Full fitting analysis of the relative intermediate form factor measured by neutron spin echo

This paper describes the dynamics of a water-in-oil microemulsion from the dilute to the dense droplet region. Using the relative intermediate form factor method for neutron spin echo data analyses [M. Nagao, H. Seto, Phys. Rev. E 78 (2008) 011507], the shape and structure fluctuations of a droplet microemulsion are successfully decoupled. In the previous paper, we used the first cumulant analysis of the shape fluctuation model, while the full fitting form of the same model is applied in this paper. The final results of the fittings using the first cumulant approximation and the full form of the model are almost identical, and therefore, the validity of the method is strengthened. The estimated bending modulus of the surfactant membrane, κ, is basically the same, within the experimental errors, in the previous and present results. The κ is not affected much by an increase of the droplet concentration. A clear dynamic slowing down of the water droplets is highlighted at the length scale corresponding to the inter-droplet distance from the structure fluctuation analysis.     

Vaporization and combustion in three-dimensional droplet arrays

The quasi-steady vaporization and combustion of multiple-droplet arrays is studied numerically. Utilizing the Shvab–Zeldovich formulation, a transformation of the governing equations to a three-dimensional Laplace’s equation is performed, and the solution to Laplace’s equation is obtained numerically to find the effects of droplet interactions in symmetric, multiple-droplet arrays. Vaporization rates, flame surface shapes, and flame locations are found for different droplet array configurations and fuels. The number of droplets, the droplet arrangement within the arrays, and the droplet spacing within the arrays are varied to determine the effects of these parameters. Computations are performed for uniformly spaced three-dimensional arrays of up to 216 droplets, with center-to-center spacing ranging from 3 to 25 droplet radii. As a result of the droplet interactions, the number of droplets and relative droplet spacing significantly affect the vaporization rate of individual droplets within the array, and consequently the flame shape and location. For small droplet spacing, the individual droplet vaporization rate decreases below that obtained for an isolated droplet by several orders of magnitude. A similarity parameter which correlates vaporization rates with array size and spacing is identified. Individual droplet flames, internal group combustion, and external group combustion can be observed depending on the droplet geometry and boundary conditions.     

Determination of Size,Evaporation Rate and Freezing of Water Droplets using light scattering and radiation pressure

Two independent optical diagnostic techniques for studying the evaporation and freezing of optically levitated droplets are described. In the first technique the size of the droplet is determined by evaluation of the fringe spacing of the light scattered in the forward hemisphere at a scattering angle of 45°. The other technique evaluates the oscillations of optically leviated droplets caused by fluctuations in the radiation pressure. The frequency of these fluctuations is a direct measure for the change of radius with time. In both methods the signals change drastically when freezing of the droplet occurs. Hence the moment of freezing can easily be detected.     

Transient convective burning of interactive fuel droplets in single-layer arrays

The transient convective burning of n-octane droplets interacting within single-layer arrays in a hot gas flow perpendicular to the layer is studied numerically, with considerations of droplet surface regression, deceleration due to the drag of the droplets, internal liquid motion, variable properties, non-uniform liquid temperature and surface tension. Infinite periodic arrays, semi-infinite periodic arrays with one row of droplets (linear array) or two rows of droplets, and finite arrays with nine droplets with centers in a plane are investigated. All arrays are aligned orthogonal to the free stream direction. This paper compares the behavior of semi-infinite periodic arrays and finite arrays with the behavior of previously studied infinite periodic arrays. Furthermore, it identifies the critical values of the initial Damköhler number for bifurcations in flame behavior at various initial droplet spacing for all these arrays. The initial flame shape is either an envelope flame or a wake flame as determined by the initial Damköhler number, the array configuration and the initial droplet spacing. The critical initial Damköhler number separating initial wake flames from initial envelope flames decreases with increasing interaction amongst droplets at intermediate droplet spacing (when the number of rows in the array increases or the initial droplet spacing decreases for a specific number of rows in the array). In the transient process, an initial wake flame has a tendency to develop from a wake flame to an envelope flame, with the moment of wake-to-envelope transition advanced for the increasing interaction amongst droplets at intermediate droplet spacing. For the array with nine droplets with centers in a plane, the droplets at different types of positions have different critical initial Damköhler number and different wake-to-envelope transition time for initial wake flame.     

Temperature and fiber optic spectroscopy composition measurements of heated propanol–acetone droplets

Time-dependent temperatures and compositions within individual fiber-supported droplets initially from about 2–3 mm in diameter were investigated. In the experiments, droplets were composed of mixtures of 1-propanol and acetone. The droplets evaporated in room air, where the air was heated by placing an electrically heated coil underneath the droplets. The experiments employed thin optical fibers to carry light from a UV–vis light source into and out of a droplet. The time-dependent UV absorption spectrum of the liquid between the fiber ends was measured using a spectrometer coupled to one of the fibers. This spectrum yielded real-time information on the composition of the liquid. Droplet temperatures were simultaneously measured using a thermocouple that was immersed into the liquid. Results demonstrate that droplet evaporation follows a multi-stage process and that acetone is preferentially gasified from a droplet.     

Bessel驻波对椭球形液滴的声辐射转矩

在实际的声操控中,由于声辐射力、表面张力和重力的共同作用,液滴往往呈现出椭球的形状,在螺旋声场中会受到力矩的作用而发生转动。从声波的散射理论出发,根据部分波展开法求解得到了椭球形液滴在Bessel驻波场中的声散射系数,并给出了其受到的声辐射转矩的解析式。在此基础上,对椭球形不可压缩液滴和椭球形可压缩液滴分别进行数值计算。仿真结果表明,不可压缩液滴的声辐射转矩与声束半锥角的关系更密切,而可压缩液滴则更依赖于特定的频率;提升Bessel驻波场的阶数有利于增强声辐射转矩的峰值,但在中低频处较难对可压缩液滴产生明显的力矩。该研究结果预期对利用螺旋声场进行液滴的操控具有理论指导作用。      

Experimental analysis of shape deformation of evaporating droplet using Legendre polynomials

Experiments involving heating of liquid droplets which are acoustically levitated, reveal specific modes of oscillations. For a given radiation flux, certain fluid droplets undergo distortion leading to catastrophic bag type breakup. The voltage of the acoustic levitator has been kept constant to operate at a nominal acoustic pressure intensity, throughout the experiments. Thus the droplet shape instabilities are primarily a consequence of droplet heating through vapor pressure, surface tension and viscosity. A novel approach is used by employing Legendre polynomials for the mode shape approximation to describe the thermally induced instabilities. The two dominant Legendre modes essentially reflect (a) the droplet size reduction due to evaporation, and (b) the deformation around the equilibrium shape. Dissipation and inter-coupling of modal energy lead to stable droplet shape while accumulation of the same ultimately results in droplet breakup.     

Hot electrons produced from long scale-length laser-produced droplet plasmas

Microplasmas produced from 15 μm methanol droplets irradiated by 100 fs laser pulses in the intensity range 10¹⁴–10¹⁶ W cm^?2 are investigated via measurements of the hot electron temperature and x-ray yields under different conditions of intensity, polarization state, and plasma scale-length. The scale length of the drop-let plasma is increased with an intentional prepulse that is 10 ns ahead of the main pulse. Hot electron temperatures up to 48 keV have been measured at intensities of 2.5 × 10¹⁵W cm^?2 and the scaling of temperature as a function of intensity is determined for a long scale-length droplet plasma. The polarization and ellipticity dependence of the hard x-ray yield from the microdroplet plasmas are used to probe the shape of the droplet after irradiation by a prepulse.     

On the vibration spectra of vesicle-like droplets: The effects of membrane density fluctuations

The dynamics of vesicle-like droplets is studied within the Helfrich’s concept of interfacial elasticity. The droplet shape fluctuations are accompanied with the membrane density changes. As distinct from the previous theories, the (linearized) hydrodynamic and boundary equations contain inertial terms and are solved exactly. Using the continuity equation for the interface, the secular equation for the vibration frequencies is obtained. Its analysis results in the prediction of a couple of relaxation modes that exist for any finite compressibility of the membrane, and a higher frequency mode determined mainly by the membrane density and compressibility. This work was supported by the grant 1/4387/97 (VEGA, Slovak Republic).     

对流速度对燃料液滴火焰形态及燃烧的影响

考虑气相非稳态及液滴内部环流,建立运动液滴非稳态蒸发燃烧模型.模型采用动网格方法精确追踪液滴表面位置,采用守恒方程组更新液滴表面边界条件.根据单步全局化学反应机理,仿真研究正庚烷燃料液滴在不同对流速度下的火焰形态及燃烧.结果表明:运动液滴内部环流使液滴内部低温区向环流中心移动.当液滴运动速度大于某临界值后,火焰形态由包覆火焰转变为尾迹火焰.包覆火焰的富燃区范围、高温区范围及燃烧速率明显较尾迹火焰大;包覆火焰的液滴表面温度及表面蒸发流率分布也明显不同于尾迹火焰.     

Real-time observation of single-molecule fluorescence in microdroplet streams

We report real-time observation of fluorescence bursts from individual Rhodamine 6G molecules in streams of microdroplets (peak signal-to-noise ratios, approximately 30) whose trajectories are constrained with a linear electric quadrupole. This approach offers a reasonable dynamic range in droplet size (3- 12-microm diameter) with <1% shot-to-shot size fluctuations and sensitivity comparable with that of droplet levitation techniques with at least 10(3) higher analysis rates. Applications to the study of single-molecule microcavity effects and stimulated emission are discussed.     

Absorption of external thermal radiation in asymmetrically illuminated droplets

A theoretical model of thermal radiation absorption in semi-transparent droplets at the surface and inside a fuel spray is presented. Asymmetry of droplet illumination is taken into account. Results of Mie calculations of thermal radiation absorption inside large spherical droplets illuminated from a hemisphere are presented. Simple approximations for the angular and radial dependencies of the absorbed radiation power are suggested. These approximations are generalisations of the approximations suggested earlier by the authors for the case of symmetric illumination of droplets. They predict the results close to those which follow from the Mie calculations. Results of approximate calculations for a typical diesel fuel droplet at the periphery of the spray are presented. As in the case of symmetrical droplet illumination, an increased absorption of thermal radiation in the central area of the droplet is predicted. Also, at the illuminated side of the droplet, the absorption of radiation in a thin layer near the surface of the droplet is predicted, as in the case of symmetrical droplet illumination. Absorption of radiation in the central area of the droplet is related to the contribution of radiation in the spectral ranges of semi-transparency. The maximum of radiation absorption near the droplet surface is linked to the contribution of radiation in the vicinity of the diesel fuel absorption peak .     

壁面静止水滴冻结过程形状变化

低温表面上的液滴冻结时会形成具有尖顶的形状。针对这一现象开展了理论与实验研究,建立了新的动态曲形相界面模型用来模拟水滴冻结过程中的形状变化。模型考虑重力和成核再辉效应的影响,将冻结过程中的冰水相界面近似为球冠形曲面,并在三相点处引入动态生长角和直角关系。对壁面上20μL静止水滴进行了冻结实验,记录水滴三相点高度的演化过程,以此拟合得到了其随时间变化的关联式,基于该关联式求解理论模型,得到了水滴最终冻结形状。模拟结果与实验结果在水滴初始轮廓、成核再辉轮廓和最终冻结轮廓以及冻结时间上均吻合良好。曲面模型的计算结果表明,固液相界面上不同位置处的冻结速率不同;随着相界面向上推移,冻结速率逐渐减小。     

Determination of temperature and concentration of a vapor–gas mixture in a wake of water droplets moving through combustion products

Characteristic temperatures and concentrations of a vapor–gas mixture in a wake of water droplets moving through combustion products (initial temperature 1170 K) were determined using the Ansys Fluent mathematical modeling package. We investigated two variants of motion: motion of two droplets (with sizes from 1 mm to 3 mm), consecutive and parallel, and motion of five staggered droplets. The influence of the relative position of droplets and also of distances between them (varied from 0.01 mm to 5 mm) on temperatures and concentrations of water vapor was established. The distances determine the relation between the evaporation areas and the total volume occupied by a droplet aggregate in the gas medium. The results of modeling for conditions that take into account vaporization on the droplet surface at average constant values of evaporation rate and also with consideration of the change in the latter, depending on the droplet temperature field, are compared. We determined conditions under which the modeling results are comparable for the assumption of a constant vaporization rate and with regard to the dependence of the latter on temperature. The earlier hypothesis on formation of a buffer vapor layer (“thermal protection”) around a droplet, which decreases the thermal flow from the external gas medium, was validated.     

Collisional dynamics of symmetric two-dimensional quantum droplets

The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross−Pitaevskii equation in two dimensions by including a logarithmic correction term in the usual contact interaction. We find the merging droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets. With increasing collision momentum the colliding droplets may separate into two, or even more, and finally into small pieces of droplets. For these dynamical phases we manage to present boundaries determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode. A stability peak for the existence of droplets emerges at the critical particle numberN_c ≃ 48 for the quasi-Gaussian and flat-top shapes of the droplets.     

The Coulomb instability of charged microdroplets: dynamics and scaling

The stability and disintegration dynamics of evaporating highly charged liquid droplets from ethylene glycol and glycerol is investigated by ultrafast microscopy and analyzed as a function of temperature and droplet size. In the moment of instability the droplets have deformed to elongated spindle like shapes from which pairs of opposite jets of highly charged liquid are emitted. The thickness of the jets and the shape of the deformed droplet are remarkably insensitive to the size and viscosity of the unstable droplet, while the speed of disintegration is found to scale with a power law for both variables, the exponent being close to 3/2.     

Parametric resonance of optically trapped aerosols

The Brownian dynamics of an optically trapped water droplet are investigated across the transition from over- to underdamped oscillations. The spectrum of position fluctuations evolves from a Lorentzian shape typical of overdamped systems (beads in liquid solvents) to a damped harmonic oscillator spectrum showing a resonance peak. In this later underdamped regime, we excite parametric resonance by periodically modulating the trapping power at twice the resonant frequency. The power spectra of position fluctuations are in excellent agreement with the obtained analytical solutions of a parametrically modulated Langevin equation.     

Droplets in two-dimensional Ising and Potts models

Droplets on a wall and droplets around a nucleus in the center of the lattice are studied in the two-dimensional Ising and three-state Potts models using Monte Carlo techniques. Finite-size effects are discussed by applying a scaling argument and by relating the shape of a droplet to a random walk.     

Absorption and velocity dispersion due to crystallization and melting of emulsion droplets

The influence of droplet crystallization and melting on the ultrasonic properties of oil-in-water emulsions has been investigated. The ultrasonic velocity and attenuation were measured in a series of 3 wt% n-hexadecane-in-water emulsions as a function of frequency (0.3–4 MHz), droplet diameter (0.4 and 1 μm) and temperature (0–25°C). The emulsified n-hexadecane crystallized at about 5°C due to supercooling effects and melted at about 18°C. As solid and liquid n-hexadecane have significantly different ultrasonic properties, an appreciable change in the velocity and attenuation is observed during the phase transition. This behaviour is modified significantly in systems where the emulsion droplets are partially crystalline because the temperature fluctuations associated with the ultrasonic wave can perturb the phase equilibria solid liquid causing excess attenuation and velocity dispersion. The magnitude of this effect depends on the ultrasonic frequency and the average droplet size.