Water Droplets In Air Research Articles

Efficient second‐order time integration for single‐species aerosol formation and evolution

SUMMARYThe dynamics of a single‐species aerosol composed of droplets in air is described in terms of nucleation, evaporation, condensation, and coagulation processes. We present a comprehensive overview of the Euler–Euler formulation, which gives rise to a model in which fast nucleation that initiates aerosol droplets co‐exists with comparably slow condensation. The latter process is responsible for the subsequent growth of the droplets. To accurately represent the dynamical consequences of the fast nucleation process, while retaining numerical efficiency, a new second‐order time‐integration method for the nucleation, evaporation, and condensation processes is proposed and analyzed. The new time‐integration method takes the form of a ‘corrected Euler forward’ method. It includes rapid nucleation bursts and their possible cessation within a time step Δt. If the current nucleation burst persists for longer than the next time step, it is included fully, whereas cessation of the nucleation burst within the next Δt implies corrections to the effective rates in the algorithm. The identification of these two situations corresponds to the physical mechanism by which nucleation of a supersaturated vapor is halted because of the progressing condensation onto the already formed droplets. The resulting time‐integration method is shown to be second‐order accurate in time, whereas the computational costs per time step were found to be increased by less than 25% compared with the Euler forward method. The new method is also applied in combination with advective transport of the aerosol forming vapor to investigate a front of rapid nucleation. Adopting robust first‐order upwinding for the spatial discretization, we arrive at a flexible method that shows an overall first‐order convergence in Δt. For the full, spatially dependent system motivated by an aerosol of water droplets in air, the computational benefits of the new time‐integration method over the Euler forward scheme, are a factor of about 10 improvements in accuracy at a given Δt and a similar factor in computing time when keeping the same level of accuracy. Copyright © 2013 John Wiley & Sons, Ltd.

On the applicability of Drop Profile Analysis Tensiometry at high flow rates using an interface tracking method

In this work studies of growing water droplets in air are presented, with the aim to assess the applicability limit of the Droplet Profile Analysis Tensiometry (PAT). High inflow rates are applied for systems containing surfactants with high adsorption rates. However, under dynamic formation conditions, the measured surface tension values deviate from the theoretical values even for pure systems. Therefore, Computational Fluid Dynamics (CFD) is applied to gain detailed insight into the hydrodynamics of the growing drop. Since the flow is dominated by surface tension forces, an interface tracking approach is applied, which is able to capture the flow in a physically correct way. At high flow rates the inflow jet is not fully dissipated before approaching the free surface. Therefore, the pressure profile inside the drop is not uniform as is required in the derivation of the Gauss Laplace equation. The shape of the drop no longer represents the Gauss Laplace profile corresponding to the theoretical surface tension coefficient. As result we can confirm that the evaluation of surface tension by fitting to the Gauss Laplace Equation is not valid for dynamic droplet formations. Indications for future improvements of the evaluation procedure are provided.

Lattice Boltzmann simulation of water and gas flow in porous gas diffusion layers in fuel cells reconstructed from micro-tomography

The porous gas diffusion layers (GDLs) are key components in hydrogen fuel cells. During their operation the cells produce water at the cathode, and to avoid flooding, the water has to be removed out of the cells. How to manage the water is therefore an important issue in fuel cell design. In this paper we investigated water flow in the GDLs using a combination of the lattice Boltzmann method and X-ray computed tomography at the micron scale. Water flow in the GDL depends on water–air surface tension and hydrophobicity. To correctly represent the water–gas surface tension, the formations of water droplets in air were simulated, and the water–gas surface tension was obtained by fitting the simulated results to the Young–Laplace formula. The hydrophobicity is represented by the water–gas-fabric contact angle. For a given water–gas surface tension the value of the contact angle was determined by simulating the formations of water droplets on a solid surface with different hydrophobicity. We then applied the model to simulate water intrusion into initially dry GDLs driven by a pressure gradient in attempts to understand the impact of hydrophobicity on water distribution in the GDLs. The structures of the GDL were acquired by X-ray micro-tomography at a resolution of 1.7 microns. The simulated results revealed that with an increase in hydrophobicity, water transport in GDLs changes from piston-flow to channelled flow.

Rapid growth of cloud droplets by turbulence

Assuming perfect collision efficiency, we demonstrate that turbulence can initiate and sustain the rapid growth of very small water droplets in air even when these droplets are too small to cluster, and even without having to take gravity and small-scale intermittency into account. This is because the range of local Stokes numbers of identical droplets in the turbulent flow field is broad enough even when small-scale intermittency is neglected. This demonstration is given for turbulence which is one order of magnitude less intense than is typical in warm clouds but with a volume fraction which, even though small, is nevertheless large enough for an estimated a priori frequency of collisions to be ten times larger than in warm clouds. However, the time of growth in these conditions turns out to be one order of magnitude smaller than in warm clouds.

Numerical prediction of airfoil characteristics in a transonic droplet-laden air flow

A transonic airfoil moving in an air–water droplet two-phase flow is investigated numerically to study the effect of droplet size and volume fraction. The droplets we consider are in the size 1–100 μm and the volume fraction is in 0.01%–10%. A compressible two-fluid model is solved by the WAF-HLL scheme developed earlier by the authors which includes drag force, heat transfer, phase change, and droplet fragmentation of the droplets. The numerical results show that the droplet breakup layer can be extended to a later distance as large as about 60% of a chord length at the trailing edge. Also the droplets have made the shock wave dissolved in compression waves and the airfoil performance seriously deteriorated.

Uncertainty Analysis in the Numerical Simulation of the Air-Water Droplet Motion Through Drift Eliminators

This work presents an uncertainty study in the numerical simulation of the air-water droplet motion through three types of drift eliminators using the grid convergence index (GCI) method. The analysis of independence of the results with respect to the fineness of mesh is developed with special emphasis on the influence of the nondimensional sub-layer scaled distance. The coefficient of pressure drop and the droplet collection efficiency are numerically calculated. It may be concluded that using the GCI method leads to reliable numerical results, but it is also necessary to establish a sufficiently fine mesh near the walls.

Self-Arraying of Charged Levitating Droplets

Diamagnetic levitation of water droplets in air is a promising phenomenon to achieve contactless manipulation of chemical or biochemical samples. This noncontact handling technique prevents contaminations of samples as well as provides measurements of interaction forces between levitating reactors. Under a nonuniform magnetic field, diamagnetic bodies such as water droplets experience a repulsive force which may lead to diamagnetic levitation of a single or few micro-objects. The levitation of several repulsively charged picoliter droplets was successfully performed in a ~1 mm(2) adjustable flat magnetic well provided by a centimeter-sized cylindrical permanent magnet structure. Each droplet position results from the balance between the centripetal diamagnetic force and the repulsive Coulombian forces. Levitating water droplets self-organize into satellite patterns or thin clouds, according to their charge and size. Small triangular lattices of identical droplets reproduce magneto-Wigner crystals. Repulsive forces and inner charges can be measured in the piconewton and the femtocoulomb ranges, respectively. Evolution of interaction forces is accurately followed up over time during droplet evaporation.

Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging

In this paper, interferometric laser imaging droplet sizing—ILIDS—is applied to incipient cavitation in the wake of a marine propeller model with the aim to evaluate simultaneously bubbles velocity and diameter. Until now, the feasibility of this technique has been demonstrated especially in sprays of water droplets in air where an optimal light scattering is obtained thanks to the spherical shape and to the given relative refractive index. In the present setup, to allow simultaneous size–velocity measurements, a single camera is used and the object distance over lens diameter ratio is kept as small as possible, thus increasing the size measurement resolution. These details, together with the algorithms used for image analysis at each single frame and in two consecutive frames, allow deriving cavitation bubble size and velocity distributions in the propeller wake.

Measurements of Gaseous NH3 and Particulate NH4+ in the Atmosphere by Fluorescent Detection after Continuous Air-water Droplet Sampling

Phase partitioning of NH(subscript x) (gaseous NH3 and particulate NH4(superscript +)) in the atmosphere is crucial for the lifetime of NH(superscript x) during atmospheric transport. Reliable data for gaseous NH3 and NH4(superscript +) in aerosols are necessary to understand phase-partitioning and atmospheric cycles of NH(superscript x). A semi-continuous microflow analytical system (MF system) was developed for measuring gaseous NH3 and particulate NH4(superscript +) in the atmosphere. Two inlet lines were used to differentiate total amounts of NH(superscript x) and particulate NH4(superscript +) after gaseous NH3 were removed by phosphoric acid coated denuder from the sample air stream. Small water droplets were mixed with sample air and separated for liquid phase analysis in the MF system. The NH4(superscript +) concentration in the liquid was measured using sensitive fluorescence detection after reaction with ophthalaldehyde and sulfite. Based on air sampling at a flow rate of 1 L/min with stripping water at a flow rate of 100 μL/min, the MF system can analyze down to 3 nmol/m^3 of atmospheric NH3 concentration at 15 min intervals. Comparison with data based on the annular denuder method for gaseous NH3 and particulate NH4(superscript +) concentrations indicated reasonable agreement with the MF system. Field tests of the MF system for one month showed good agreement with NH4(superscript +) concentrations of fine particles collected daily on PTFE filters at the site. The MF system can monitor gaseous NH3 and particulate NH4(superscript +) concentrations at 30 min intervals, thereby providing short-term phase partitioning data of NH(superscript x).

Contactless Dielectrophoretic Handling of Diamagnetic Levitating Water Droplets in Air

Micromagnets have been reported to successfully levitate picoliter water droplets in air. Manipulation of levitating water droplets is a contamination-free alternative to digital-microfluidic labs-on-chip where droplets are handled in channels or on a substrate. An integrated electromagnetic hybrid device combining dielectrophoretic (DEP) forces to control the position of levitating droplets along a magnetic groove, is proposed. Diamagnetic forces are analytically computed with CADES while Comsol Multiphysics™ (FEM) is used for the DEP forces. Approximations of the `point dipole model' are compared to the Maxwell Stress Tensor method applied on the 3-D model. Based on these results, an electric sequence for polarizing planar parallel Indium Tin Oxide (ITO) electrodes is proposed in order to provide a stable and accurate control of the droplet microposition along the gap. The use of these electrodes as micro-conductors to produce variable magnetic fields for magnetophoretic droplet actuation is considered and compared to DEP actuation.

Laser trapping and picosecond time-resolved spectroscopy of water droplets in air: cavity-enhanced spontaneous emission of Ru(bpy)3Cl2

Whispering gallery mode (WGM) resonances were observed in the emission spectrum of Ru(bpy)(3)(2+) (bpy = 2,2'-bipyridine) in a single laser-trapped water droplet levitated in air. The emission decay profiles of Ru(bpy)(3)(2+) in the water droplets comprised fast and slow decay components. The emission lifetime of the slow decay component was independent of the diameter of the droplet, and corresponded to the value in a bulk aqueous solution. On the other hand, the emission lifetime of the fast decay component decreased with decreasing the droplet diameter, which could be ascribed to the cavity-enhanced spontaneous emission. The decrease in the emission lifetime of the fast decay component as a function of the droplet diameter was explained on the basis of cavity quantum electrodynamic (QED) effects. It was shown that the mode characteristic of WGM resonances and the enhancement factor of the radiative rate of Ru(bpy)(3)(2+) were controlled by the size of the water droplet.

An empirically validated model of the pressure within a droplet confined between plates at equilibrium for low Bond numbers

An analytical model is presented that describes the equilibrium pressure within a confined droplet for small Bond numbers without prior knowledge of the interface shape. An explicit equation for the pressure was developed as a function of the gap height, surface tension, and contact angle. This equation was verified empirically. The shape of the interface was found based on the pressure predicted by both the proposed model and a model commonly used in electrowetting on dielectric (EWOD) investigations. These shapes were compared against experimentally observed interfaces for aspect ratios between 3.5 and 18. The pressures and shapes predicted by the proposed model were at least an order of magnitude more accurate than those predicted with a more commonly used model. At an aspect ratio of 3.5, the average error in the predicted shape was almost 4%, but decreased below the experimental error at an aspect ratio of 6. An aspect ratio of 15 is required for an EWOD device to split water droplets in air. The error in the model pressure and its predicted interface in this case were approximately 0.3%. The analytical pressure model proposed here can be used to increase the accuracy of models of practical EWOD devices. Better accuracy can be attained for small aspect ratios by iteratively calculating pressure using the model proposed here.

A phase screen model for simulating numerically the propagation of a laser beam in rain

The method based on the generalisation of the phase screen method for a continuous random medium is proposed for simulating numerically the propagation of laser radiation in a turbulent atmosphere with precipitation. In the phase screen model for a discrete component of a heterogeneous 'air—rain droplet' medium, the amplitude screen describing the scattering of an optical field by discrete particles of the medium is replaced by an equivalent phase screen with a spectrum of the correlation function of the effective dielectric constant fluctuations that is similar to the spectrum of a discrete scattering component — water droplets in air. The 'turbulent' phase screen is constructed on the basis of the Kolmogorov model, while the 'rain' screen model utilises theexponential distribution of the number of rain drops with respect to their radii as a function of the rain intensity. Theresults of the numerical simulation are compared with the known theoretical estimates for a large-scale discrete scattering medium.

Underdamped modes in a hydrodynamically coupled microparticle system

When micron-sized particles are trapped in a linear periodic array, for example, by using optical tweezers, they interact only through the hydrodynamic forces between them. This couples the motion of the spheres and it has been predicted that an extended system might behave as an elastic medium that could support underdamped propagating waves. In practice, these underdamped modes can be observed only with massive particles in very stiff traps and very low viscosity fluids. We have been able to realize these conditions by trapping water droplets in air. Even with a system of just two particles we were able to observe the coupled oscillatory motion predicted: underdamping of the symmetric (collective) mode and overdamping of the asymmetric (relative) mode.

Nonlinear Mie theory for second-harmonic and sum-frequency scattering

We present a theory for second-order nonlinear light scattering from spherical particles using source waves of arbitrary frequency and direction based on a combination of linear Mie scattering and reciprocity theory. The theory presented in this work extends existing theory applied to second-harmonic scattering by allowing noncollinear excitation waves of unequal frequency. The absence of an intrinsic symmetry axis was overcome by using a nonstandard expansion for the linear interaction. Numerical results obtained for water droplets in air show an increase in the number of observed maxima in the sum-frequency scattering pattern compared to index-matched theories, as well as a strong backscatter peak, which eventually dominates the scattering pattern. Our method opens up possibilities for studying increasingly complex colloidal systems with nonlinear light scattering spectroscopy.

Effect of relative humidity on heat transfer across the surface of an evaporating water droplet in air flow

A three-dimensional direct numerical simulation (DNS) is applied to flows inside and outside an evaporating spherical water droplet in air, and the effect of relative humidity on the heat transfer between the droplet and ambient air is investigated. The initial air temperature is set to be 15 K higher than the initial droplet temperature. The results show that the local evaporation heat loss indicates the maximum on the front of the droplet and decreases on going from the front to the rear, and the reduction on the rear becomes marked for high-droplet Reynolds numbers. This is because the evaporation rate is suppressed on the rear surface by the presence of flow separations behind the droplet. The droplet temperature decreases in the low-humidity condition, whereas it increases in the high-humidity condition. This difference is caused by the heat balance of evaporation heat loss and convective heat gain from ambient air at the droplet surface.

液滴群による音の減衰効果

Attenuation of sound by water droplets in air is analytically investigated. This is one of the mechanisms of the noise reduction in actual rocket launch where water is injected to jet plume. The scattering and absorption by the droplets are considered as the attenuation mechanisms. It is found that the absorption is superior to the scattering for fine droplets, such as fog or mist. Then we estimate the attenuation of sound for the experiment using subscale solid rocket motors. The result agrees well with the experimental data within the frequency range where the assumptions of this study are valid.

A coupling algorithm for partitioned solvers applied to bubble and droplet dynamics

Bubbles and droplets both consist of a liquid in contact with a gas. In this paper, we consider the interface between the incompressible liquid and the gas as a zero thickness structure. The position of the interface is determined by the equilibrium between surface tension effects and the fluid pressure difference across the interface. So, the structure interacts with the fluids on either side. The behaviour of a limited number of bubbles and droplets can therefore be simulated as a Fluid–Structure Interaction (FSI) problem. Most existing techniques frequently used for studying bubble and droplet dynamics, such as Level Set or Volume Of Fluid, use monolithic schemes. The flow on both sides of the interface and the position of the interface are calculated in a single code. In this contribution, a partitioned approach is presented. The position of the interface is calculated with a structural solver. Given a displacement of the interface, a separate flow solver calculates the flow on the liquid side of the interface with the Arbitrary Lagrangian–Eulerian (ALE) technique. The structural solver uses a reduced order model of the flow solver to obtain implicit coupling between both solvers. This reduced order model is built up during the coupling iterations of a time step. Grid and time converged solutions of two axisymmetric problems are calculated: an oscillating water droplet in air and the growth and detachment of an air bubble from the outlet of a vertical needle, submerged in quiescent water.

The Effect of Relative Humidity on Mass and Heat Transfer Across the Surface of an Evaporating Droplet

A three-dimensional direct numerical simulation (DNS) is applied to flows inside and outside an evaporating spherical water droplet in air, and the effect of relative humidity on the mass and heat transfer between the droplet and ambient air is investigated. The initial air temperature is set to be 15 K higher than the droplet temperature. The results show that the droplet temperature decreases in the low-humidity condition, whereas increases in the high-humidity condition. As the relative humidity increases, Sherwood and Nusselt numbers decreases and increases, respectively. The reason can be explained in terms of the heat transfer between the droplet and ambient air with the heat loss due to the droplet evaporation. In addition, the evaluation of heat flux suggests that the contribution of dispersed droplets to the total heat transfer in wind-driven turbulence with breaking waves is about 0.5%.

Condensation of water vapor: Experimental determination of mass and thermal accommodation coefficients

Experimental determinations of mass and thermal accommodation coefficients αm and αt for condensation of water vapor in air have been conducted covering a temperature range from about 250 to 290 K. For the first time, both coefficients have been determined directly and simultaneously. To this end, growth of water droplets in air has been observed at different total gas pressures ranging from about 1000 down to 100 hPa. Monodispersed seed particles have been used as condensation nuclei. After addition of water vapor with well‐defined partial vapor pressure, supersaturation was achieved by adiabatic expansion in an expansion chamber. Most experiments reported in the present paper were performed at vapor saturation ratios ranging from 1.30 to 1.50. Monodispersed Ag particles with a diameter of 9 nm have been used as condensation nuclei, and for humidification a diffusion humidifier was applied. One experiment was performed at the saturation ratio of 1.02, which resembles conditions observed in the Earth's lower atmosphere. In this experiment, monodispersed DEHS particles with a diameter of 80 nm were used as condensation nuclei, and water vapor was generated by quantitative evaporation of a liquid jet. Droplet growth was monitored using the CAMS method. For determination of the accommodation coefficients, experimental droplet growth curves were compared to corresponding theoretical curves. Quantitative comparison was performed by varying the respective accommodation coefficient and the starting time of droplet growth in a two‐parameter best fit procedure. Considering the uncertainty with respect to the starting time of droplet growth and the uncertainties of the experimental water vapor supersaturation, corresponding maximum errors have been determined. From the results obtained it can be stated that αt is larger than 0.85 over the whole considered temperature range. For 250–270 K, values of αm below 0.8 are excluded, and for higher temperatures up to 290 K we can exclude values of αm below 0.4. Both coefficients are likely to be unity for all studied conditions. The results of this study enable accurate predictions of the formation and growth of cloud droplets required to parameterize cloud light scattering/absorption and precipitation properties in climate models.