e.g., supersonic jet engines. In this Letter we use a combination of experiments and numerical simulations to show that in addition to the very similar shape, also the structure of the air flow through the impact cavity resembles closely the high-speed flow of gas through such a nozzle. Not only is the flow to a good approximation one-dimensional, but it even attains supersonic velocities. Nevertheless, the pressure inside the cavity is merely 2% higher than the surrounding atmosphere. The key difference, however, is that in our case the "nozzle" is a liquid cavity whose shape is evolving rapidly in timea situation for which no equivalent exists in the scientific or engineering literature.Our experimental setup consists of a thin circular disc with radius R 0 = 2 cm which is pulled through the liquid surface by a linear motor mounted at the bottom of a large water tank [16] with a constant speed of V 0 = 1 m/s. To visualize the air flow we use small glycerin droplets (diameter roughly 3 µm) produced by a commercially available smoke machine (skytec) commonly used for light effects in theaters and discotheques. Before the start of the experiment the atmosphere above the water surface is filled with this smoke which is consequently entrained into the cavity by the impacting disc.A laser sheet (Larisis Magnum II, 1500mW) shining in from above illuminates a vertical plane containing the axis of sy...