Microbubble formation and pinch-off scaling exponent in flow-focusing devices

We investigate the gas jet breakup and the resulting microbubble formation in a microfluidic flow-focusing device using ultra high-speed imaging at 1 million frames/s. In recent experiments [Dollet et al., Phys. Rev. Lett. 100, 034504 (2008)] it was found that in the final stage of the collapse the radius of the neck scales with time with a 1/3 power-law exponent, which suggested that gas inertia and the Bernoulli suction effect become important. Here, ultra high-speed imaging was used to capture the complete bubble contour and quantify the gas flow through the neck. It revealed that the resulting decrease in pressure, due to Bernoulli suction, is too low to account for an accelerated pinch-off. The high temporal resolution images enable us to approach the final moment of pinch-off to within 1 {\mu}s. We observe that the final moment of bubble pinch-off is characterized by a scaling exponent of 0.41 +/- 0.01. This exponent is approximately 2/5, which can be derived, based on the observation that during the collapse the neck becomes less slender, due to the exclusive driving through liquid inertia

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 wm~tau1/3 between the neck width wm and the time tau before breakup indicates that breakup is driven by the inertia of both gas and liquid, not by capillarity

Bubble size prediction in co-flowing streams

In this paper, the size of bubbles formed through the breakup of a gaseous jet in a co-axial microfluidic device is derived. The gaseous jet surrounded by a co-flowing liquid stream breaks up into monodisperse microbubbles and the size of the bubbles is determined by the radius of the inner gas jet and the bubble formation frequency. We obtain the radius of the gas jet by solving the Navier-Stokes equations for low Reynolds number flows and by minimization of the dissipation energy. The prediction of the bubble size is based on the system's control parameters only, i.e. the inner gas flow rate $Q_i$, the outer liquid flow rate $Q_o$, and the tube radius $R$. For a very low gas-to-liquid flow rate ratio ($Q_i / Q_o \rightarrow 0$) the bubble radius scales as $r_b / R \propto \sqrt{Q_i / Q_o}$, independently of the inner to outer viscosity ratio $\eta_i/\eta_o$ and of the type of the velocity profile in the gas, which can be either flat or parabolic, depending on whether high-molecular-weight surfactants cover the gas-liquid interface or not. However, in the case in which the gas velocity profiles are parabolic and the viscosity ratio is sufficiently low, i.e. $\eta_i/\eta_o \ll 1$, the bubble diameter scales as $r_b \propto (Q_i/Q_o)^\beta$, with $\beta$ smaller than 1/2

Breakup of diminutive Rayleigh jets

Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale $\tau_\mathrm{c} = \sqrt{\rho r^3 / \gamma}$ of the order of 100\,ns{}, and requires imaging at 14 million frames per second. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Shi, Brenner, and Nagel, Science 265, 219 (1994)]. The lubrication model allows to efficiently explore the parameter space to investigate the effect of jet velocity and liquid viscosity on the formation of satellite droplets. In the phase diagram we identify regions where the formation of satellite droplets is suppressed. We compare the shape of the droplet at pinch-off between the lubrication approximation model and a boundary integral (BI) calculation, showing deviations at the final moment of the pinch-off. Inspite of this discrepancy, the results on pinch-off times and droplet and satellite droplet velocity obtained from the lubrication approximation agree with the high-speed imaging results

Determination of a potential quantitative measure of the state of the lung using lung ultrasound spectroscopy

B-lines are ultrasound-imaging artifacts, which correlate with several lung-pathologies. However, their understanding and characterization is still largely incomplete. To further study B-lines, lung-phantoms were developed by trapping a layer of microbubbles in tissue-mimicking gel. To simulate the alveolar size reduction typical of various pathologies, 170 and 80 μm bubbles were used for phantom-Type 1 and 2, respectively. A normal alveolar diameter is approximately 280 μm. A LA332 linear-Array connected to the ULA-OP platform was used for imaging. Standard ultrasound (US) imaging at 4.5 MHz was performed. Subsequently, a multi-frequency approach was used where images were sequentially generated using orthogonal sub-bands centered at different frequencies (3, 4, 5, and 6 MHz). Results show that B-lines appear predominantly with phantom-Type 2. Moreover, the multi-frequency approach revealed that the B-lines originate from a specific portion of the US spectrum. These results can give rise to significant clinical applications since, if further confirmed by extensive in-vivo studies, the native frequency of B-lines could provide a quantitative-measure of the state of the lung

Microbubble generation in a co-flow device operated in a new regime

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 db as function of the control parameters are accounted for by a scaling theory, which predicts db/w ∝ (μg/μ)1/12(Qg/Q)5/12, where μg and μ indicate, respectively, the gas and liquid viscosities and Qg and Q 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 (db 5 μm) and a production rate exceeding 10

Microbubble generation in a co-flow device operated in a new regime

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 db as function of the control parameters are accounted for by a scaling theory, which predicts db/w ∝ (μg/μ)1/12(Qg/Q)5/12, where μg and μ indicate, respectively, the gas and liquid viscosities and Qg and Q 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 (db 5 μm) and a production rate exceeding 10

Determination of a potential quantitative measure of the state of the lung using lung ultrasound spectroscopy

\u3cp\u3eB-lines are ultrasound-imaging artifacts, which correlate with several lung-pathologies. However, their understanding and characterization is still largely incomplete. To further study B-lines, lung-phantoms were developed by trapping a layer of microbubbles in tissue-mimicking gel. To simulate the alveolar size reduction typical of various pathologies, 170 and 80 μm bubbles were used for phantom-Type 1 and 2, respectively. A normal alveolar diameter is approximately 280 μm. A LA332 linear-Array connected to the ULA-OP platform was used for imaging. Standard ultrasound (US) imaging at 4.5 MHz was performed. Subsequently, a multi-frequency approach was used where images were sequentially generated using orthogonal sub-bands centered at different frequencies (3, 4, 5, and 6 MHz). Results show that B-lines appear predominantly with phantom-Type 2. Moreover, the multi-frequency approach revealed that the B-lines originate from a specific portion of the US spectrum. These results can give rise to significant clinical applications since, if further confirmed by extensive in-vivo studies, the native frequency of B-lines could provide a quantitative-measure of the state of the lung.\u3c/p\u3