Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session GC: Drops and Bubbles VII |
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Chair: David Thiessen, Washington State University Room: Salt Palace Convention Center 150 G |
Monday, November 19, 2007 10:30AM - 10:43AM |
GC.00001: Slow capillary jets in normal gravity: stability analysis and excitation by ultrasonic and electrostatic stresses David Thiessen, Joel Lonzaga, Philip L. Marston The convective stability of a liquid jet in normal gravity issuing from a nozzle has been investigated experimentally and theoretically. The modes of the jet are excited downstream from the nozzle by a localized, modulated ultrasonic radiation pressure or modulated electrostatic stress. The spatially amplifying mode is detected using an optical extinction apparatus sensitive to small-amplitude fluctuation. Experimental data show that the commonly used stability analysis for homogeneous jets does not apply to accelerating jets with low nozzle velocities. Consequently, an asymptotic stability analysis is developed that incorporates the gravitational effect. General agreement between the theory and experiment is obtained including on some novel features unique to accelerating jets. The upstream propagating neutral mode is also excited under special conditions. Conversion of this mode (from neutral to amplifying) upon reflection from the nozzle results in interference with the original amplifying mode. The interference effect detected downstream modulates the growth of the instability and thus significantly affects the break up length. [Preview Abstract] |
Monday, November 19, 2007 10:43AM - 10:56AM |
GC.00002: Atomization of Non-Newtonian Liquids by a High Momentum Coaxial Gas Jet. Stability Analysis, Modelling and Experimental Validation Alberto Aliseda, Emil Hopfinger, Douglas M. Kremer, Alfred Berchielli, Emilia K. Connolly, Juan C. Lasheras The atomization of a liquid jet by a co-flowing, high-speed gas has been studied for non-Newtonian polymer solutions. In this study, the R-T model originally developed by Varga et al. (2003) is extended to viscous and non-Newtonian fluids by applying the general dispersion relation developed by Joseph et al. (2002). When viscous effects are negligible the maximum amplification wavenumber is $k_{\sigma}=\sqrt{a \rho_l/(3\sigma)}$. On the contrary, when viscous effects are dominant, the wavenumber for maximum amplification can be approximated by $k_{\alpha}=\sqrt[3]{a \rho_l^2/\alpha_l^2}$. If the effects of surface tension and viscosity are assumed to be additive, the resulting R-T instability wavelength can be estimated as $\lambda_{RT} = 2 \pi (\sqrt{3 \sigma/ (a \rho_l)} + C_2 \sqrt[3]{\alpha_l^2/(a \rho_l^2)})$. The model obtained from the theoretical analysis has been validated from droplet diameter measurements of the atomization of six different liquids under a wide range of experimental conditions. The diameter and axial velocity of the liquid droplets was measured by Phase Doppler Particle Analyzer. [Preview Abstract] |
Monday, November 19, 2007 10:56AM - 11:09AM |
GC.00003: Effect of Nozzle Length/Diameter Ratio on the Breakup of Liquid Jets in Crossflow Anu Osta, Khaled Sallam An experimental research is performed to study the effect of injector geometry (passage length/diameter ratio) on the atomization of liquid jets in crossflow at normal temperature and pressure, large liquid/gas density ratios and small Ohnesorge numbers. Double pulsed shadowgraphy and holographic microscopy was used to observe jet primary breakup for nozzles with different length to diameter ratio which injected into uniform crossflow. Shadowgraphy was used to observe the jet breakup locations and surface waves while digital microscopic holography was used to observe the near surface droplet and ligament distribution. The hologram is captured digitally on a CCD and reconstructed numerically using convolution. Present results show that the breakup length, decreases with increasing nozzle length because of the stronger interaction between the turbulent eddies originating from the boundary layer inside the nozzle and the free surface of the liquid jet. This leads to significantly more atomization and erosion of liquid core. The breakup of turbulent liquid jets was influenced by a new dimensionless number in terms of liquid/gas momentum ratio and jet Weber number. [Preview Abstract] |
Monday, November 19, 2007 11:09AM - 11:22AM |
GC.00004: Computational analysis of DOD drop formation Qi Xu, Osman Basaran A fundamental theoretical understanding of drop-on-demand (DOD) ink jet printing remains weak despite the widespread use of the method in practical applications for two decades. To overcome this deficiency, a computational analysis is carried out to simulate the formation of liquid drops of incompressible Newtonian fluids from a nozzle by imposing a transient flow rate upstream of the nozzle exit. The dynamics are studied as functions of the Ohnesorge number Oh (viscous/surface tension force) and the Weber number We (inertial/surface tension force). For a common ink forming from a nozzle of 10 micrometer radius, Oh=0.1. For this typical case, a phase or operability diagram is developed that shows that three regimes of operation are possible. In the first regime, where We is low, breakup does not occur, and drops remain pendant from the nozzle and undergo time periodic oscillations. Thus, the simulations show that sufficient fluid inertia, or a sufficiently large We, is required if a DOD drop is to form, in accord with intuition. At high We, two regimes exist. In the first of these two regimes, DOD drops do form but have negative velocities, i.e. they would move toward the nozzle upon breakup, which is undesirable. In the second breakup regime, not only are DOD drops formed but they do so with positive velocities. [Preview Abstract] |
Monday, November 19, 2007 11:22AM - 11:35AM |
GC.00005: Inertial jets Arnaud Antkowiak, Emmanuel Villermaux We investigate the dynamics and ultimate fragmentation of jets formed from the sudden acceleration of a curved liquid gas interface. This configuration is generic of many natural or man made processes leading to drops via the formation of a concentrated jet (Antkowiak et al., \textit{J. Fluid Mech.} \textbf{577}, 2007). Here, we establish the axial velocity distribution in the jet as a spatial analogue to the Frankel \& Weihs (1985) similarity solution, and compare it successfully to PIV measurements made inside the jet itself. The stability of this original base flow is made accounting for the influence of the deforming substrate on the perturbation dynamics, and assessed by the observed jet radius modulations. As an outcome, the link between these predictions and the liquid jet fragmentation is discussed. This solution is a step forward from the classical Plateau-Rayleigh treatment of quiescent liquid jets, and a new paradigm for impulsively formed liquid jets. [Preview Abstract] |
Monday, November 19, 2007 11:35AM - 11:48AM |
GC.00006: 1D modelling of very viscous dripping flows with surface tension Yvonne Stokes, Ernie Tuck, Christopher Voyce, Bronwyn Bradshaw-Hajek Honey dripping from an upturned spoon is an everyday example of a flow that extends and breaks up into drops. Such flows have been of interest for over 300 years, attracting the attention of Plateau and Rayleigh among others. Ink-jet printing has motivated considerable interest in recent times. Nevertheless aspects of these flows are still not fully understood. One that has been relatively unexplored is the influence of initial conditions on the evolution of a drop and filament and the final breakup. We consider a drop of very viscous fluid hanging beneath a solid boundary, similar to honey dripping from a spoon. Potentially, gravity, surface tension and inertia all play a role. We here focus on 1D modelling including gravity and surface tension but neglecting inertia which has little effect for some time. The inclusion of surface tension in a 1D model presents a challenge, since the model breaks down at the very bottom of the drop. We present a method for solving the outer problem. [Preview Abstract] |
Monday, November 19, 2007 11:48AM - 12:01PM |
GC.00007: Unconditional jetting Alfonso M. Ganan-Calvo It is well known that steady capillary jetting of a fluid dispersed into another immiscible continuum fluid phase is possible when surface tension forces are overcome by either inertia or viscous forces, depending on the flow Reynolds number. In terms of stability, it is necessary that the upstream component of the propagation speed of perturbations be smaller than the downstream convective jet velocity. The parametrical realm of the existence of capillary jetting is limited by the Capillary number as functions of the Reynolds number and the fluid properties ratios. These critical conditions are obtained when the so called upstream marginal stability velocity is set to zero. A detailed study of parametrical windows for steady capillary jetting reveals two distinguished, striking limits where the upstream marginal stability velocity is always positive (no signal is propagated upstream) independently of the issued liquid flow rate. In these rather ample limits, where the jet does not undergo the usual dripping-jetting transition, either the jet can be made arbitrarily thin (yielding droplets of any imaginably small size), or its bulk speed can be made zero. Those conditions are here analytically and experimentally analyzed for their particular technological relevance. [Preview Abstract] |
Monday, November 19, 2007 12:01PM - 12:14PM |
GC.00008: Automating Digital Holographic Spray Analysis David Olinger, Khaled Sallam The physics of the breakup of liquid jets are of interest in many disciplines. Primary breakup along the liquid jet surface and the secondary breakup in the dense spray region drive the droplets' size and velocity distributions. Experimental techniques, such as shadowgraphy and Phase Doppler Interferometry, can be inadequate due to the limited depth of field or the restriction to spherical droplets. Holographic diagnostics have been successful in probing this dense region, providing 3D size and velocity measurements. Current digital holographic reconstruction has solved most of the problems associated with chemical development of holographic plates; however, the current methods of holographic data reduction using visual focusing is time consuming and subject to human error. The objective of the present research is to automate the process of identifying, locating, and measuring liquid droplets in the dense spray region near the liquid core. Edge detection and dynamic filtering are tested on droplets in ``cluttered'' holograms in the near injector region of an aerated liquid jet in subsonic crossflow. The results include automatic identification of the droplets' locations and velocities using particle tracking techniques. [Preview Abstract] |
Monday, November 19, 2007 12:14PM - 12:27PM |
GC.00009: Role of the channel geometry on the bubble pinch-off in flow-focusing devices Wim van Hoeve, Benjamin Dollet, Jan-Paul Raven, Philippe Marmottant, Michel Versluis The role of the orifice geometry in the production of bubbles by flow focusing of a gas and a liquid in an orifice of rectangular cross-section is investigated. It is experimentally shown that the aspect ratio of the orifice dramatically influences the duration of bubble breakup, characterized by a slow linear 2D collapse, followed by a final fast 3D pinch-off. A stability analysis predicts that the 2D collapse is always stable, whereas the 3D pinch-off is always unstable. The ultimate stage of the pinch- off is recorded by high-speed imaging, yielding a scaling $w_m \sim\tau^{1/3}$ between the neck width $w_m$ and the time $\tau$ before breakup, which indicates that breakup is driven solely by the inertia of both gas and liquid, and that it is not a capillary process. The presented study of the bubble breakup shows that elongated rectangular orifices favors high monodispersity, whereas the highest frequency of bubble production is achieved in square orifices. [Preview Abstract] |
Monday, November 19, 2007 12:27PM - 12:40PM |
GC.00010: A numerical study of bubble pinch-off Shaoping Quan, Jinsong Hua The buoyancy-driven less viscous bubble pinch-off immersed in another more viscous fluid is numerically studied. The radius of the neck region is found to decrease in a power law mode $R \sim \tau ^\alpha$, and the exponent $\alpha$ is between $0.5-1.0$ for a large range of the fluids' properties. These are in a good agreement with the previous available investigations. The effect of the liquid viscosity on the bubble pinch-off is investigated, and it is found that the viscosity has significant effect on the dynamics of the bubble pinch-off. A higher viscosity in the continuous phase results in slower pinch-off and a larger bubble. Then, we find that the surface tension tends to retard the pinch-off process and to generate large bubble. Finally, it is showed that, unlike the viscosity and surface tension, the density has minimal effect on the necking process and the bubble volume. Previous experimental results showed that there is a sharp change for the exponent for a viscosity of 20-70cP, while our numerical prediction shows a rather smooth transition and the transition happens at a viscosity bigger than 68cP which corresponds the Archimedes (Ar) number of $\mathcal {O}(1)$. As the viscosity and surface tension affect the exponent in a significant way while density does not, we could explain that the difference is due to the variation of the surface tension coefficients in the experiments. [Preview Abstract] |
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