Initial Drop Diameter Research Articles

Detailed numerical investigation of the drop aerobreakup in the bag breakup regime

Aerobreakup of drops is a fundamental two-phase flow problem that is essential to many spray applications. A parametric numerical study was performed by varying the gas stream velocity, focusing on the regime of moderate Weber numbers, in which the drop deforms to a forward bag. When the bag is unstable, it inflates and disintegrates into small droplets. Detailed numerical simulations were conducted using the volume-of-fluid method on an adaptive octree mesh to investigate the aerobreakup dynamics. Grid-refinement studies show that converged three-dimensional simulation results for drop deformation and bag formation are achieved by the refinement level equivalent to 512 cells across the initial drop diameter. To resolve the thin liquid sheet when the bag inflates, the mesh is refined further to 2048 cells across the initial drop diameter. The simulation results for the drop length and radius were validated against previous experiments, and good agreement was achieved. The high-resolution results of drop morphological evolution were used to identify the different phases in the aerobreakup process, and to characterize the distinct flow features and dominant mechanisms in each phase. In the early time, the drop deformation and velocity are independent of the Weber number, and a new internal-flow deformation model, which respects this asymptotic limit, has been developed. The pressure and velocity fields around the drop were shown to better understand the internal flow and interfacial instability that dictate the drop deformation. Finally, the impact of drop deformation on the drop dynamics was discussed.

Formation of Gold Nanoparticles in Water-in-Oil Microemulsions: Experiment, Mechanism, and Simulation

Self-assembled water-in-oil (W/O) microemulsions have been reported as a suitable route for synthesis of size-controlled nanoparticles. However, the mechanism of formation of nanoparticles in microemulsions is still not completely understood. In this work, gold nanoparticles (GNPs) were synthesized via the W/O microemulsion route. As the molar ratio of water and dioctyl sodium sulphosuccinate (AOT) (R) increased from 2.5 to 5.0 to 7.5, the corresponding water drop diameter increased from 2.7 to 5.0 to 7.3 nm. In parallel, the mean hydrodynamic diameter of GNPs increased from 6.5 to 11.3 to 15.6 nm for corresponding R values of 2.5, 5.0, and 7.5. Therefore, although there is a monotonically increasing trend of the mean diameter of GNPs with the initial drop diameter, for all values of R, the mean diameter of GNPs was significantly higher than the initial drop diameter. Consequently, previously known simulation vastly underpredicts the experimental GNP diameter. However, only on redefining the particle-particle coagulation event (during coalescence of microemulsion drops containing particles) does the current kinetic Monte Carlo (kMC) simulation agree well with the experimental results. In addition, we also find that the coagulation efficiency of solid nanoparticles (βp) increases with R, and βp is lesser than the coalescence efficiency of liquid drops (βd) over the range of R values concerned. Hence, a combined simulation and experimental study enumerates the dynamics of size evolution of nanoparticles and the events involved in their formation in a W/O microemulsion system.

Experimental study on two water drops successively impinging on a solid surface

The present study pertains to the experimental impingement of two successive water drops on the solid surface. The drops were generated by a free-falling drop technique and a drop severance device with a velocity of 1.9 m/s at low Weber number. The initial drop diameter was fixed to either 930 μm or 1025 µm. Different from previous works, this study focused on four cases of drop impacts on stainless steel plates classified by the impingement timing of the leading drop deformation: case 1—single drop impingement for reference, case 2—the moment of the leading drop starting its spreading after impacting the surface, case 3—the instant of the leading drop reaching its maximum spreading, and case 4—the timing of the leading drop staying its maximum height. It is observed that the deformation behavior of two successive drops impacting on the surface is highly dependent on the impingement timing, which has minor effects on the change of the maximum drop spreading diameter, but affects significantly the change of the maximum height. The results reveal that the maximum spreading diameter of two drop impact for various cases is around 1.3 times larger than that of the single drop impingement. It is first observed that the maximum drop height for case 3 occurs at second recoil and is greater than those for case 2 and case 4 since the case 3 momentum effect at impingement timing acts in the inward direction, but the other two are in the outward direction.

Investigation of mechanisms leading to water drop breakup at Mach 4.4 and Weber numbers above 105

The paper presents an investigation on water drop breakup in the ‘catastrophic’ mode at Weber numbers above 105. Experimental data have been obtained on a detonation shock tube operated at a Mach number between 4.2 and 4.6. Displacement and deformation of the mist cloud generated around the droplet were observed with a shadowgraph system, and Schlieren imagery was used to visualise the bow and wake shocks around the droplet. We observe that all measured quantities scale with the initial drop diameter. In order to analyse the experimental results and relate these observables to the breakup process, numerical hydrodynamic simulations have been performed. Once validated by direct comparison with our experimental observations, the simulation results are used to see “through” the mist and infer the droplet evolution with dimensionless time T. According to our results, the breakup mechanism can be divided into 3 steps. First (T < 1), most of the liquid mass remains in one main drop, whose shape flattens due to the hydrodynamic forces; then (1 < T < 2) fragmentation begins along the outer rim of the liquid drop and splits the corresponding mass into two parts; the first spreads out radially in small fragments while the remains finally (2 < T < 3.5) take the shape of a filament aligned with the flow. Our results are consistent with a complete breakup time Tb = 5.5.

Predictive Framework for the Spreading of Liquid Drops and the Formation of Liquid Marbles on Hydrophobic Particle Bed.

In this work, we have developed a model to describe the behavior of liquid drops upon impaction on hydrophobic particle bed and verified it experimentally. Poly(tetrafluoroethylene) (PTFE) particles were used to coat drops of water, aqueous solutions of glycerol (20, 40, and 60% v/v), and ethanol (5 and 12% v/v). The experiments were conducted for Weber number ( We) ranging from 8 to 130 and Reynolds number ( Re) ranging from 370 to 4460. The bed porosity was varied from 0.8 to 0.6. The experimental values of βmax (ratio of the diameter at the maximum spreading condition to the initial drop diameter) were estimated from the time-lapsed images captured using a high-speed camera. The theoretical βmax was estimated by making energy balances on the liquid drop. The proposed model accounts for the energy losses due to viscous dissipation and crater formation along with a change in kinetic energy and surface energy. A good agreement was obtained between the experimental βmax and the estimated theoretical βmax. The proposed model yielded a least % absolute average relative deviation (% AARD) of 5.5 ± 4.3 compared to other models available in the literature. Further, it was found that the liquid drops impacting on particle bed are completely coated with PTFE particles with βmax values greater than 2.

Direct contact evaporation of a single two-phase bubble in a flowing immiscible liquid medium. Part I: two-phase bubble size

The evaporation of a single n-pentane drop in another warm flowing liquid (water) medium has been studied experimentally. A Perspex column with an internal diameter of 10 cm and height of 150 cm was used throughout the experiments. N-pentane liquid at its saturation temperature and warm flowing water with flow rate of 10, 20, 30 and 40 L/h were employed as the dispersed and continuous phases, respectively. The active height of the continuous phase in the column (i.e. the level of the continuous phase in the column) covered only 100 cm of the column’s height. A Photron FASTCAM high-speed camera (~ 65,000 f/s) was used to film the evaporation of the drop, while AutoCAD was used to analyse the images from the camera. The diameter ratio (diameter of growing two-phase bubble to initial drop diameter) of the two-phase bubble formed because of the evaporation of the pentane drop in direct contact with the water was measured. Also, the vaporisation ratio (x), the open angle of vapour (β), the total height for complete evaporation and the total evaporation time were measured. The effects of the continuous phase flow rate and the temperature difference between the contacting phases, in terms of Jakob number (Ja), on the measured parameters were investigated. Furthermore, a statistical model to fit the experimental data was developed. The experimental results showed that the diameter of the two-phase bubble is strongly influenced by varying the continuous phase flow rate. The final size of the evaporated vapour bubble was unaffected by the flow rate of the continuous phase, while both the total height required for complete evaporation and hence the time required was significantly influenced. A similar impact was observed for the vaporisation ratio and the open angle of vapour.

Drop spreading and drifting on a spatially heterogeneous film: capturing variability with asymptotics and emulation

A liquid drop spreading over a thin heterogeneous precursor film (such as an inhaled droplet on the mucus-lined wall of a lung airway) will experience perturbations in shape and location as its advancing contact line encounters regions of low or high film viscosity. Prior work on spatially one-dimensional spreading over a precursor film having a random viscosity field [Xu & Jensen 2016, Proc. Roy. Soc. A 472, 20160270] has demonstrated how viscosity fluctuations are swept into a narrow region behind the contact line, where they can impact drop dynamics. Here we investigate two-dimensional drops, seeking to understand the relationship between the statistical properties of the precursor film and those of the spreading drop. Assuming the precursor film is much thinner than the drop and viscosity fluctuations are weak, we use asymptotic methods to derive explicit predictions for the mean and variance of drop area and the drop's lateral drift. For larger film variability, we use Gaussian process emulation to estimate the variance of outcomes from a restricted set of simulations. Stochastic drift of the droplet is predicted to be greatest when the initial drop diameter is comparable to the correlation length of viscosity fluctuations.

Maximum spreading of liquid drop on various substrates with different wettabilities

This paper describes a novel model developed for a priori prediction of the maximal spread of a liquid drop on a surface. As a first step, a series of experiments were conducted under precise control of the initial drop diameter, its falling height, roughness, and wettability of dry surfaces. The transient liquid spreading was recorded by a high-speed camera to obtain its maximum spreading under various conditions. Eight preexisting models were tested for accurate prediction of the maximum spread; however, most of the model predictions were not satisfactory except one, in comparison with our experimental data. A comparative scaling analysis of the literature models was conducted to elucidate the condition-dependent prediction characteristics of the models. The conditioned bias in the predictions was mainly attributed to the inappropriate formulations of viscous dissipation or interfacial energy of liquid on the surface. Hence, a novel model based on energy balance during liquid impact was developed to overcome the limitations of the previous models. As a result, the present model was quite successful in predicting the liquid spread in all the conditions.

Thermal infrared mapping of the Leidenfrost drop evaporation

The paper presents an author complementary study on the Leidenfrost drop evaporation. The research was conducted under ambient conditions and in the film boiling regime. Large water drops were placed on the copper substrate of the constant temperature Tw ranging from 297.6 to 404oC. The initial single drop diameter and its mass was D0 ≈ 1cm and m0 ≈ 1g respectively. One of the obtained results, for each Tw are the drop thermal images versus time. They were used to calculate an average temperature over the drop upper surface (Td). For an exemplary heating surface temperature of Tw = 297.6oC the average drop temperature is approximately 11oC lower than the saturation one and equals Td = 88,95oC. This value is estimated for the first 200s of evaporation and with time step size Δt = 0,5s. The drop upper surface temperature is highly variable and indicates strong convection inside it. This is due to the complex nature of heat and mass transfer. The maximum standard deviation from Td = 88,95oC is SD = 1.21.

Simulated growth of GaAs nanowires: Catalytic and self-catalyzed growth

The kinetic lattice Monte Carlo model of GaAs nanowire growth by the vapor-liquid-crystal mechanism is suggested. The catalytic and self-catalyzed growth of nanowires on the GaAs (111)B surface is simulated. The dependence of the morphology of the growing nanowires on the growth parameters is demonstrated. Upon self-catalyzed growth with gallium drops serving as the growth catalyst, the growth rate of the nanowires linearly depends on the arsenic flow in a wide range of arsenic flow rates. The decreasing dependence of the self-catalyzed growth rate of the nanowires on the initial gallium drop diameter is less steep, and the optimal growth temperature is higher than that for catalytic growth. It is shown that self-catalyzed growth is more sensitive to the ratio between the gallium and arsenic flow rates than catalytic growth.

INFLUENCE OF DROP SPACING ON BURNING OF AN EMULSIFIED-DROP STRING

Combustion characteristics of water-in-dodecane emulsion drops with various initial spacings were stud ied experimentally by using a free-falling drop burning apparatus. The initial drop spacings ( Si) were 2.5, 5, 10, 40, 75 (70), 100. Si (s/d i) was defined as the ratio of the drop center-to-ce nter distance ( s) to the initial drop diameter (di). The water content (β) and the oxygen concentration (ΩO2 ) were fixed at 5% and 21%, while two drop sizes 550 µm and 450 µm were compared. The results showed that the transi tion of the drop flame occurred for all cases in the experiment. For Si > 10 along the flow direction, the flame around the drops would change from a blue spherical flame to a yellow flame and a wake f lame, and the drop flame extinguished later in the downstream region. Soot particles was generated and drops collision and merging occurred to form a flame tube for Si =2.5 in both cases of di = 550 µm and 450 µm. Besides, drop expansion was observed in both cases of di = 550 µm and di = 450 µm, while micro-explosion only occurred in the far d ownstream region for Si = 40, di = 450 µm. It was also shown that the emulsion drop evapora tion rate was not a constant, and the trend of the drop evaporation rate was strongly influenced by changin g the initial drop size.

Effect of surface roughness and surface energy on molten fly ash deposition

One of the ways to mitigate fouling and slagging in downstream sections of boilers, power plants, and gas turbines employing coal combustion is to coat the boiler tubes with low surface energy materials. Such a coating not only reduces the surface energy but can potentially offer a rough surface as well. Hence, the simultaneous effects of surface energy and roughness on fly ash deposition need to be understood. Slag-layer deposition involves drop dynamics associated with arrival of molten ash droplets. While recoiling after reaching maximum spread diameter, the drop may bounce or stick depending on the retraction energy. Bouncing potential of the recoiling droplet decides its fate—to stick or to bounce. In order to quantify the bouncing potential, the spread ratio—maximum spread diameter to initial drop diameter—needs to be evaluated. In this study, models are presented to calculate the spread ratio and bouncing potential of impacting drops on rough surfaces; these incorporate the phenomenon of air/gas pockets present beneath the spreading and recoiling splat. The velocity profiles of the spreading droplet, derived by solving axisymmetric creeping flow, are employed to theoretically estimate the dissipation energy while spreading. The predictions of the proposed spread ratio model—free from fitting parameters—are compared with experimental data in literature and are shown to be within ±5 % of the reported values. With the capability to predict whether the droplet bounces or sticks, the bouncing potential model is exploited to suggest choices of roughness and surface energy to mitigate slagging deposits.

Isolated n-heptane droplet combustion in microgravity: “Cool Flames” – Two-stage combustion

Recent experimentally observed two stage combustion of n-heptane droplets in microgravity is numerically studied. The simulations are conducted with detailed chemistry and transport in order to obtain insight into the features controlling the low temperature second stage burn. Predictions show that the second stage combustion occurs as a result of chemical kinetics associated with classical premixed “Cool Flame” phenomena. In contrast to the kinetic interactions responsible for premixed cool flame properties, those important to cool flame droplet burning are characteristically associated with the temperature range between the turnover temperature and the hot ignition. Initiation of and continuing second stage combustion involves a dynamic balance of heat generation from diffusively controlled chemical reaction and heat loss from radiation and diffusion. Within the noted temperature range, increasing reaction temperature leads to decreased chemical reaction rate and vice versa. As a result, changes of heat loss rate are dynamically balanced by heat release from chemical reaction rate as the droplet continues to burn and regress in size. At reaction temperatures below the turnover, heat loss over takes the heat release rate and extinction occurs. Should heat release exceed heat loss as the temperature increases to that for hot ignition, initiation of a high temperature burning phase may be possible. Parametric study on factors leading to initiation of the second stage burning phenomena are studied. Results show that both carbon dioxide and helium diluents can promote initiation of low temperature burning at smaller initial drop diameters than found with nitrogen as diluent. Small amounts of carbon dioxide and helium in the ambient is sufficient to activate the phenomena. The chemical kinetics dictating the second stage combustion and extinction process is also discussed.

Experimental study of water drop impact on wood surfaces

Experiments of water drop impact on wood surfaces were performed. The initial drop diameter was fixed at 2.4 mm ± 0.1 mm, while the drop impact Weber numbers were varied from 42 to 258. Three kinds of wood, such as Paulownia, Fraxinus mandshurica and Jatoba were considered, since they are combustible materials and popularly used for timber flooring, office furniture, etc. in China. In addition, they have different basic density, surface properties and water absorbability. The experimental results show that the critical impact Weber number of droplet splashing decreases as basic density of the wood increases. The spread factor is affected by wood surface properties and its basic density. It was also found that the water drop spreads along the direction of the grooves after it impacts on wood surface which phenomenon depends on pore grooves of wood surface.

Measuring of coalescence in polymer melt blends flowing through converging channels

AbstractDroplets of polymer blends flowing through convergent channels undergo collisions and coalescence because of the appropriate wineglass‐shaped flow paths with essential flow constriction at the entrance zone. Therefore, an attempt has been undertaken to use capillary flow for studying coalescence phenomena in polymer blends. When the initial drop diameters in a barrel (before extrusion), db, and in the extrudate, de, are measured, coalescence efficiency can be easily calculated as Ec = d/d, provided that no breakup of elongated domains occurs. Compared with methods employing simple shear flow, it has several advantages. For example, the convergent flow pattern combining both shear and extensional flows is directly related to industrial processing operations like extrusion, injection molding, blowing, etc. The method imposes minor limitations on processing parameters and materials used. Applicability of the technique proposed was verified by systematic studies of coalescence in PMMA/PS binary melts blends during capillary extrusion and by comparing these results to theoretical predictions and experimental data from literature. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Impact of Marangoni instabilities on the fluid dynamic behaviour of organic droplets

Marangoni instabilities in dispersed liquid/liquid systems occur if the local solute concentration varies over the interface. The additional shear stress at the interface between a droplet and an ambient phase generates complex convection patterns which increase temporarily the global drag coefficient of the drop and thus retard the drop rise velocity. When Marangoni effects get weaker, the shear forces decrease and the drop reaccelerates. In the present experimental study, the transient drop rise velocity has been intensely investigated in the system toluene ( d )/acetone ( s )/water ( c ) for different initial solute concentrations and different drop diameters. Both mass transfer directions have been considered. The reacceleration time as an indicator of the end of Marangoni dominance can be expressed as a function of drop diameter and initial solute concentration.

Mass transfer enhancement through Marangoni instabilities during single drop formation

The impact of Marangoni convection on the extraction efficiency during the drop formation stage is investigated in the system toluene/acetone/water for different initial solute concentrations and different drop diameters. Both mass transfer directions of the solute have been considered. Marangoni instabilities are supposed to increase the internal mixing and thus enhance mass transfer coefficients. Experimental results show a strong dependency on the mass transfer direction. The amount of solute extracted is between 19% and 55%. The total transferred mass M A increases with drop diameter and initial concentration. Present models from the literature which predict extraction efficiencies do not take into account interfacial effects like Marangoni convection. A correlation is proposed introducing an effective diffusivity which depends on the initial solute concentration. The diffusivity factor increases linearly with initial solute concentration and is more sensitive in the mass transfer direction c → d.

Crystallization dynamics of a liquid metal drop impinging onto a multilayered substrate

Thermal and hydrodynamic processes that occur during impingement of a liquid metal drop onto a multilayered substrate are numerically studied. The mathematical model is based on the Navier–Stokes equations for an incompressible liquid and on substrate and drop heat‐transfer equations that take into account the surface‐tension forces and metal solidification. The effect of the impact velocity, initial drop diameter, metal overheating, and temperature and thermophysical characteristics of the substrate on the morphology of the solid drop, its height, contact‐spot diameter, and total solidification time was examined numerically. The simulation results are found to be in satisfactory agreement with experimental data.

B214単一落下液滴がシリコーン油面に衝突する際の液滴の変形に及ぼす液滴物性値の影響

Deformation of a liquid drop impacted with the silicone oil surface was observed by using a high-speed video reconler. The silicone oils used here cover a wide range of the kinematic viscosity, υT = 1 to 105 mm2/s. Focussing attention on the effects of liquid drop properties, i.e., surface tension σL and kinematic viscosity υL, various kinds of ethanol and glycerin solutions were adopted for the drop as well as water. The maximum drop diameter observed after impact dM was remarkably influenced by σL than υL. However, in the case of the silicone oil of υT = 5 × 102 mm2/s, dM not affected very much by both σL and υL. For the silicone oils of υT > 104 mm2/s, dM/dL can be correlated by the non-dimensional group of ReL2Oh, where dL is the initial drop diameter.

Pickering emulsions stabilised by Laponite clay particles

The type and stability of Pickering emulsions stabilised by disc-like Laponite RD clay particles are described. By establishing the phase diagram of aqueous dispersions as a function of clay and salt (NaCl) concentration, we deduce that toluene-in-water (o/w) emulsions, stable to creaming and coalescence for at least 6 months, are only formed under conditions where the colloidal particles are flocculated. The initial average drop diameter is independent of clay concentration but depends markedly on oil volume fraction, ranging from 10 to 28 μm. Changes in the drop size distributions with time are shown to be due to Ostwald ripening, which, due to the irreversible nature of particle adsorption at oil/water interfaces, is rapid at first and ceases completely at long times. It is suggested that ripening is arrested when the Laplace pressure inside drops of different sizes becomes equal. For optimum conditions, emulsions prepared using a variety of oils including non-polar alkanes and polar alcohols are always o/w even at high oil phase volume fraction, reflecting the hydrophilic nature of this synthetic clay in oil–water systems.