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Register a new userFrequency selection in a gravitationally stretched capillary jet in the jetting regime
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A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency producing the most unstable jet is found to be highly dependent on the forcing amplitude. Taking benefit of the one-dimensional Eggers & Dupont (J. Fluid Mech., vol. 262, 1994, 205-221) equations, we investigate the case through nonlinear simulations and linear stability analysis. In the local framework the WKBJ formalism, established for weakly non-parallel flows, fails to capture the nonlinear simulation results quantitatively. However in the global framework, the resolvent analysis supplemented by a simple approximation of the required response norm inducing breakup, is shown to correctly predict the optimal forcing frequency at a given forcing amplitude and the resulting jet breakup length. The results of the resolvent analysis are found to be in good agreement with those of the nonlinear simulations.
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We study a liquid jet that breaks up into drops in an external co-flowing liquid inside a confining microfluidic geometry. The jet breakup can occur right after the nozzle in a phenomenon named dripping or through the generation of a liquid jet that breaks up a long distance from the nozzle, which is called jetting. Traditionally, these two regimes have been considered to reflect the existence of two kinds of spatiotemporal instabilities of a fluid jet, the dripping regime corresponding to an absolutely unstable jet and the jetting regime to a convectively unstable jet. Here, we present quantitative measurements of the dripping and jetting regimes, both in an unforced and a forced state, and compare these measurements with recent theoretical studies of spatiotemporal instability of a confined liquid jet in a co-flowing liquid. In the unforced state, the frequency of oscillation and breakup of the liquid jet is measured and compared to the theoretical predictions. The dominant frequency of the jet oscillations as a function of the inner flow rate agrees qualitatively with the theoretical predictions in the jetting regime but not in the dripping regime. In the forced state, achieved with periodic laser heating, the dripping regime is found to be insensitive to the perturbation and the frequency of drop formation remains unaltered. The jetting regime, on the contrary, amplifies the externally imposed frequency, which translates in the formation of drops at the frequency imposed by the external forcing. In conclusion, the dripping and jetting regimes are found to exhibit the main features of absolutely and convectively unstable flows respectively, but the frequency selection in the dripping regime is not ruled by the absolute frequency predicted by the stability analysis.
Despite their fundamental and applied importance, a general model to predict the natural breakup length of steady capillary jets has not been proposed yet. In this work, we derive a scaling law with two universal constants to calculate that length as a function of the liquid properties and operating conditions. These constants are determined by fitting the scaling law to a large set of experimental and numerical measurements, including previously published data. Both the experimental and numerical jet lengths conform remarkably well to the proposed scaling law. This law is explained in terms of the growth of perturbations excited by the jet breakup itself.
Harnessing fluidic instabilities to produce structures with robust and regular properties has recently emerged as a new fabrication paradigm. This is exemplified in the work of Gumennik et al. [Nat. Comm. 4:2216, DOI: 10.1038/ncomms3216, (2013)], in which the authors fabricate silicon spheres by feeding a silicon-in-silica co-axial fiber into a flame. Following the localized melting of the silicon, a capillary instability of the silicon-silica interface induces the formation of uniform silicon spheres. Here, we try to unravel the physical mechanisms at play in selecting the size of these particles, which was notably observed by Gumennik et al. to vary monotonically with the speed at which the fiber is fed into the flame. Using a simplified model derived from standard long-wavelength approximations, we show that linear stability analysis strikingly fails at predicting the selected particle size. Nonetheless, nonlinear simulations of the simplified model do recover the particle size observed in experiments, without any adjustable parameters. This shows that the formation of the silicon spheres in this system is an intrinsically nonlinear process that has little in common with the loss of stability of the underlying base flow solution.
High frequency thickness mode ultrasound is an energy-efficient way to atomize high-viscosity fluid at high flow rate into fine aerosol mists of micron-sized droplet distributions. However the complex physics of the atomization process is not well understood. It is found that with low power the droplet vibrates at low frequency (O[100 Hz]) when driven by high-frequency ultrasound (O[1 MHz] and above). To study the mechanism of the energy transfer that spans these vastly different timescales, we measure the droplets interfacial response to 6.6~MHz ultrasound excitation using high-speed digital holography. We show that the onset of low-frequency capillary waves is driven by feedback interplay between the acoustic radiation pressure distribution and the droplet surface. These dynamics are mediated by the Young-Laplace boundary between the droplet interior and ambient environment. Numerical simulations are performed via global optimization against the rigorously defined interfacial physics. The proposed pressure-interface feedback model is explicitly based on the pressure distribution hypothesis. For low power acoustic excitation, the simulations reveal a stable oscillatory feedback that induces capillary wave formation. The simulation results are confirmed with direct observations of the microscale droplet interface dynamics as provided by the high resolution holographic measurements. The pressure-interface feedback model accurately predicts the on-source vibration amplitude required to initiate capillary waves, and interfacial oscillation amplitude and frequency. The radiation pressure distribution is likewise confirmed with particle migration observations. Viscous effects on wave attenuation are also studied by comparing experimental and simulated results for a pure water droplet and 90% wt.- 10% wt. glycerol-water solution droplet.
The results of experimental and theoretical studies of the parametric decay instability of capillary waves on the surface of superfluid helium He-II are reported. It is demonstrated that in a system of turbulent capillary waves low-frequency waves are generated along with the direct Kolmogorov-Zakharov cascade of capillary turbulence. The effects of low-frequency damping and the discreteness of the wave spectrum are discussed.
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