Miguel A. Herrada

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.

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...

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.

Analysis of the dripping-jetting transition in compound capillary jets

We examine the behaviour of a compound capillary jet from the spatio-temporal linear stability analysis of the Navier–Stokes equations. We map the jetting–dripping transition in the parameter space by calculating the Weber numbers for which the convective/absolute instability transition occurs. If the remaining dimensionless parameters are set, there are two critical Weber numbers that verify Brigg’s pinch criterion. The region of absolute (convective) instability corresponds to Weber numbers smaller (larger) than the highest value of those two Weber numbers. The stability map is affected significantly by the presence of the outer interface, especially for compound jets with highly viscous cores, in which the outer interface may play an important role even though it is located very far from the core. Full numerical simulations of the Navier–Stokes equations confirm the predictions of the stability analysis.

Vortex breakdown in compressible flows in pipes

The effects of compressibility on vortex flows in pipes have been analyzed using both the axisymmetric Navier–Stokes (NS) equations and the quasi-cylindrical (QC) approximation. Numerical simulations of the full axisymmetric NS equations show that, for sufficiently large values of the Reynolds number, compressible flows present a multiplicity of steady-state solutions in a range of values of the swirl strength. The sensitivity of the vortex flow structure to the parameters of the problem: Mach number, Reynolds number, velocity profiles at the pipe entrance and pipe geometry has been also investigated. In particular, the critical swirl parameter necessary for the occurrence of vortex breakdown has been determined as a function of both the Mach number and the axial momentum of the flow at the pipe entrance. For large Reynolds number, the results of the QC approximation are found to be in good agreement with those of the full NS simulations. These results show that the upstream propagation of the sound waves...

Control of vortex breakdown by temperature gradients

An axial gradient of temperature can either suppress or enhance vortex breakdown (VB). The underlying mechanism of such VB control is centrifugal or/and gravitational convection. An additional thermal-convection flow directed oppositely to the base flow suppresses VB while a co-flow enhances VB. Our numerical simulations of a compressible flow in a sealed cylinder induced by a rotating bottom disk clearly reveal these effects. We vary the temperature gradient (e), Mach (Ma), Froude (Fr), and Reynolds (Re) numbers, and the aspect ratio (h). As e increases (e>0 corresponding to a temperature gradient parallel to the downward near-axis flow), the VB “bubble,” which occurs at e=0, diminishes and then totally disappears. The opposite temperature gradient (e<0) enlarges the VB bubble and makes the flow unsteady. These effects of centrifugal convection become more prominent with increasing Ma and Re. Density variations induced by the temperature gradients are more important for VB control than those induced by t...

Downstream evolution of unconfined vortices: mechanical and thermal aspects

We present a numerical study of the downstream evolution (mechanical and thermal) of vortex-jet cores whose velocity and temperature elds far from the axis match a family of inviscid and non-conducting vortices. The far-velocity eld is rotational, except for a particular case which corresponds to the well-known Long’s vortex. The evolution of the vortex core depends on both the conditions at a certain upstream station, characterized by the dimensionless value of the velocity at the axis, and a dimensionless swirling parameter L dened as the ratio of the values of the azimuthal and axial velocities outside the vortex core. This numerical study, based on the quasi-cylindrical approximation (QC) of the Navier{Stokes equations, determines the conditions under which the vortex evolution proceeds smoothly, eventually reaching an asymptotic self-similar behaviour as described in the literature (Fern andez-Feria, Fern andez de la Mora & Barrero 1995; Herrada, P erez-Saborid & Barrero 1999), or breaks in a non-slender solution (vortex breakdown). In particular, the critical value L = Lb(a) beyond which vortex breakdown occurs downstream is a function of a dimensionless parameter a characterizing the axial momentum of the vortex jet at an initial upstream station. It is found numerically that for very large values of a this vortex breakdown criterion tends to an asymptote which is precisely the value L = L predicted by the self-similar analysis, and beyond which a self-similar structure of the vortex core does not exist. In addition, the computation of the total temperature eld provides useful information on the physical mechanisms responsible for the thermal separation phenomenon observed in Ranque{Hilsch tubes and other swirling jet devices. In particular, the mechanical work of viscous forces which gives rise to an intense loss of kinetic energy during the initial stages of the evolution has been identied as the physical mechanism responsible for thermal separation.

Dynamical behavior of electrified pendant drops

The electrohydrodynamic response of low-conductivity pendant drops to a step change in the electric field magnitude was examined both numerically and experimentally. Both the leaky-dielectric and perfect-conductor models were solved in the simulations. Experiments were conducted to precisely measure the drop interface shape as a function of time. The drop oscillated for applied voltages smaller than a critical value which depended on the rest of governing parameters. It stretched and subsequently emitted a microjet from its tip for electric potentials above that critical value. The perfect-conductor model described accurately the oscillations of subcritical drops. This model also provided satisfactory results for the prejetting regime in the supercritical case. We found a good agreement between the leaky-dielectric model and the experiments for the drop-jet transitional region, despite the fact that the tip streaming arose on a time scale much shorter than the electric relaxation time. This result shows t...

Effect of swirl decay on vortex breakdown in a confined steady axisymmetric flow

This numerical study of the steady axisymmetric motion of a viscous incompressible fluid in a sealed cylindrical container with one end wall rotating reveals that swirl decay, induced by friction at the sidewall, plays an important role in the development of vortex breakdown (VB). When the flow is slow, it is multi-cellular. As the flow strength increases (i) meridional circulation becomes global, (ii) flow convergence toward the axis focuses near the still end wall, (iii) a few local minima of pressure appear, (iv) a few flow reversals occur near the axis, and (v) circulation regions merge and an elongated double counterflow develops. Stages (i)–(v) are common for a number of vortex devices. If the swirl decay is diminished by additional rotation of the sidewall, VB disappears.

Liquid Capillary Micro/Nanojets in Free‐Jet Expansion

Perfectly steady liquid micro/nanojets can be produced by simply using a free-jet gas expansion to accelerate a coaxially flowing liquid core. Images of these jets have been obtained by electron microscopy (Figure 1a), which reveal their steadiness and beauty. We show that the spatial pressure distribution resulting at the discharge of a gas stream into a vacuum through a conveniently shaped small aperture creates huge forces per unit volume sufficient to shape and extrude a liquid nanoscale jet in an open environment: the inertia of fast gas stream downstream of the aperture creates a focusing effect after the discharge associated to the radial convergence imposed by the innerwalls of theaperture.Experiments at the small scales used can be compared with the results of full numerical simulations, which reveals the detailed structure of the momentum and energy-transfer process between liquid and gas occurring at the discharge. This work opens an untrodden way to observe nanocapillary flows; nanojets and fibers in unconfined environments are accessible to electron and soft ray probes for which confining walls would otherwise be opaque. These liquid jets can be used in, for example, hydrated injection of biomolecules into vacuum and in atomic spectroscopy. The existence and nature of this class of capillary tapering micro/nanojets (cone jets) produced by a co-flowing gas stream without confinement is reported in this work. The flow rate of these jets is sufficiently small as to permit nozzle operation within an environmental scanning electron microscopy (ESEM) system at conditions tolerable to the microscope vacuum system. Forming a liquid jet in a free-jet gas expansion allows the entire liquid jet from exit aperture to the point of jet break-up to be imaged by secondary electrons (Figure 1a). Numerical simulation of the phenomenon (Figure 1–e) shows that the strong focusing effect observed is due to the inertial