E. J. Vega

Global and local instability of flow focusing: The influence of the geometry

In the flow focusing technique, a liquid flow rate Q is injected through a microcapillary to form a meniscus attached to its edge. The meniscus is stretched until a thin jet tapers from its tip due to the action of a gas stream driven by a pressure drop Δp. Both the liquid jet and the gas stream cross the orifice of a plate located in front of the capillary at a distance H. In the present work, the stability of both the tapering liquid meniscus and the emitted jet is analyzed experimentally. Three regimes are identified: (i) the steady jetting regime, where the liquid meniscus is stable and the jet is convectively unstable; (ii) the local instability regime, where the liquid meniscus is stable and the jet is absolutely unstable; and (iii) the global instability regime, where the liquid meniscus is unstable. The mechanisms responsible for the transitions between those regimes are described. The experiments show the existence of a minimum value Qmin of the flow rate Q below which flow focusing is globally unstable independent of the pressure drop Δp applied to the gas stream. The dependence of the stability threshold Qmin with respect to the capillary-to-orifice distance H is analyzed considering different liquids. If the rest of the geometrical parameters are fixed, there is an optimum value Hopt of the capillary-to-orifice distance H for which the stability threshold Qmin is minimum. We also determine the dependence of Hopt and the corresponding minimum flow rate Qopt with respect to the capillary diameter. In addition, we find that Qmin diverges as the capillary-to-orifice distance H decreases and approaches a certain critical value, at which the transition from flow focusing to “flow blurring” takes place. We confirm our interpretation of the experimental results by conducting numerical simulations for the aforementioned three regimes.In the flow focusing technique, a liquid flow rate Q is injected through a microcapillary to form a meniscus attached to its edge. The meniscus is stretched until a thin jet tapers from its tip due to the action of a gas stream driven by a pressure drop Δp. Both the liquid jet and the gas stream cross the orifice of a plate located in front of the capillary at a distance H. In the present work, the stability of both the tapering liquid meniscus and the emitted jet is analyzed experimentally. Three regimes are identified: (i) the steady jetting regime, where the liquid meniscus is stable and the jet is convectively unstable; (ii) the local instability regime, where the liquid meniscus is stable and the jet is absolutely unstable; and (iii) the global instability regime, where the liquid meniscus is unstable. The mechanisms responsible for the transitions between those regimes are described. The experiments show the existence of a minimum value Qmin of the flow rate Q below which flow focusing is globally u...

Micrometer glass nozzles for flow focusing

We discuss the use of flame-shaped glass micro-nozzles for ultra-fine liquid atomization by flow focusing (DePonte et al 2008 J. Phys. D: Appl. Phys. 41 195505), which may have great importance in very varied technological fields, such as biotechnology, biomedicine and analytical chemistry. Some advantages offered by these nozzles over the original plate orifice configuration (Ganan-Calvo 1998 Phys. Rev. Lett. 80 285) are: (i) they are extraordinarily smooth even at the micrometer scale, (ii) one can readily obtain nozzles with neck diameters in the range of a few tens of microns, (iii) they demand gas flow rates significantly smaller than those required by the plate orifice configuration and (iv) they are transparent. However, highly demanding applications require a precise characterization of their three-dimensional shape by non-destructive means. This characterization cannot be obtained straightforwardly from optical transmission or electron microscopy mainly due to optical distortion. We propose in this paper a method for measuring the shape and size of micrometer nozzles formed inside millimetric and submillimetric capillaries made of transparent materials. The inside of the capillary is colored, and the capillary is put in a liquid bath with almost the same refractive index as that of the capillary to eliminate optical distortion. The nozzle image, acquired with a microscope using back-light illumination to get a silhouette effect, is processed to locate the contours of the nozzle with sub-pixel resolution. To determine the three-dimensional shape of the nozzle, the capillary is rotated in front of the camera. The method provides precise results for nozzle sizes down to a few microns.

Numerical simulation of a liquid bridge in a coaxial gas flow

The dynamical response of an isothermal liquid bridge to a coaxial gas stream is examined from axisymmetric numerical simulations of the Navier–Stokes equations. The simulation method is previously validated by calculating the temporal evolution of the first oscillation mode in both cylindrical and axisymmetric liquid bridges. The comparison with other theoretical approaches and experiments shows good agreement in most cases, although significant discrepancies are found between the simulation and the experimental values of the damping rate for hexadecane. The simulation of a liquid bridge in a coaxial gas stream shows that a recirculation cell always appears in the liquid driven by the gas viscous stress on the free surface. The recirculation cell speed depends quasilinearly on the gas velocity for the range of gas flow rates considered. If the gas stream and gravity have the same direction, then the speed of the recirculation cell increases considerably due to the free surface deformation of the liquid b...

Damping of linear oscillations in axisymmetric liquid bridges

We analyzed experimentally the damping of both axial and lateral free oscillations of small amplitude in axisymmetric liquid bridges. We excited the first oscillation mode in nearly inviscid and in moderately viscous liquid bridges, and measured the parameters which characterize that mode. The axial spatial dependence of those parameters was determined, and the influence of the equilibrium shape on the oscillation frequency and damping rate was analyzed by considering liquid bridges with very different volumes. The experimental results were compared with the solution of the Navier–Stokes equations in the limit of zero viscous Capillary number and of two one-dimensional models. These theoretical approaches predicted accurately the axial spatial dependence of the parameters characterizing the oscillation mode. Comparison with the experimental data showed remarkable agreement for the oscillation frequency, while significant discrepancies were found for the damping rate.

Measurement of relaxation times in extensional flow of weakly viscoelastic polymer solutions

The characterization of the extensional rheology of polymeric solutions is important in several applications and industrial processes. Filament stretching and capillary breakup rheometers have been developed to characterize the extensional properties of polymeric solutions, mostly for high-viscosity fluids. However, for low concentration polymer solutions, the measurements are difficult using available devices, in terms of the minimum viscosity and relaxation times that can be measured accurately. In addition, when the slow retraction method is used, solvent evaporation can affect the measurements for volatile solvents. In this work, a new setup was tested for filament breakup experiments using the slow retraction method, high-speed imaging techniques, and an immiscible oil bath to reduce solvent evaporation and facilitate particle tracking in the thinning filament. Extensional relaxation times above around 100 μs were measured with the device for dilute and semi-dilute polymer solutions. Particle tracking velocimetry was also used to measure the velocity in the filament and the corresponding elongation rate, and to compare with the values obtained from the measured exponential decay of the filament diameter.

Influence of the Surface Viscosity on the Breakup of a Surfactant-Laden Drop

We examine both theoretically and experimentally the breakup of a pendant drop loaded with an insoluble surfactant. The experiments show that a significant amount of surfactant is trapped in the resulting satellite droplet. This result contradicts previous theoretical predictions, where the effects of surface tension variation were limited to solutocapillarity and Marangoni stresses. We solve numerically the hydrodynamic equations, including not only those effects but also those of surface shear and dilatational viscosities. We show that surface viscosities play a critical role to explain the accumulation of surfactant in the satellite droplet.

On the validity of a universal solution for viscous capillary jets

In this paper, we assess the validity of a universal solution based on the slenderness approximation to describe the velocity and shape of viscous capillary jets produced by two very different mechanisms: the action of the constant gravity force and the focusing effect of a coflowing gas stream. In the gravitational case, the jet’s velocity distribution given by the universal solution is compared with that calculated numerically from the Navier-Stokes equations. The universal solution provides remarkably good predictions for the wide range of parameters considered in this work. Its accuracy generally improves as the Reynolds number increases and/or the Froude number decreases, probably because the jet viscous region decreases in this case. The flow focusing method was examined experimentally by acquiring and processing images of the tapering liquid meniscus formed between the feeding capillary and the discharge orifice. In this case, the universal solution provides satisfactory results for sufficiently sl...

Sub-micrometer precision of optical imaging to locate the free surface of a micrometer fluid shape.

In this note, we explore the precision of the optical imaging method for measuring the free surface position of a micrometer fluid shape. For this purpose, images of a liquid film deposited on a rod were acquired and processed. The resulting contour was compared with the corresponding solution to the Young-Laplace equation. The average deviation was about 30nm, 25 times smaller than the pixel size, reflecting the validity of optical imaging for most applications in microfluidics.

An experimental technique to produce micrometer waves on a cylindrical sub-millimeter free surface

We propose and validate an experimental method to analyze the propagation of micrometer surface waves over a liquid column held between two rods, 100 μm in radius. One of the rods vibrates at frequencies of the order of several kHz, while the other remains still. Surface waves, very few microns in amplitude, travel from the oscillating rod to the opposite end. They are almost damped by viscous stresses before reaching that end. We use a super-resolution image processing technique to measure the spatial decay of those waves down to the submicrometer scale. The results are validated from comparison with the numerical solution of the full Navier–Stokes equations.

Stabilization of axisymmetric liquid bridges through vibration-induced pressure fields

Previous theoretical studies have indicated that liquid bridges close to the Plateau-Rayleigh instability limit can be stabilized when the upper supporting disk vibrates at a very high frequency and with a very small amplitude. The major effect of the vibration-induced pressure field is to straighten the liquid bridge free surface to compensate for the deformation caused by gravity. As a consequence, the apparent Bond number decreases and the maximum liquid bridge length increases. In this paper, we show experimentally that this procedure can be used to stabilize millimeter liquid bridges in air under normal gravity conditions. The breakup of vibrated liquid bridges is examined experimentally and compared with that produced in absence of vibration. In addition, we analyze numerically the dynamics of axisymmetric liquid bridges far from the Plateau-Rayleigh instability limit by solving the Navier-Stokes equations. We calculate the eigenfrequencies characterizing the linear oscillation modes of vibrated liquid bridges, and determine their stability limits. The breakup process of a vibrated liquid bridge at that stability limit is simulated too. We find qualitative agreement between the numerical predictions for both the stability limits and the breakup process and their experimental counterparts. Finally, we show the applicability of our technique to control the amount of liquid transferred between two solid surfaces.