Evidence of the harmonic Faraday instability in ultrasonic atomization experiments with a deep, inviscid fluid

A popular method for generating micron-sized aerosols is to submerge ultrasonic (ω~MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (ω/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by increasing the driving amplitude of the oscillator, and that this effect becomes more pronounced for large driving frequencies. It is shown that these observations are consistent with a transition from droplets associated with subharmonic (ω/2) capillary waves to harmonic (ω) capillary waves induced by larger driving frequencies and amplitudes, as predicted by a stability analysis of the capillary waves.     

A practical method for diameter,number density and material characterization of 40–90 µm size droplets by stimulated Raman scattering

We demonstrate that the technique of Stimulated Raman Scattering (SRS) is a practical method for the simultaneous characterization of diameter, number density and constituent material of microsize droplets. The method is applicable to all Raman active materials and to droplets with a diameter of at least 8 µm. Our experimental study was focused on water and ethanol monodisperse droplets in the diameter range of 40–90 µm. Results of a single laser pulse and multiple pulses are analyzed, indicating that the SRS method can diagnose droplets of mixed liquids and ensembles of polydisperse droplets.     

Monodisperse drop formation in square microchannels

The electrohydrodynamic instability of the interface between two liquids with different physical and electrical properties in plane Poiseuille flow is used to form monodisperse droplets in a square channel. The drop size and formation rate are controlled by simply controlling the flow rates and the amplitude of the electric field applied across the channel.     

Numerical investigation of the effects of polydisperse water sprays on extinction conditions of counterflow methane non-premixed flames

Water, sprayed in the form of tiny droplets, has emerged as a potential fire suppressant after the halon compounds such as trifluorobromomethane (CF₃Br, Halon 1301) were banned by the Montreal protocol. The size distribution of the water droplet plays a crucial role in the effectiveness of the water spray in fire suppression. A numerical investigation of the influence of size distribution of a polydisperse water spray on extinction of counterflow diffusion flames is presented in this paper. This study uses laminar finite rate model with reduced CHEMKIN chemistry for numerical simulations. The discrete phase, namely the water spray, is simulated using Lagrangian Discrete Phase Modelling approach. In this work, the polydispersity of water spray is taken into account in the numerical simulation by a suitable Rosin–Rammler distribution. Results obtained from numerical simulation are validated with the experimental results reported in the literature. This study demonstrates that the representation of the polydisperse spray by a monodisperse spray (with droplet diameter same as the SMD of the polydisperse spray) in numerical simulations is not always justified and it leads to deviation from the experimental results. The effects of number mean diameter and spread parameter on the efficacy of flame suppression are investigated for polydisperse sprays. A comprehensive comparison is done between the effectiveness of monodisperse and polydisperse water sprays. An optimum droplet diameter is obtained for monodisperse sprays for which the effectiveness of the spray is maximum. The effects of evaporation Damköhler number and Stokes number of water droplets on flame suppression have also been explained.     

Thermodynamically stable pickering emulsions

We show that under appropriate conditions, mixtures of oil, water, and nanoparticles form thermodynamically stable oil-in-water emulsions with monodisperse droplet diameters in the range of 30-150 nm. This observation challenges current wisdom that so-called Pickering emulsions are at most metastable and points to a new class of mesoscopic equilibrium structures. Thermodynamic stability is demonstrated by the spontaneous evolution of binary droplet mixtures towards one intermediate size distribution. Equilibrium interfacial curvature due to an asymmetric charge distribution induced by adsorbed colloids explains the growth of emulsion droplets upon salt addition. Moreover, the existence of a minimal radius of curvature with a concomitant expulsion of excess oil is in close analogy with microemulsions.     

Evaluation method for radiative heat transfer in polydisperse water droplets

Simplifications of the model for nongray radiative heat transfer analysis in participating media comprised of polydisperse water droplets are presented. Databases of the radiative properties for a water droplet over a wide range of wavelengths and diameters are constructed using rigorous Mie theory. The accuracy of the radiative properties obtained from the database interpolation is validated by comparing them with those obtained from the Mie calculations. The radiative properties of polydisperse water droplets are compared with those of monodisperse water droplets with equivalent mean diameters. Nongray radiative heat transfer in the anisotropic scattering fog layer, including direct and diffuse solar irradiations and infrared sky flux, is analyzed using REM². The radiative heat fluxes within the fog layer containing polydisperse water droplets are compared with those in the layer containing monodisperse water droplets. Through numerical simulation of the radiative heat transfer, polydisperse water droplets can be approximated by using the Sauter diameter, a technique that can be useful in several research fields, such as engineering and atmospheric science. Although this approximation is valid in the case of pure radiative transfer problems, the Sauter diameter is reconfirmed to be the appropriate diameter for approximating problems in radiative heat transfer, although volume-length mean diameter shows better accordance in some cases. The CPU time for nongray radiative heat transfer analysis with a fog model is evaluated. It is proved that the CPU time is decreased by using the databases and the approximation method for polydisperse particulate media.     

水滴烧蚀多脉冲激光推进性能

 用实时的推力测试方法研究了水滴烧蚀模式多脉冲TEA CO2激光推进的推进性能。用纹影法研究了伴随水滴烧蚀产生的激波等流场变化过程。多脉冲激光推进的比冲和冲量耦合系数等性能参数随激光脉冲重复频率的变小和脉冲数目的增加而逐渐下降。与激光传输相反和相同方向的激波传播最大速度分别为10 km/s和7 km/s。与纹影法结果同步获得的推力曲线表明：汽化过程对推力的形成过程贡献最大,激波也对推力的形成过程有一定贡献。     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998     

Reconstruction of Real Size Distributions Hidden in Phase-Doppler Anemometry results obtained form droplets of inhomogeneous liquids

Real process fluids such as emulsions and suspensions are optically absordent as well as inhomogeneous. Using phase-Doppler anemometry (PDA)for investigating the spray cone, the inhomogeneites have led to incomprehensible size distributions. In this paper, solutions of instant coffee and condensed milk, representing typical process fluids, were chosen for PDA measurements in comparison with PDA applied to water droplets with the same atomization process in order to clarify the reasons for the measured broad size distributions. By applying PDA to monodisperse droplets and to “monodisperse” and real polydisperse sprays consisting of such fluids, it is shown how the measured size distributions arise, Based on this knowledge, the real size distributions are reconstructed and compared with that of water atomization. Therefore, PDA can in future also be applied to real process fluids, and process control, based on the information provided by PDA, is coming nearer.     

大气重力波产生中纬电离层不均匀体的理论

研究中纬电高层Ｆ区大尺度不均匀休的基本性质及其与大气重力波的关系。分析了等离子体Ｐｅｒｋｉｎｓ不稳定性的非线性发展，发现这种不稳定性饱和在很小的幅度上。讨论了Ｐｅｒｋｉｎｓ不稳定性与重力波的耦合，表明重力波能触发中纬电离层Ｆ区等离子体不稳定性。由重力波触发的等离子体不稳定性可能演变成大幅度的波形结构，空间和时间调制的不均匀体理论揭示了大尺度中纬电离层不均匀体的产生机制。 关键词：     

电离层等离子体交换不稳定性与大气重力波的耦合

研究了赤道电离层等离子体交换不稳定性和大气重力波的耦合性质。如果没有外部扰动的影响，非线性效应使交换不稳定性饱和在一个很小的幅度上。在适当的条件下，重力波能触发交换不稳定性。如果重力波的幅度足够大，所触发的交换不稳定性的扰动幅度能达到５０％甚至更大，产生等离子体泡，本文的理论揭示了电离层大尺度扩展Ｆ的产生机制，可以解释许多重要的电离层观测现象。 关键词：     

A high-order nonlinear envelope equation for gravity waves in finite-depth water

A third-order nonlinear envelope equation is derived for surface waves in finite-depth water by assuming small wave steepness, narrow-band spectrum, and small depth as compared to the modulation length. A generalized Dysthe equation is derived for waves in relatively deep water. In the shallow-water limit, one of the nonlinear dispersive terms vanishes. This limit case is compared with the envelope equation for waves described by the Korteweg-de Vries equation. The critical regime of vanishing nonlinearity in the classical nonlinear Schrödinger equation for water waves (when kh ≈ 1.363) is analyzed. It is shown that the modulational instability threshold shifts toward the shallow-water (long-wavelength) limit with increasing wave intensity.     

Bulk heterogeneous plane waves propagation through viscoelastic plates and stratified media with large values of frequency domain

This paper introduces the bulk heterogeneous waves concept into the well known Thomson-Haskell method for computing transmission/reflection coefficients through stratified media. If one of the layers is absorbing, bulk heterogeneous waves are generated at interfaces with other layers and the generalized Snell's laws for heterogeneous modes have to be used. This method was reported to be unstable for large values of frequency domain (FD), the product of the frequency and the medium thickness. The new expression for the matrix transfer between interfaces given in this paper is tested with large values of FD, without showing instability. Large values of FD imply significant effects of attenuation, which is frequency dependent. One particular effect is the interface transmission of modes beyond the limit angle if it is defined with the homogeneous waves concept. This is shown with acquired and simulated waveforms, after transmission through an epoxy layer. Waveforms transmitted by adhesive joints are also presented.     

Electrospray with electrostatic precipitator enhances fine particles collection efficiency

Electrospray was combined with an electrostatic precipitator (ESP) to enhance the collection efficiency of monodisperse nanometer-sized particles. The electrospray of deionized water produced water droplets with sizes ranging from 10 to 300 μm. The combination of the ESP with the electrospray enhanced collection of particles by 21–36% depending on the particle size. The combination of the ESP and the electrospray was also found to reduce the energy consumption of the ESP.     

Nonlinear instability of elementary stratified flows at large Richardson number

Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319-350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin-Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. (c) 2000 American Institute of Physics.     

On the theory of the noncoalescence effect for oppositely charged droplets

A theory is proposed and numerical simulation is conducted for oppositely charged mutually approaching droplets of an aqueous electrolytic solution in silicon oil. It is shown that at small distances between droplets, a conductive bridge leveling out the potentials of the droplets may form between them due to electrohydrodynamic instability of the equilibrium surface of one of the droplets. As a result, the droplets start to repel each other and may drift apart without coagulation. The proposed theory is confirmed by the effect of nonconfluent droplets observed in experiments [W.D. Ristenpart, J.C. Bird, A. Belmonte, et al., Nature 461, 377 (2009)].     

Auto-ignition of a polydisperse fuel spray

In the present paper, the effect of fuel spray polydispersity on the auto-ignition process in a fuel cloud is considered. In many engineering applications it is common practice to relate to the actual polydisperse spray as being equivalent to a monodisperse spray with all droplets therein having some average diameter. In combustion systems, the Sauter mean diameter (SMD) is frequently used for this purpose; it is based on the ratio between the total droplet volume and the total droplet surface area of all the droplets in the polydisperse spray. The main purpose of the current work is to examine qualitatively the dynamics of ignition of a truly polydisperse spray in a combustible gas medium and compare it with the dynamics of an equivalent monodisperse spray based on the SMD. Since the system of governing equations represents a multi-scale problem the method of integral manifolds is applied in order to extract the dynamical behavior. Preliminary computed results suggest that the use of the usual SMD-based monodisperse spray leads to quite a significant over-estimate of the ignition time. An alternative modified definition of the SMD, in which the overall liquid fuel volume is also conserved in the averaging process, reduces the discrepancy between the ignition time for the polydisperse spray and that of the equivalent monodisperse spray. However, it seems that some other sort of average droplet size needs to be determined to minimize the aforementioned discrepancy. These results highlight the care that must be exercised before dispensing with the behavior of the actual polydisperse spray in favor of that of an equivalent monodisperse spray, even at the expense of complexity.     

Unstable Surface Waves in Running Water

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that the free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves is demonstrated at all wave numbers. We show the linear instability of small nontrivial waves that appear after bifurcation at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of free-surface water waves.     

Extreme waves statistics for the Ablowitz-Ladik system

We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz-Ladik (AL) system. Modulation instability depends on one free parameter h that has the meaning of the coupling between the nodes on the lattice. For strong coupling h ? 1, the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical nonlinear Schrödinger equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak h ～ 1, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called “fat tails” when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical nonlinear Schrödinger equation.     

Shape oscillations and stability of charged microdroplets

Classical Rayleigh theory predicts an instability of a surface charged liquid sphere, when the Coulomb energy E(C) exceeds twice the surface energy E(S). Previously, electrified liquid droplets have been found to disintegrate at a fissility X=E(C)/2E(S) well below one, however. We determine the stability of charged droplets in an electrodynamic levitator by observing the amplitude and phase of their quadrupolar shape oscillations as a function of the fissility. With this novel approach, which does not rely on an independent determination of the charge and surface tension of the droplets, we are able to confirm for the first time the Rayleigh limit of stability at X=1 for micrometer sized droplets of ethylene glycol.