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Register a new userSub-critical asymmetric Rayleigh breakup of a charged drop induced by finite amplitude perturbations in a quadrupole trap
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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 superimposed over the center-of-mass oscillations. The shape oscillations result in sufficient deformations to act as triggers for the onset of instability well below the Rayleigh limit (a subcritical instability). At the same time, the center-of-mass oscillations which are out of phase with the applied voltage, lead to an asymmetric breakup such that the Rayleigh fission occurs upwards via the ejection of a jet at the pole of the deformed drop. As an important application, it follows from corollarial reasoning that the nanodrop generation in electrospray devices will occur, more as a rule rather than as an exception, via asymmetric, subcritical Rayleigh fission events of micro drops due to inherent directionality provided by the external electric fields.
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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.
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 (recorded at 100-130 thousand Frames Per Second (fps)). It is observed that the drop surface oscillates in sphere-prolate-sphere-oblate (SPSO) mode and seldom in the sphere-prolate-sphere (SPS) mode depending on the intricate interplay of various forces due to charge(q), the intensity of applied field ($Lambda$) and shift of the droplet from the geometric center of the trap ($z_{shift}$). The Fast Fourier Transformation (FFT) analysis shows that the droplet oscillates with the forced frequency irrespective of the type of the applied waveform. While in the sinusoidal case, the nonlinearities are significant, in the square and ramp potentials, there is an admittance of all the harmonic frequencies of the applied potential. Interestingly, the breakup characteristics of a critically charged droplet is found to be unaffected by the type of the applied waveform. The experimental observations are validated with an analytical theory as well as with the Boundary Integral (BI) simulations in the potential flow limit and the results are found to be in a reasonable agreement.
Understanding the mechanics of detrimental convective instabilities in drying polymer solutions is crucial in many applications such as the production of film coatings. It is well known that solvent evaporation in polymer solutions can lead to Rayleigh-Benard or Marangoni-type instabilities. Here we reveal another mechanism, namely that evaporation can cause the interface to display Rayleigh-Taylor instabilities due to the build-up of a dense layer at the air-liquid interface. We study experimentally the onset time ($t_p$) of the instability as a function of the macroscopic properties of aqueous polymer solutions, which we tune by varying the polymer concentration ($c_0$), molecular weight and polymer type. In dilute solutions, $t_p$ shows two limiting behaviors depending on the polymer diffusivity. For high diffusivity polymers (low molecular weight), the pluming time scales as $c_0^{-2/3}$. This result agrees with previous studies on gravitational instabilities in miscible systems where diffusion stabilizes the system. On the other hand, in low diffusivity polymers the pluming time scales as $c_0^{-1}$. The stabilizing effect of an effective interfacial tension, similar to those in immiscible systems, explains this strong concentration dependence. Above a critical concentration, $hat{c}$, viscosity delays the growth of the instability, allowing time for diffusion to act as the dominant stabilizing mechanism. This results in $t_p$ scaling as $( u/c_0)^{2/3}$.
We present mesoscale numerical simulations of Rayleigh-Benard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration Phi_0 is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux. In marked contrast, emulsions exhibit a non-steady dynamics with fluctuations in the heat flux. In this paper, we aim at the characterisation of such non-steady dynamics via detailed studies on the time-averaged heat flux and its fluctuations. To understand the time-averaged heat flux, we propose a side-by-side comparison between the emulsion system and a single-phase (SP) system, whose viscosity is constructed from the shear rheology of the emulsion. We show that such local closure works well only when a suitable degree of coarse-graining (at the droplet scale) is introduced in the local viscosity. To delve deeper into the fluctuations in the heat flux, we propose a side-by-side comparison between a Newtonian emulsion and a non-Newtonian emulsion, at fixed time-averaged heat flux. This comparison elucidates that finite-size droplets and the non-Newtonian rheology cooperate to trigger enhanced heat-flux fluctuations at the droplet scales. These enhanced fluctuations are rooted in the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation function. The observed findings offer insights on heat transfer properties for confined systems possessing finite-size constituents.
This fluid dynamics video depicts the evolution of a suspension of paramagnetic colloids under the influence of a uniform, pulsed magnetic field. At low pulse frequencies, the suspension condenses into columns which decompose via a Rayleigh-Plateau instability. At high pulse frequencies, the suspension forms a kinetically arrested, system spanning network. We demonstrate the degeneration of the Rayleigh-Plateau instability with increasing pulse frequency.
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