Droplet Model Research Articles

Effect of Low Ambient Pressure on Spray Cone Angle of Pressure Swirl Atomizer

Pressure swirl atomizers are widely used in gas turbine combustor; this paper is aimed at researching the effect of low ambient pressure (0.1 MPa to 0.01 MPa, lower than an atmosphere) on the spray cone angle of pressure swirl atomizer. The spray angle is captured by high-speed photography; then, an image post program is used to process the spray angle magnitude. A mathematical model of a single droplet’s movement and trajectory based on force analysis is proposed to validate the spray angle variation. The maximum variation of the spray cone angle, which is observed when fuel supply pressure drop through the atomizer is 1 MPa as the ambient pressure decreases from 0.1 MPa to 0.01 MPa, is found to be 23.9%. The experimental results show that the spray cone angle is expected to increase with the ambient pressure decrease; meanwhile, mathematical results agree well with this trend.

Nuclear symmetry energy from neutron skins and pure neutron matter in a Bayesian framework

We present an inference of the nuclear symmetry energy magnitude $J$, the slope $L$, and the curvature ${K}_{\mathrm{sym}}$ from combining neutron skin data on calcium, lead and tin isotopes, and our best theoretical information about pure neutron matter. A Bayesian framework is used to consistently incorporate prior knowledge of the pure neutron matter equation of state from chiral effective field theory calculations. Neutron skins are modeled in a fully quantum Skyrme-Hartree-Fock approach using an extended Skyrme energy-density functional which allows for independent variation of $J$, $L$, and ${K}_{\mathrm{sym}}$ without affecting the symmetric nuclear matter equation of state. The effect of using neutron skin data obtained with different physical probes is quantified. We argue that, given the existing data, combining the errors in quadrature is the more appropriate way to obtain unified errors for each nuclide, and in doing so we obtain 95% credible values of $J=31.3\begin{array}{c}+4.2\\ \ensuremath{-}5.9\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=40\begin{array}{c}+34\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, and ${K}_{\ensuremath{\tau}}=L\ensuremath{-}6{K}_{\mathrm{sym}}=\ensuremath{-}444\begin{array}{c}+100\\ \ensuremath{-}84\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ using uninformative priors in $J$, $L$, and ${K}_{\mathrm{sym}}$, and $J=31.9\begin{array}{c}+1.3\\ \ensuremath{-}1.3\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=37\begin{array}{c}+9\\ \ensuremath{-}8\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, and ${K}_{\ensuremath{\tau}}=\ensuremath{-}480\begin{array}{c}+25\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ using pure neutron matter (PNM) priors. We also show that the nonpositive correlation between $J$ and $L$ induced by neutron skin data is consistent with the nuclear droplet model. Neutron skin data alone are shown to place limits on the symmetry energy parameters as stringent as those obtained from chiral effective field theory alone, and when combined the 95% credible intervals are reduced by a factor of 4--5. It is also shown that the majority of nuclear interactions used in the literature have subsaturation density dependencies that are inconsistent with the combination of PNM priors and neutron skin data. We show measurements of lead and calcium neutron skins from upcoming parity-violating electron scattering experiments at Jefferson Lab and Mainz Superconducting Accelerator should obtain total error ranges $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}50\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}240\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for uninformative priors and $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}30\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for PNM priors at 67% credible bounds. Ahead of those experiments, we make predictions based on existing data on neutron skins of tin alone for the neutron skins of calcium and lead of $0.166\ifmmode\pm\else\textpm\fi{}0.008$ fm and $0.169\ifmmode\pm\else\textpm\fi{}0.014$ fm, respectively, using uninformative priors and $0.167\ifmmode\pm\else\textpm\fi{}0.008$ fm and $0.172\ifmmode\pm\else\textpm\fi{}0.015$ fm, respectively, using PNM priors.

Active coacervate droplets are protocells that grow and resist Ostwald ripening

Active coacervate droplets are liquid condensates coupled to a chemical reaction that turns over their components, keeping the droplets out of equilibrium. This turnover can be used to drive active processes such as growth, and provide an insight into the chemical requirements underlying (proto)cellular behaviour. Moreover, controlled growth is a key requirement to achieve population fitness and survival. Here we present a minimal, nucleotide-based coacervate model for active droplets, and report three key findings that make these droplets into evolvable protocells. First, we show that coacervate droplets form and grow by the fuel-driven synthesis of new coacervate material. Second, we find that these droplets do not undergo Ostwald ripening, which we attribute to the attractive electrostatic interactions and translational entropy within complex coacervates, active or passive. Finally, we show that the droplet growth rate reflects experimental conditions such as substrate, enzyme and protein concentration, and that a different droplet composition (addition of RNA) leads to altered growth rates and droplet fitness. These findings together make active coacervate droplets a powerful platform to mimic cellular growth at a single-droplet level, and to study fitness at a population level.

A Simple Mechanistic Model for Friction of Rough Partially Lubricated Surfaces

We report experimental measurements of friction between an aluminum alloy sliding over steel with various lubricant densities. Using the topography scans of the surfaces as input, we calculate the real contact area using the boundary element method and the dynamic friction coefficient by means of a simple mechanistic model. Partial lubrication of the surfaces is accounted for by a random deposition model of oil droplets. Our approach reproduces the qualitative trends of a decrease of the macroscopic friction coefficient with applied pressure, due to a larger fraction of the micro-contacts being lubricated for larger loads. This approach relates direct measurements of surface topography to realistic distributions of lubricant, suggesting possible model extensions towards quantitative predictions.

Numerical simulation of oil droplets spreading on solid surface in water

Plate separators are widely used for oil-water separation in the petrochemical industry. The spreading process of oil droplets at the solid surface is the key to understanding the oil-water separation mechanism in the plate separator. This study uses VOF method to capture oil-water phase interface change and sets up a two-dimensional model of oil droplets spreading on solid surface in water. The influences of droplet diameter, oil-water interfacial tension and viscosity are studied. The numerical simulation results show that the maximum spreading length of oil droplets increases with the increase of droplet size and interfacial tension. The average spreading speed of oil droplets decreases with the increase of oil droplet size, and increases with the increase of surface tension. The maximum spreading length and average spreading speed of oil droplets decrease with the increase of the dynamic viscosity of the oil droplets.

Microscopic study of shape evolution and some important ground state properties of 190–210Au isotopes

In this paper, we have examined the nuclear structural properties of 190–210Au isotopes within the framework of the Hartree–Fock–Bogoliubov Model. For the theoretical calculations, we have used the UNEDF2 and SKP interactions. The studies include the shape evolution, quadrupole deformation parameter [Formula: see text], nuclear electric quadrupole moment Q(b), single-particle energy levels, the binding energy per nucleon, nuclear charge radius, neutron rms radius, proton rms radius and neutron skin thickness. To analyze the accuracy of our theoretical results, we have presented the comparative analysis with experimental data and finite-range droplet model calculations. The adequate resemblance with experimental data is supporting our studies. We observe the oblate-prolate shape coexistence for 190Au, 193Au and 195Au using the UNEDF2 interaction.

Analysis of supersonic shear effects on flame characteristics of an evaporating flame-holder

Flame stabilization and its interaction with flow characteristics are crucial to the development of air-breathing propulsion engine. In this paper, experiments and numerical simulations have been conducted in both uniform and nonuniform inflowing streams to investigate supersonic shear effects on flame characteristics of an evaporating-flame holder. Specifically, supersonic shear is imposed by introducing a mixing layer between a subsonic stream of Mach number Ma=0.15 and a supersonic stream of Ma=1.55. The flames are imaged by high-speed photography with the flame boundary being identified. Three dimensional simulations with k-ε turbulence model, discrete phase model (DPM) for liquid droplets, and eddy-dissipation-concept (EDC) combustion model, are further performed to shed lights on the complex flow characteristics and interactions with flame shapes. Results show that the vortex structure and the size of recirculation zone after the flame holder are similar with and without shear implying that the presence of shear flow will not affect flame stabilization. The supersonic shear instead can modulate the flame shape and location within a combustor by shortening 30% of the overall flame length. Specifically, the hot products can be pulled away from the top wall and entrained towards the mixing layer. The flame shape is less sensitive to the increase of fuel supply due to the blockage of flame development from the recirculation zone in further downstream and the flame being entrained toward the mixing layer. Further flow and fuel/air mixing analysis shows that the outer shear layer of the recirculation zone after the flame holder plays an important role on flame stabilization. The flame front adjusts adaptively with the spatial distribution of the outer shear layer, which would be modulated by the presence of supersonic shear.

Spray Drying of Cellulose Nanofibers: Drying Kinetics Modeling of a Single Droplet and Particle Formation

AbstractMicroparticles embedded with cellulose nanofibers (CNFs) are produced via spray drying. The microdroplets are created in the spray dryer by atomization. The solvent evaporates from the droplet, and the dried particles are formed. The drying kinetics on the scale of one droplet is still not well understood. Drying of a single droplet CNF suspension was investigated in an acoustic levitator. The drying kinetics and morphology evolution during the drying process were obtained. The reaction engineering approach (REA) model provided a reasonable prediction of the drying kinetics. An absolute relative error of 2.5 % between the measured initial mass of the droplet and the REA model's estimated value was reported.

Experimental and mathematical study on jet atomization and flash evaporation characteristics of droplets in a depressurized environment

The effect of depressurized ambient condition on spray flash atomization process was of great importance. However, the process of droplet atomization and flash in depressurized environment was complex and coupled with a variety of physical and thermal behaviors. Thus, characteristics of jet flash atomization evaporation under a depressurized condition were mainly investigated in our present work. The experimental analysis and mathematical method were both adopted in order to consider the influence of factors (vacuum degree and superheat degree) on the spatial distribution of near-field region and the flash evaporation characteristics of far-field region. In particular, a laser particle sizer instrument was used to measure the droplets characteristics in the near-field region and a single sphere model of droplet was established to reveal features of flash evaporation process in the far-field region by the analysis of momentum transfer, heat transfer and mass transfer. The results showed that the droplets size distribution in the axial direction exhibited a fine uniform state, while it showed a disordered distribution in the radial direction of the near-field region analysis. In terms of the far-field region, velocity gradient still existed in far field according to the model analysis. The initial diameter had a more significant impact on drop rate of temperature reported at the initial temperature. Moreover, droplets with smaller diameter had a tendency to possess greater evaporation rate and this progress could be enhanced as decreasing the ambient pressure. The coupling process of jet atomization and flash evaporation could accelerate the temperature change process obviously and simultaneously thus promote the mass transfer.

The transient flow mechanism and intermittent film thickness evolution regulation of droplet mode for horizontal tube falling film

The behavior of falling film over horizontal has significant impacts on the efficiency of heat and mass transfer for the horizontal tube evaporators and absorbers especially for intermittent droplet model at low spray density, which has lower heat and mass transfer resistance. Thus it is critical to illuminate transient and intermittent flow mechanism of droplet dynamic behavior and film thickness evolution regulation over horizontal tube falling film at low spray density. A two dimension multi-phase flow mode for superhydrophilic surface was established to capture the microscopic flow mechanism. The results indicated that droplet generation and growth stages accounted for more than half of the droplet life cycle and an obvious droplet retraction and pulsation were first observed during droplet generation due to surface tension and local additional pressure. Further, the whole life cycle transient and intermittent film thickness map of droplet mode was depicted. And found that the liquid film thickness transient evolution regulation of droplet mode could be split into two zones: impact zone and stable zone. For impact zone, the film thickness was rapidly decreased with the spreading of the liquid film from the millimeter level to 200 μm within 0.2 s. While for stable zone, film thickness almost maintained stable over a long period time until the next droplet impacted. Because of the intermittent of droplet generation and movement, the change of film thickness of droplet mode with spray Reynolds was achieved by increasing impact frequency of droplet impact instead of the volume of a single droplet.

Two-proton radioactivity of exotic nuclei beyond proton drip-line

To search for new candidates of the true and simultaneous two-proton (2p) radioactivity, the 2p decay energies (Q 2p ) are extracted by the Weizsäcker–Skyrme-4 (WS4) model, the finite-range droplet model (FRDM), the Koura–Tachibana–Uno–Yamada (KTUY) model and the Hartree–Fock–Bogoliubov mean-field model with the BSk29 Skyrme interaction (HFB29). Then, the 2p radioactivity half-lives are calculated within the generalized liquid drop model by inputting the four types of Q 2p values. By the energy and half-life constraints, it is found that the probable 2p decay candidates are the nuclei beyond the proton-drip line in the region of Z ≤ 50 based on the WS4 and KTUY mass models. For the FRDM mass model, the probable 2p decay candidates are found in the region of Z ≤ 44. However, the 2p-decaying candidates are predicted in the region of Z ≤ 58 by the HFB29 mass model. It means that the probable 2p decay candidates of Z > 50 are only predicted by the HFB29 mass model. Finally, the competition between the true 2p radioactivity and α-decay for the nuclei above the N = Z = 50 shell closures is discussed. It is shown that 101Te, 111Ba and 114Ce prefer to 2p radioactivity and the dominant decay mode of 107Xe and 116Ce is α-decay.

Remote Sensing of Dispersed Oil Pollution in the Ocean-The Role of Chlorophyll Concentration.

In the contrary to surface oil slicks, dispersed oil pollution is not yet detected or monitored on regular basis. The possible range of changes of the local optical properties of seawater caused by the occurrence of dispersed oil, as well as the dependencies of changes on various physical and environmental factors, can be estimated using simulation techniques. Two models were combined to examine the influence of oceanic water type on the visibility of dispersed oil: the Monte Carlo radiative transfer model and the Lorenz–Mie model for spherical oil droplets suspended in seawater. Remote sensing reflectance, Rrs, was compared for natural ocean water models representing oligotrophic, mesotrophic and eutrophic environments (characterized by chlorophyll-a concentrations of 0.1, 1 and 10 mg/m3, respectively) and polluted by three different kinds of oils: biodiesel, lubricant oil and crude oil. We found out that dispersed oil usually increases Rrs values for all types of seawater, with the highest effect for the oligotrophic ocean. In the clearest studied waters, the absolute values of Rrs increased 2–6 times after simulated dispersed oil pollution, while Rrs band ratios routinely applied in bio-optical models decreased up to 80%. The color index, CI, was nearly double reduced by dispersed biodiesel BD and lubricant oil CL, but more than doubled by crude oil FL.

CONCEPTUALIZATION, THERMAL ANALYSIS, AND MANUFACTURING OF NANO-TEXTURED MICRO-STRUCTURED SURFACES FOR ENHANCED CONDENSATION HEAT TRANSFER

In the present study, nano-micro-structured surfaces have been systematically designed and manufactured in order to generate controlled dropwise condensation mode for enhanced heat transfer during phase-change from vapor to liquid. The conceptualization of micro-structures was conducted by using thermal modelling of an individ-ual droplet pinned at a single micro-hexagonal cavity. By varying droplet radius, resulting contact angles and geo-metric dimensions of micro-structure, threshold values have been determined for the later manufacturing process. According to the calculations for instance at contact angles of 150°, a subcooling of 1 K and a maximum droplet radius of 100 µm, the edge length and the depth of the micro-structures should be kept below 50 µm and 25 µm, respectively. Ensuring these parameters, a roughly 100 % larger heat transfer coefficient would result compared to that predicted by the classical Nusselt theory for filmwise condensation. Taking into account the mathematical analysis, laser ablation technique was adopted on 7075 aluminum samples to emboss hexagonal structures with respect to the predicted dimensions. After this step, the samples were electrochemically etched in order to achieve contact angles of more than 150° to ensure superhydrophobic solid-liquid interaction at the surface. Measurements with a high-precision microscope show that most of the structure dimensions and geometric shape were precisely manufactured. The Tensiometer results disclosed that the surface topography at all samples exhibit contact angles larger than 150° for a sessile droplet with a radius of 100 µm pinned on an individual micro-hexagon.

Modelling reflooding of intact core geometries in ASTEC V2.1: Improvements and validation on PERICLES experiments

The injection of water into core (core reflooding) is a key Accident Management strategy to prevent or mitigate core degradation in water-cooled nuclear reactors. Among the flow regimes implicated during reflooding, the most significant one in terms of core heat transfer removal is the transition boiling, which takes place over a short distance near the quench front. In the ASTEC V2.1 integral severe accident code, the user can select among two concurrent two-phase thermalhydraulics modelling (five- or six-equation scheme) and for each one, two alternative reflooding models to describe the transition boiling region (TBR). On one hand, the DROPLET model calculates a large heat transfer coefficient over a user-defined distance above the quench front. On the other hand, the EXPCHF model calculates the heat flux downstream by imposing the Critical Heat Flux at the quench front and prescribing an exponentially decreasing heat flux along a flow-dependent length. This article aims at selecting the most appropriate reflooding model for the evaluation of the heat transfer associated with transition boiling in ASTEC V2.1 both for the five and the six-equation hydrodynamic model. For that purpose, experimental data from the PERICLES facility dealing with the reflooding of intact core geometries have been used. After an exhaustive analysis of the different reflooding and hydrodynamic models, this study has found that the DROPLET model should be selected when using the five-equation scheme, since it provides enough rod precooling above the quench front. However, the EXPCHF model should be selected when using the six-equation scheme, since it benefits from the larger amount of liquid available near the quench front. This last combination gives the best results on the simulated PERICLES tests and is thus recommended for reactor applications.

How acidity rules synergism and antagonism in liquid–liquid extraction by lipophilic extractants—Part II: application of the ienaic modelling

ABSTRACT In this article Part II, we consider the application of ienaic modeling for solvent extraction of rare earths in the case of the mixed DMDOHEMA/HDEHP extractant system. The system exhibits a synergistic extraction effect depending on the acid concentration and the extractant mole fraction, as demonstrated in the experimental article Part I. In this work, we directly compare experimental findings with theoretical predictions of the droplet model. The model considers the effective free energy of transfer as a combination of competing molecular forces, but contrary to previous micelle models that focus only on the dominant stoichiometry, it allows calculations of free energies of every possible spherical aggregate. The resulting image of the extraction process is that different behaviors can be obtained depending on the acidity and mole fraction of extractants, which are associated with different aggregation regimes in a complex free energy landscape of the system. Nevertheless, self-assembly is tuned by the extraction of all solutes, and not only the target metal cations.

NEW SOLUTION TO THE DROPLET KERNEL MODEL

The droplet model of the nucleus is revived, for which an exact solution for an incompressible fluid is obtained using the hydrodynamic potential solution obtained from the Schrödinger equation. Moreover, for an incompressible fluid, there are formulas for the pressure or potential. There is the main part of the hydrodynamic potential, which is obtained by replacing the modulus of the inverse difference of vectors by the difference in moduli of the values of the vectors. The bulk of the potential is expressed in a finite formula with singularities. A formula is obtained for the integral containing the modulus of the difference between the exact values of the vectors minus the main part of the potential. This difference defines a continuous correction with the features taken into account. The main part of the potential at the boundary of the nucleus turned out to be infinitely large with an imaginary part, locking particles in the nucleus. In this case, the real part of the main potential decreases with decreasing radius, becomes negative, and determines the bound state. At half the radius of the nucleus, there is a linear term along the radius. At the zero radius, there is an infinite negative potential with an imaginary part. An expression for the quantum of the emitted energy is obtained. Note that the added mass was not used due to the rotational regime of the nucleus. An algorithm for calculating the spectrum of the kernel is proposed, and each state of the action of the kernel sn corresponds to n calculated frequencies, determined by n angles in the configuration space. The main space is n + 1 dimensional, and each dimension of space has its own energy. But without special means, the potential of the nucleus tends to infinity. It is necessary to introduce the imaginary degree of roughness of the corners, in expressions containing singularities, then the infinities disappear.

Reflating the nucleus: The pachydermous droplet model

It is shown that the excessive squeezing characteristic of the leptodermous droplet model can be eliminated by taking into account the finite thickness of the nuclear surface. The same objective was achieved in the finite-range droplet model by the introduction of an exponential correction term, but this model breaks down at the large deformations encountered in fission barriers. With this term now being seen to be superfluous, a unified droplet-model treatment of masses and fission barriers becomes possible.

Simulation Analysis of Emulsion Droplet Excited by Chaotic Frequency Pulse Electric Field

The frequency of the chaotic pulse electric field is random in a limited range, which can be adjusted and controlled, thus can effectively cover the harmonic resonance frequency of the droplets in the oil, and realize the efficient coalescence and demulsification of the droplets. In this study, the chaotic frequency pulse electric field is constructed by embedding the chaotic sequence into the pulse interval with the Chaotic-Pulse-Position Modulation method, and the vibration dynamics simulation model of the emulsion droplet in the chaotic frequency electric field is established. The vibration dynamics response of the emulsion droplet under the action of the chaotic frequency pulse electric field is obtained by numerical calculation, and the dynamic analysis, phase diagram analysis and maximum Lyapunov exponent calculation of the response output are carried out. It is found that under the action of chaotic frequency pulse electric field, the emulsion droplet can obtain large tensile deformation at high frequency, but relatively small at low frequency, and the fluctuation is stable, which can qualitatively and quantitatively identify the chaotic vibration characteristics of the droplet.

Eulerian-Lagrangian modeling of cough droplets irradiated by ultraviolet-C light in relation to SARS-CoV-2 transmission.

It is well known that several viruses, as well as SARS-CoV-2, can be transmitted through airborne diffusion of saliva micro-droplets. For this reason, many research groups have devoted their efforts in order to gain new insight into the transport of fluids and particles originated from human respiratory tracts. This paper aims to provide a contribution to the numerical modeling of saliva droplets' diffusion produced by coughing. It is worth noting that droplets' diameters of interest in this work are such that represent typical emission during a cough. Aerosolization effects are neglected since emitted droplets' diameters are greater than 10 µm. In particular, the well-known problem around the safety distance to be held for avoiding virus transmission in the absence of external wind is further investigated. Thus, new indices capable of evaluating the contamination risk are introduced, and the possibility to inactivate virus particles by means of an external ultraviolet-C (UV-C) radiation source is studied. For this purpose, a new model which takes into account biological inactivation deriving from UV-C exposure in an Eulerian–Lagrangian framework is presented.

Water droplet motion under the influence of Surface Acoustic Waves (SAW)

The water droplet motion processes actuated by applying surface acoustic waves at various RF powers and frequencies were investigated by numerically modelling and compared with experiment. A three-dimensional computational model of a free water droplet streaming on the surface of the substrate have been developed using Finite Element Method (FEM) with Laminar Two-Phase Flow Moving Mesh approach for Navier–Stokes equations which were coupled with Convection Wave equation (CWE) module of the COMSOL Multiphysics. Water droplet motion speeds were experimentally measured and confirmed for water droplets with the volumes of 2 and 5 μl, at SAW frequencies 34 and 58 MHz, and power range 0.1–1.23 W. The effect of frequency on microfluidic performance such as streaming flows and droplet motion has been studied both numerically and experimentally toward developing MEMS devices for future energy sources, e.g., for direct methanol fuel cells, hydrogen energy, as well as for use in a wide variety of chemical, water desalination and purification of other fluids from salts, germs, bacteria, and viruses based on perspective multiphysical effects.