Initial Droplet Radius Research Articles

Heat exchange of an evaporating water droplet in a high-temperature environment

In this research, we present the results of experiments capturing the characteristics of high-temperature heating and evaporation of water droplets. The experimental parameters are as follows: initial droplet radius 1–2.5 mm, temperature 20–1100 °C, air flow velocity 0–5 m/s. We use two schemes of water droplet fixation in the heated air flow. In the experiments, we record the heating and evaporation of free-falling droplets so that the holder does not interfere with the experimental results. Typical water droplet heating rates range from 0.4 to 92.4 °C/s and evaporation rates from 0.003 to 0.178 kg/(m2s). Criterial processing of our experimental data is based on the classical equations formulated by Ranz and Marshall and equations proposed by a set of research groups and scientists. We determine the variation ranges of the Reynolds numbers, in which one can only use a limited set of Nu(Re,Pr) correlations. Adjustment coefficients are proposed to take into account the droplet surface temperatures and evaporation rates as functions of the gas medium temperature. Finally, we hypothesize as to how modern mathematical models can be modified to bring the simulation results closer to the experimental data in droplet heating and evaporation rates during fast heat supply.

Micro-explosion and autoignition of composite fuel/water droplets

The results of experimental investigations of puffing, micro-explosions and autoignition of composite fuel/water droplets free falling in a high temperature air are presented. The measurements were performed for non-mixed and premixed Diesel fuel/water and rapeseed oil/water droplets. Air temperature was in the range 850–1100 °C, initial droplet radii were in the range 0.62–1.34 mm, and relative volume fractions of fuel (Diesel fuel or rapeseed oil) were in the range 3–97%. It is shown that the time to micro-explosion decreases with increasing temperature, weakly depends on the volume fraction of fuel, and increases with increasing droplet sizes. The latter trend is shown to be consistent with the prediction of the previously developed simple model for droplet puffing/micro-explosion based on the assumption that the water component forms a spherical sub-droplet located in the centre of a fuel droplet. It is shown that the autoignition delay time for composite droplets, close to the time to micro-explosion for both fuels under consideration, is almost an order of magnitude less than that for pure fuel droplets.

Effect of hydrolyzed polyacrylamide used in polymer flooding on droplet–interface electro-coalescence: Variation of critical electric field strength of partial coalescence

Polymer flooding is widely used in petroleum industry to enhance oil recovery. However, presence of polymer molecules in produced liquids can influence the droplet coalescence at oil–water interface in electric dehydration separators. In this study, the influence of hydrolyzed polyacrylamide (HPAM) on droplet–interface coalescence was examined through high-speed recording and observation. Deformation of droplets of aqueous polymer solution under electric fields was experimentally observed. The images showed droplets collapsed to filament without pinch-off due to viscoelasticity. Meanwhile, fine secondary droplets erupted from the summit of filament, which was detrimental to dehydration efficiency. A critical electric field strength (Ecrit) beyond which partial coalescence occurred was identified. The effects of the initial droplet size, HPAM concentration, electric field waveform and frequency were explored. The results showed that Ecrit increased with the decrease in initial droplet radius or the increase in HPAM concentration. Four kinds of AC or pulsatile electric fields (PEFs) were used including sinusoidal AC (sine AC), square, pulsed DC (PUDC) and pulsed AC (PUAC) waveforms. The increase in frequency suppressed the electro-induced stretching of droplets in the vertical direction, inhibiting partial coalescence. For these different electric fields, the increase in Ecrit with elevated frequencies followed different ways. Overall, Ecrit of square waveform was larger than those of other waveforms; however, Ecrit of PUAC and sine AC waveforms may exceed that of square waveform at high frequencies. These findings are useful for the development of electro-dehydration separators for oils containing dissolved polymers in the dispersed aqueous phase.

Partial coalescence of droplets at oil–water interface subjected to different electric waveforms: Effects of non-ionic surfactant on critical electric field strength

Electro-coalescence technology is commonly used for separation of water from oil. However, the coalescence may not be complete at high field strengths, forming secondary droplets. This process is, hence, undesirable for separation due to the challenging removal of fine droplets. In this study, the effects of non-ionic surfactant (Tween 80) on the critical electric field strength (Ecrit) of partial coalescence of droplets present at oil–water interface were investigated. Different waveforms and frequencies were employed to gain better understanding of the phenomena. The results showed that the increase in initial droplet radius (R) or surfactant concentration may reduce Ecrit. Also, Ecrit was found to vary linearly with R−0.5 and the slope Ecrit/R−0.5 was proportional to the interfacial tension. Compared to DC electric fields, pulsatile electric field (PEF) can affect Ecrit by periodically deforming the droplet. The deformation of droplets was found to be suppressed with elevated frequencies, resulting in an increase in Ecrit. Generally, Ecrit of DC and bipolar square waveforms were the highest, indicating they were more effective in suppressing formation of secondary droplets. However, Ecrit of pulse AC may exceed that of sinusoidal AC and DC at high frequencies. These findings are useful for optimizing electro-coalescence systems.

Coalescence characteristics of droplets at oil–water interface subjected to different electric waveforms

Droplet–interface electrocoalescence may be partial, which is undesirable for separating water from oil. This paper focused on the coalescence characteristics of water droplets at oil–water interface, and the influences of droplet diameter, electric field strength (E), waveform and frequency were experimentally evaluated. The results showed that the normalized volume of secondary droplets (Vnor) increased as E rose, and it was larger for large initial droplet. Increasing the frequency of pulsatile electric fields (PEF) reduced Vnor. The droplet was periodically stretched under PEF according to the waveform’s periodic characteristic. It was proved that the increase of frequency suppressed the deformation of the droplet in vertical direction, which was conducive to droplet’s vertical collapse, and therefore inhibited the formation of secondary droplets. Critical electric field strength (Ecrit) for the occurrence of partial coalescence also increased with the elevated frequency, and the increase became relatively slow at high frequencies. Ecrit of square waveform was the largest in experiments, indicating it was most effective in suppressing partial coalescence; moreover, Ecrit of PUAC could exceed that of sine AC and DC waveforms at high frequencies. As the initial droplet radius (R) reduced, Ecrit increased and showed a linear correlation with R−0.5.

Morphology evolution and dynamics of droplet coalescence on superhydrophobic surfaces

In this work, the coalescence of two equal‐sized water droplets on superhydrophobic surfaces (SHSs) is experimentally investigated. The morphologies of droplet coalescence are observed from side‐view and bottom‐view using high‐speed camera system. The related morphology evolution and dynamics of droplet coalescence are explored. The dynamic behaviors of droplet coalescence on SHSs can be decomposed into liquid bridge growth, contact line evolution, and droplet jumping. The liquid bridge radius is proportional to the square root of time, whereas the dimensionless prefactor is decreased from 1.18 to 0.83 due to the transition of interface curvature. The retraction velocity of the contact line shows limited dependence on initial droplet radii as the retraction dynamics considered here are governed by the capillary–inertial effect. The coalesced droplet finally departs the substrate with a dimensionless jumping velocity of around 0.2. A heuristic argument is made to account for the nearly constant dimensionless jumping velocity. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2913–2921, 2018

Numerical investigation of droplet spreading and heat transfer on hot substrates

Droplet spray cooling has wide applications in electronic cooling, steam generators, evaporators and condensers etc due to its high efficiency. The cooling effect depends on the droplet spreading dynamics greatly. In our study the transient two-dimensional axisymmetric model for droplet cooling is developed with a level set method, where the dynamics of the moving contact line is described with the Molecular Kinetic Theory (MKT). After validation with experimental data, the effect of impact velocity, surface tension, initial droplet radius, equilibrium contact angle and liquid viscosity on droplet spreading is investigated. It is found that the dynamics of the moving contact line can be described accurately with MKT, and the predicted droplet spreading radius agrees quite well with the experimental data, while the Constant Contact Angle (CCA) model overpredicts the droplet spreading rate. The maximum heat flux occurs at the point when the droplet spreading transits from capillary-inertial spreading to capillary-viscous spreading. The droplet spreading rate will increase with the increasing impact velocity, surface tension and initial radius, or decreasing equilibrium contact angle and liquid viscosity. Due to the effect of thermo-capillary force, the cold substrate can promote the droplet spreading, and the hot substrate can retard the droplet spreading. These findings may be of great significance for effective droplet spreading cooling.

Investigation of the effect of nozzle inlet rounding on diesel spray formation and combustion

In this study, the effect of nozzle inlet rounding on diesel spray formation and combustion is investigated. In order to take into account nozzle geometry, two different nozzle geometries (sharp inlet and rounded inlet) were used in the experiments. Diesel spray injected into a constant volume combustion chamber was modeled by using KIVA3V R2 code. One dimensional nozzle flow model was used in numerical simulations. This model calculates nozzle discharge coefficient and updates the initial droplet radius and droplet velocities according to nozzle inlet geometry. Diesel fuel is represented by diesel oil surrogate mechanism which consists of 71 species and 323 reactions. The numerical spray results were validated with macroscopic spray characterization data obtained by constant volume experiments. Results showed that inlet rounding increases discharge coefficient. At high ambient pressure conditions, sharp and rounded nozzles have similar spray internal structure. However, it is observed that sharp inlet nozzle produces smaller droplets that shorten spray tip penetration and autoignition delay period due to low discharge coefficient. Comparing spray combustion of rounded and sharp inlet nozzles, it is showed that rounded inlet nozzle has lower combustion temperature, less NO and soot concentration than sharp inlet nozzle.

Gas phase amine depletion created by aerosol formation and growth

Aerosols are systems of droplets or wet particles suspended in gases. In post combustion CO2 absorption systems aerosols can be formed by spontaneous phase transitions in supersaturated gas phases or by droplets or particles entering the absorber with the gas to be treated. Micron and sub-micron mist droplets and fog formed in these processes cannot be removed by conventional demisting devices and because amine may be absorbed in the droplets this may increase dramatically the amine emissions from absorption columns as reported previously (Khakharia et al., 2015; Schaber et al., 2002). Thus, it is important to understand the mechanisms governing droplet growth and amine uptake through absorber as well as the effect large numbers of aerosol droplets can have on the bulk gas phase composition.A model developed and implemented in Matlab, predicts how the gas phase composition and temperature change along the absorber taking into account mass and heat transfer to and from both the bulk liquid and the droplet phase. The objective of this work, compared to earlier work, Majeed et al. (2017), is to study the possible effect of gas phase component depletion on the droplet growth and droplet internal variable profiles and how this varies with initial droplet size and composition, droplet number concentration and amine volatility.For MEA, as a relatively volatile solvent it is seen that gas phase depletion already takes place at number concentrations above 105 droplets/cm3 with an initial droplet radius of 1.5μ and 5M MEA initial concentration. For initial droplet radius 0.15μ and 0.0001M MEA initial concentration, which may be a more realistic case, hardly any depletion effect is seen up to 107 droplets/cm3. With change in amine volatility it is seen that the gas phase depletion effect is significantly stronger in the case of low volatility than for MEA at high droplet number concentrations. It is found that gas phase amine depletion has a strong effect on droplet growth.

Pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss interferometry in a viscous granular source model**Supported by National Natural Science Foundation of China (11675034, 11275037)

We examine the evolution of quark-gluon plasma (QGP) droplets with viscous hydrodynamics and analyze the pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss (HBT) interferometry in a granular source model consisting of viscous QGP droplets. The shear viscosity of the QGP droplet speeds up and slows down the droplet evolution in the central and peripheral regions of the droplet, respectively. The effect of the bulk viscosity on the evolution is negligible. Although there are viscous effects on the droplet evolution, the pion momentum spectrum and elliptic flow change little for granular sources with and without viscosity. On the other hand, the influence of viscosity on HBT radius Rout is considerable. It makes Rout decrease in the granular source model. We determine the model parameters of granular sources using the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii together, and investigate the effects of viscosity on the model parameters. The results indicate that the granular source model may reproduce the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii in heavy-ion collisions of Au-Au at and Pb-Pb at in different centrality intervals. The viscosity of the droplet leads to an increase in the initial droplet radius and a decrease of the source shell parameter in the granular source model.

Enhanced Evaporation of Droplet of Ternary Component Under the Effect of Thermo-physical and Transport Properties Variability

This work simulates the heat and mass transfer of the fuel droplets evaporated in a hot medium. The proposed model includes the vaporization of multi-component fuel droplet, in laminar forced convection. The results show that the various components, of different molecular weights, vaporize at different temperatures. Furthermore, the non-miscibility of the mixture of the hydrocarbons liquid droplet is observed. The profile of the regression of the droplet square diameter does not follow the \(d^{2}\) law and presents three evaporation rates rather than a single one. New correlations for the evaporation rate versus Reynolds and Schmidt numbers are proposed for different air velocities, different initial droplet radii, and different initial mass fractions.

A level-set method for droplet impact and penetration into a porous medium

Abstract A level-set method is presented for computation of droplet impact and penetration into a porous medium. The volume averaged conservation equations of mass and momentum are employed for the porous region including the effects of porosity and drag force caused by the porous solid matrix. They are coupled to the conservation equations in the external fluid region through the matching conditions of velocity and stress on the porous surface. Computations are conducted to investigate the effects of initial droplet radius, impact velocity, contact angles, particle size and porosity on the droplet spreading and penetration. A simple analytical formulation is developed for the initial droplet penetration depth and compared with the numerical results. The present level-set method is also applied to the computation of droplet-droplet interaction in the porous medium.

Temperature measurement in the trace of water droplet when heating by hot air

In this study, the temperature of a mixture of water vapor and air was measured behind the droplet, which is fixed in a hot air flow. The initial droplet radius varied from 1.3mm to 1.7mm. Air flow velocity was 2.5m/s. The measurements were performed at a distance of 2mm, 4mm, and 8mm from the back droplet surface. The initial air temperature varied in the range of 450–750K. For the first time, the hypothesis was experimentally proved about significant reduction (from 10K to 100K) of gas temperature in the trace of the evaporating water droplet (even when the droplet size is less than 2mm). The results explained the reasons for considerably different evaporation rates of water droplets during their motion in the form of an aerosol flow in a combustion zone. The study reported the sizes of the temperature trace of droplet, beyond which the temperature of the mixture of water vapor and air differed insignificantly (by less than 10K) from the temperature of the air stream flowing around the droplet. The results of measuring the temperature of vapor/air mixture in the trace of the evaporating droplet proved the validity of the known models of high-temperature heating and evaporation of water droplets.

Analytical Solutions of the Supersaturation Equation for a Warm Cloud

Abstract Approximate solutions of the supersaturation equation are derived for a warm cloud. These solutions take account of the growth of the droplet radius but are only valid for small times. However, the validity of the solutions extends far enough to obtain reasonable estimates of the maximum supersaturation smax. It is shown that when the initial droplet radius and supersaturation are sufficiently small the scaling relation smax ∝ w3/4N−1/2 is obtained, where w is the vertical velocity and N is the droplet number density, in agreement with previous results. The range of validity of this result is discussed and other analytical expressions are derived when this result is not valid. It is shown that these analytical expressions generally agree well with numerical solutions.

Redistribution of mobile surface charges of an oil droplet in water in applied electric field

Most researches on oil droplets immersed in aqueous solutions assume that the surface charges of oil droplets are, similar to that of solid particles, immobile and distributed uniformly under external electric field. However, the surface charges at the liquid–liquid interface are mobile and will redistribute under external electric field. This paper studies the redistribution of surface charges on an oil droplet under the influence of the external electrical field. Analytical expressions of the local zeta potential on the surface of an oil droplet after the charge redistribution in a uniform electrical field were derived. The effects of the initial zeta potential, droplet radius and strength of applied electric field on the surface charge redistribution were studied. In analogy to the mobile surface charges, the redistribution of Al2O3-passivated aluminum nanoparticles on the oil droplet surface was observed under applied electrical field. Experimental results showed that these nanoparticles moved and accumulated towards one side of the oil droplet under electric field. The redistribution of the nanoparticles is in qualitative agreement with the redistribution model of the mobile surface charges developed in this work.

The ignition parameters of the coal-water slurry droplets at the different methods of injection into the hot oxidant flow

Two different experimental approaches were realized for investigations of integral characteristics of single droplet ignition of coal-water slurry containing petrochemicals (CWSP) inside the hot flow of the gas oxidant. At first, the droplet was fixed inside the flow by special holder and the second way is free injection of the soaring droplet into the volume of combustion chamber. Research reports an experimental estimation of influence of material holder on ignition characteristics for typical CWSP. This is important, since many researchers use various holders (the ceramic rod, thermocouple junction, metal wire) when inserting droplets of coal-water slurry (CWS) and CWSP into the combustion chamber. There were three types of the droplet holders: the junction of the high-speed thermocouple, metallic wire and the ceramic rod. The basic components of the CWSP were filter-cake (the coal processing waste), the used turbine oil, the plasticizer (wetting agent) and water. Initial droplet radius was 0.5–1mm, and the temperature and the oxidant flow velocity were 400–1000K and 0.5–5m/s correspondingly. The ignition delays and the combustion times for the fuel droplets together with minimal temperatures of the stable ignition (with further combustion) were defined. Comparison of parameters of the flying droplet ignition with corresponding values for droplets that were fixed by holder was done. Soaring droplets have smaller ignition delay times (for 7–25%) relative to the case of droplet fixed inside the oxidant flow by holder (when the all rest parameters are similar). Influence of the holder material onto the values of times of ignition delay and combustion become essentially weaker with oxidant temperature growth. The obtained numerical results show the limitations and advances of the two approaches for laboratory investigations of the CWSP ignition and combustion.

Regimes of radial growth for Ga-catalyzed GaAs nanowires

We present a non-stationary growth model of Ga-catalyzed GaAs nanowires which is based on the two kinetic equations for the nanowire elongation rate and a time-dependent base radius of the droplet. We show that self-catalyzed nanowire growth is principally different from the Au-catalyzed one because a stationary droplet size cannot be maintained at all times. Close examination of the model enables us to separate different regimes of radial growth in which the droplet shrinks, inflates or converges to a certain stationary size as nanowires grow, depending on the initial droplet radius and the growth conditions. We also discuss some experimental data on the growth modes of Ga-catalyzed GaAs nanowires from the viewpoint of the obtained results.

Shrinkage of bubbles and drops in the lattice Boltzmann equation method for nonideal gases.

One characteristic of multiphase lattice Boltzmann equation (LBE) methods is that the interfacial region has a finite (i.e., noninfinitesimal) thickness known as a diffuse interface. In simulations of, e.g., bubble or drop dynamics, for problems involving nonideal gases, one frequently observes that the diffuse interface method produces a spontaneous, nonphysical shrinkage of the bubble or drop radius. In this paper, we analyze in detail a single-fluid two-phase model and use a LBE model for nonideal gases in order to explain this fundamental problem. For simplicity, we only investigate the static bubble or droplet problem. We find that the method indeed produces a density shift, bubble or droplet shrinkage, as well as a critical radius below which the bubble or droplet eventually vanishes. Assuming that the ratio between the interface thickness D and the initial bubble or droplet radius r0 is small, we analytically show the existence of this density shift, bubble or droplet radius shrinkage, and critical bubble or droplet survival radius. Numerical results confirm our analysis. We also consider droplets on a solid surface with different curvatures, contact angles, and initial droplet volumes. Numerical results show that the curvature, contact angle, and the initial droplet volume have an effect on this spontaneous shrinkage process, consistent with the survival criterion.

Mass Transfer in the Dissolution of a Multicomponent Liquid Droplet in an Immiscible Liquid Environment

The Epstein-Plesset equation has recently been shown to predict accurately the dissolution of a pure liquid microdroplet into a second immiscible solvent, such as oil into water. Here, we present a series of new experiments and a modification to this equation to model the dissolution of a two-component oil-mixture microdroplet into a second immiscible solvent in which the two materials of the droplet have different solubilities. The model is based on a reduced surface area approximation and the assumption of ideal homogeneous mixing [mass flux d(m(i))/dt = A(frac(i))D(i)(c(i) - c(s)){(1/R) + (1/(πD(i)t)(1/2)}] where A(frac(i)) is the area fraction of component i, c(i) and c(s) are the initial and saturation concentrations of the droplet material in the surrounding medium, R is the radius of the droplet, t is time, and D(i) is the coefficient of diffusion of component i in the surrounding medium. This new model has been tested by the use of a two-chamber micropipet-based method, which measured the dissolution of single individual microdroplets of mutually miscible liquid mixtures (ethyl acetate/butyl acetate and butyl acetate/amyl acetate) in water. We additionally measured the diffusion coefficient of the pure materials-ethyl acetate, butyl acetate, and amyl acetate-in water at 22 °C. Diffusion coefficients for the pure acetates in water were 8.65 × 10(-6), 7.61 × 10(-6), and 9.14 × 10(-6) cm(2)/s, respectively. This model accurately predicts the dissolution of microdroplets for the ethyl acetate/butyl acetate and butyl acetate/amyl acetate systems given the solubility and diffusion coefficients of each of the individual components in water as well as the initial droplet radius. The average mean squared error was 8.96%. The dissolution of a spherical ideally mixed multicomponent droplet closely follows the modified Epstein-Plesset model presented here.

The physicochemical stability and in vitro bioaccessibility of beta-carotene in oil-in-water sodium caseinate emulsions

Beta-carotene (BC), the most important dietary source of provitamin A, is necessary for optimum human health. BC is insoluble or only slightly soluble in most liquids but its bioavailability improves when ingested with fat. Therefore lipid emulsions are ideal matrices for BC delivery. BC (0.1%) in corn oil, the dispersed phase (5 or 10%), was homogenized with 2% sodium caseinate solution in a microfluidizer. Homogenization at different pressures produced droplet diameters (Dz = 368–124 nm) that were linear and inversely related to homogenization pressures in the pressure range 10–100 MPa. Nanoemulsions (r < 200 nm) were prepared at 100 MPa. The sodium caseinate emulsions were generally very stable to coalescence or flocculation over 30 days and the slow rate of volume increase was found to be related to the square of the initial droplet radius following Stokes velocity of settling equation. BC stability towards oxidation was lower as droplet diameter decreased. The extent of lipolysis in an in vitro system was higher and linearly related to the inverse of droplet diameter. Bioaccessibility, as defined by the amount of BC recovered in the aqueous phase after ultracentrifugation, was linearly related to smaller emulsion droplet diameter. These results show that sodium caseinate, a food grade emulsifier, can be used to prepare stable emulsions of food oils carrying beta-carotene. Since food oils facilitate the uptake of beta-carotene this may be a preferred system to deliver beta-carotene.