Rayleigh instability that results in the breakup of a charged droplet, levitated in a quadrupole trap, has been investigated in the literature, but only scarcely. We report here asymmetric breakup of a charged drop, levitated in a loose trap, wherein, the droplet is stabilized at an off-center location in the trap. This aspect of levitation leads to an asymmetric breakup of the charged drop, predominantly in a direction opposite to that of gravity. In a first of its kind of study, we capture the successive events of the droplet deformation, breakup and relaxation of the drop after jet ejection using high speed imaging at a couple of hundred thousand frames per second. A pertinent question of the effect of the electrodynamic trap parameters such as applied voltage as well as physical parameters such as the size of the drop, gravity and conductivity on the characteristics of droplet breakup is also explored. A clear effect of the trap strength on the deformation (both symmetric and asymmetric) is observed. Moreover, the cone angle at the pole undergoing asymmetric breakup is almost independent of the applied field investigated in the experiments. All the experimental observations are compared with numerical simulations carried out using the boundary element method (BEM) in the Stokes flow limit. The BEM simulations are also extended to other experimentally achievable parameters. It is observed that the breakup is mostly field influenced, and not field induced. A plausible theory for the observations is reported, and a sensitive role of the sign of the charge on the droplet and the sign of the end cap potential, as well as the off-center location of the droplet in the trap.
The experimental time-lapse images of the breakup phenomenon of a charged droplet (diameter ~100-300 micro-m) levitated in an electrodynamic (ED) balance is reported. During the breakup process, a levitated charged droplet undergoes evaporation leading to a reduction in droplet size and increase in the corresponding surface charge density. As the surface charge density reaches to a critical value, known as the Rayleigh limit, the droplet undergoes breakup by forming a jet which further ejects highly charged progeny droplets. All the successive events of the droplet breakup process such as drop…
A charged droplet can be electrodynamically levitated in the air using a quadrupole trap by typically applying a sinusoidal electric field. When a charged drop is levitated it exhibits surface oscillations simultaneously building charge density due to continuous evaporation and subsequently undergoes breakup due to Rayleigh instability. In this work, we examined large-amplitude surface oscillations of a sub-Rayleigh charged drop and its subsequent breakup, levitated by various applied signals such as sine, square and ramp waveform at various imposed frequencies, using high-speed imaging (recor…
The breakup pathway of Rayleigh fission of a charged drop is unequivocally demonstrated by first of its kind, continuous, high-speed imaging of a drop levitated in an AC quadrupole trap. The experimental observations consistently exhibited asymmetric, sub-critical Rayleigh breakup with an upward (i.e. opposite to the direction of gravity) ejection of a jet from the levitated drop. These experiments supported by numerical calculations show that the gravity induced downward shift of the equilibrium position of the drop in the trap cause significant, large amplitude shape oscillations superimpose…
The breakup pathway of the Rayleigh fission process observed experimentally using high-speed imaging of a charged drop levitated in an AC quadrupole trap is shown to undergo asymmetric breakup by ejecting a jet in the upward direction ((i.e., opposite to the direction of gravity)). To explain this typical experimental observation, we carry out numerical calculations based on the boundary element method considering inertial droplets levitated electrodynamically using quadrupole electric fields. The simulations show that the gravity-induced downward shift in the equilibrium position of the drop …
Atomization of emulsion droplets is ubiquitous across a variety of application domains ranging from NextGen combustors to fabrication of biomedical implants. An understanding of the atomization mechanism in emulsions can result in a paradigm shift in customized designs of efficient systems, be it in energy or biotechnology sectors. In this paper, we specifically study the breakup mechanism of an evaporating contact-free (acoustic levitation) emulsion droplet (water-oil) under external heating. Three distinct regimes are observed during the lifespan of the evaporating droplet. Initially, the dr…
The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity $\hat{U}$ (negligible external forces) must be determined by the selection of normal modes with time-independent amplitude and wavelength (invariant modes, IMs). Both positive and negative group velocity IMs exist in ample ranges of the parameter domain (Weber and Ohnesorge numbers), which explains (i) the average breakup length independence on ambient conditions (long-term resonance), and (ii) its proportionality to the inverse of the spatial growth rate of the dominant…
We investigate the effect of electrical charge on the normal mode frequencies of electrically-charged diamagnetically levitated water droplets with radii 4.5-7.5 mm using diamagnetic levitation. This technique allows us to levitate almost spherical droplets and therefore to directly compare the measured vibrational frequencies of the first seven modes of the charged droplet with theoretical values calculated by Lord Rayleigh, for which we find good agreement.
We report development of generators for periodic, satellite-free fluxes of mono-disperse drops with diameters down to 10 mikrometers from cryogenic liquids like H_2, N_2, Ar and Xe (and, as reference fluid, water). While the breakup of water jets can well be described by Rayleigh's linear theory, we find jet regimes for H_2 and N_2 which reveal deviations from this behavior. Thus, Rayleigh's theory is inappropriate for thin jets that exchange energy and/or mass with the surrounding medium. Moreover, at high evaporation rates, axial symmetry of the dynamics is lost. When the drops pass into vac…
The experimental observation of D. Duft, T. Achtzehn, R. Muller, B. A. Huber, and T. Leisner, Nature 421, 128 (2003) on the sequential progression of the instability of a charged liquid drop points at the formation of a jet followed by the emission of progeny droplets as a crucial pathway of the Rayleigh fission process. In spite of considerable theoretical progress, a quantitative understanding of this breakup pathway through mathematical models has largely remained inconclusive. This limitation has mainly been due to the fact that the generally applied electrostatic boundary condition of the…
The question whether liquid atomization (or pulverization) resorts to instability dynamics (through refinements of Rayleigh-Plateau, Rayleigh-Taylor or Kelvin-Helmholtz mechanism) or to turbulent cascades similar to Richardson and Kolmogorov first ideas seems to be still open. In this paper, we report experimental evidences that both mechanisms are needed to explain the spray drop PDF obtained from an industrial nozzle. Instability of Rayleigh-Taylor kind governs the size of the largest droplets while the smallest ones obey a PDF given by a turbulent cascading mechanism resulting in a log-Lévy…
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 $τ_\mathrm{c} = \sqrt{ρr^3 / γ}$ 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 …
The early-time interface instabilities in high intensity (high Weber number and high Reynolds number) aero-breakup of a liquid drop are investigated by numerical simulations. A combined analysis based on simulation results and linear-instability theory show that both RT (Rayleigh-Taylor) and KH (Kelvin-Helmholtz) instabilities contributes the dominant disturbances originate from about the half way from the stagnation point to the equator. This is verified further with a specially modified simulation, which decreases the effect of KH instability while keeps other flow properties unchanged.
Bubbles under vibration can behave in unusual ways, e.g., moving downward against the force of buoyancy. While the bubble downward motion due to the Bjerknes force is well known at acoustic frequencies close to the bubble resonant frequency, these experiments demonstrate that these effects can be observed at relatively low frequencies as well. Experiments were performed in a thin, quasi-two-dimensional rectangular acrylic box partially filled with 20-cSt PDMS silicone oil with overlying ambient air. The apparatus was subjected to sinusoidal axial vibration that produced breakup of the gas-liqu…
The deformation and breakup of droplets in airflows is important in spray and atomisation processes, but the shear effect in non-uniform airflow is rarely reported. In this study, the deformation and breakup of droplets in a shear flow of air is investigated experimentally using high-speed imaging, digital image processing, and particle image velocimetry. The results show that in airflow with a strong shear effect, the droplet breakup exhibits unique features due to the uplift and stretching produced by the interaction between the deformed droplet and the shear layer. The breakup process can b…
Experimental and modelling study is presented for the effect of a wide range of liquid viscosities on the droplet impact on a smooth solid surface at atmospheric pressure. A non-monotonic variation of threshold between droplet deposition and splash was observed experimentally. Specifically, the critical Weber number separating deposition from splashing decreases and then increases with increasing the Ohnesorge number. The observations of splash in low viscosity region and receding breakup in high viscosity region were analyzed qualitatively from the perspectives of Kelvin-Helmholtz instability…
A spontaneous breakup of a liquid jet results in the formation of a chain of droplets, which is a daily observed phenomenon, such as in the raining process and under an open water-faucet. We here report inkjet printing experiments for the formation of droplets which are inconsistent with existing theories and thereafter propose a novel concept of surface area minimization to address the droplet-formation condition. The novel concept is also capable of predicting the formation of satellite and subsatellite droplets, which cannot be comprehended by the classic Rayleigh theory for the formation o…
With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation. This novel scheme can significantly reduce the computational cost while retaining the same accuracy as the original procedure. Our phase-field method is built on top of a direct numerical simulation solver, named AFiD (www.afid.eu) and open-sourced by our research group. It relies on a pencil distributed parallel strategy and a FFT-based Poisson solver. To deal…
