Axisymmetric free-surface flow simulation using the moving surface mesh particle method and application to drop formation

Abstract. The reactive uptake of carbonyl-containing volatile organic compounds (cVOCs) by aqueous atmospheric aerosols is a likely source of particulate organic material. The aqueous-phase secondary organic products of some cVOCs are surface-active. Therefore, cVOC uptake can lead to organic film formation at the gas-aerosol interface and changes in aerosol surface tension. We examined the chemical reactions of two abundant cVOCs, formaldehyde and acetaldehyde, in water and aqueous ammonium sulfate (AS) solutions mimicking tropospheric aerosols. Secondary organic products were identified using Aerosol Chemical Ionization Mass Spectrometry (Aerosol-CIMS), and changes in surface tension were monitored using pendant drop tensiometry. Hemiacetal oligomers and aldol condensation products were identified using Aerosol-CIMS. Acetaldehyde depresses surface tension to 65(±2) dyn cm−1 in pure water (a 10% surface tension reduction from that of pure water) and 62(±1) dyn cm−1 in AS solutions (a 20.6% reduction from that of a 3.1 M AS solution). Surface tension depression by formaldehyde in pure water is negligible; in AS solutions, a 9% reduction in surface tension is observed. Mixtures of these species were also studied in combination with methylglyoxal in order to evaluate the influence of cross-reactions on surface tension depression and product formation in these systems. We find that surface tension depression in the solutions containing mixed cVOCs exceeds that predicted by an additive model based on the single-species isotherms.

1. The surface tension of 161 films of DPL have been measured on a Langmuir trough using a Wilhelmy balance under conditions controlled to simulate the state of the alveolar lining in vivo.2. The parameters controlled were temperature (maintained at 37 degrees C), humidity (100% at 37 degrees C), surfactant concentrations (encompassing the best available estimates), area changes (consistent with normal respiration), frequency adaptation to continuous cycling and composition and pH of the aqueous hypophase.3. Simultaneously maintaining all of these parameters within the best estimates of physiological limits, the relationships between surface tension and surface area showed appreciable differences from previous studies, our results showing higher minimum values of surface tension, appreciably less change in surface tension with compression and far less hysteresis between surface tension and surface area.4. The higher minimum values are consistent with original estimates of alveolar surface tension made by von Neergaard, namely 35-41 dyne cm(-1).5. Although appreciably smaller than hitherto reported, the change in surface tension with change in area is still adequate to impart alveolar stability.6. The reversibility between surface tension and surface area under physiological conditions is discussed in connection with compliance hysteresis which is considered to be more dependent upon geometric irreversibility of the alveolar surface than upon any intrinsic property of the surfactant.

The controlled production of especially monodisperse emulsions is highly soughtafterin food, cosmetics, pharmaceutical, and chemical industries and is required toproduce well-structured multiphase systems (e.g. double emulsions, microcapsules,tailor-made structures with functional properties) as well as for lab-on-the-chipanalysis. Narrow droplet size distribution is difficult to achieve and therefore majoreffort has been put into development and optimization of various dispersing machines,such as high pressure homogenizers, rotor-stator toothed disk turbines, staticand dynamic membrane systems, or opposed jet micro fluidizer in order to producemonodisperse emulsions, however, without satisfying results. The drop size and sizedistribution, interfacial properties, and structuring elements in the bulk phase ofemulsions determine quality characteristics of the final product. Monodisperseemulsions are also very useful for fundamental studies of emulsion processes andproperties, because the interpretation of experimental results is simplified. In orderto design dispersing devices and droplet based reactors, a thorough understanding ofthe dispersing process mechanism and precise investigation of drop generation dynamicsare required. In laboratory research, microchannels are often utilized to analyzethe droplet formation kinetics in coflow, flow-focusing, or T-flow channel configurations.Precise control of drop size and formation dynamics, constant laminarflow field, high energy efficiency, significant reduction of the sample material, andthe simple manufacturing of the devices are some of the great advantages of thisrather new technology.The present work focuses on single w/o droplet formation and breakup at a capillarytip in coflow devices, where the disperse phase is injected parallel to a laminarcoflowing stream. The main objective was to investigate the effect of process andmaterial parameters on the drop formation dynamics at different processing lengthscales, as we varied the capillary size (0.03 - 0.11 mm), device material (glass,PDMS, stainless steel), cell diameter (0.1 - 20 mm) and length (3 - 100 cm), and theflow rate of both phases (0.001 ≤ Qc ≤ 1900 ml/min, 0.0002 ≤ Qd ≤ 0.9 ml/min). Ahomological row of food-grade Tween-surfactants and aqueous solutions containingsurface active biopolymer (HPGG; hydroxypropylether guar gum) were used for thedisperse phase illustrating in particular the influence of interfacial tension forces andelasticity on the drop formation into sunflower oil. We visualized and analyzed thedroplet dynamics systematically with high-speed imaging systems applying framerates from 1000 to 90’000 fps. Using microchannel, streak imaging (StrIm) and microparticle image velocimetry (μPIV) were employed to map and visualize the entireflow situation in and around the forming droplet, which is influenced by theflow geometry, processing conditions, and material parameters.The dripping droplet formation mechanism can be categorized into three stages: (i)start of the droplet forming called filling stage, (ii) necking stage in which the dropletis still continuously provided with liquid from the capillary, and (iii) pinching orbreaking-off after that the droplet starts to flow along the channel following thestream of the ambient fluid. The kinetics at the capillary tip in the coflow systemstrongly depends on the stresses acting on the droplet during generation. We foundthat at high velocity difference (or at lower velocity ratio, vd/vc) between bothphases, the drag forces imposed by the ambient fluid dominate interfacial tensionforces in macro as well as in mini scaled coflow devices. The presence of surfactanthas little influence under such flow conditions but the droplets are highly uniform.At lower velocity difference (or at higher vd/vc) in the same channel scales the interfacialforces strongly affect the drop filling, breakup and satellite droplet formation.In microchannel, however, we observed that the droplet production shows most pronounceddependency on the viscous drag forces due to the smaller geometricallengths scale and lower velocity differences in general. With the addition of HPGGpolymer into the disperse phase, additional differences in the droplet dynamics areclearly detected. As a result of the elastic extra stresses developed within the viscoelasticfluid, elongated drop creation and the generation of a thread, while pinchingoff, were visualized.The drop breakup experiments, including all available solutions and process parameters,were finally characterized in terms of Weber, Reynolds, Capillary, Ohnesorge,and S-numbers (surface tension number). The resulting Ca-We-phase diagram coversa wide range of parameters (2.96·10-09 ≤ We ≤ 5.9·103, 2.56·10-05 ≤ Ca ≤ 11.5,10-4 ≤ Re ≤ 2.5·104, 1.3·10-03 ≤ Oh ≤ 3.53, and 1.7·10-4 ≤ S ≤ 3.62·1004). The graphrepresents a significant contribution to predict the flow behavior of drop breakupdynamics in geometrically similar drop dispersing devices. Additionally, it is a generalizedillustration of the main forces acting in coflow channels at three differentlength scales under approximate similar flow conditions in the vicinity of the formingdroplet at the capillary tip. A preliminary force balance based on an analyticalmodel is discussed for the approximate prediction of the primary droplet size.

The molecular simulation of interfacial systems is a matter of debate because of the choice of many input parameters that can affect significantly the performance of the force field of reproducing the surface tension and the coexisting densities. After developing a robust methodology for the calculation of the surface tension on a Lennard-Jones fluid, we apply it with different force fields to calculate the density and surface tension of pure constituents of epoxy resins. By using the model that best reproduces the experimental density and surface tension, we investigate the impact of composition in mass fraction on uncured epoxy resins and the effects of degree of cross-linking on cured resins.

Characterisation by drop tensiometry and by ellipsometry of the adsorption layer formed at the air/champagne wine interface

Early indicators of radiation injury in the lung: Are they useful predictors for late changes?

The structure and stability of Stewartson shear layers with different heights are investigated numerically via axisymmetric simulation and linear stability analysis, and a validation of the quasi-two-dimensional model is performed. The shear layers are generated in a rotating cylindrical tank with circular disks located at the lid and base imposing a differential rotation. The axisymmetric model captures both the thick and thin nested Stewartson layers, which are scaled by the Ekman number ($\mathit{E}\,$) as $\mathit{E}\,^{1/4}$ and $\mathit{E}\,^{1/3}$ respectively. In contrast, the quasi-two-dimensional model only captures the $\mathit{E}\,^{1/4}$ layer as the axial velocity required to invoke the $\mathit{E}\,^{1/3}$ layer is excluded. A direct comparison between the axisymmetric base flows and their linear stability in these two models is examined here for the first time. The base flows of the two models exhibit similar flow features at low Rossby numbers ($\mathit{Ro}$), with differences evident at larger $\mathit{Ro}$ where depth-dependent features are revealed by the axisymmetric model. Despite this, the quasi-two-dimensional model demonstrates excellent agreement with the axisymmetric model in terms of the shear-layer thickness and predicted stability. A study of various aspect ratios reveals that a Reynolds number based on the theoretical Ekman layer thickness is able to describe the transition of a base flow that is reflectively symmetric about the mid-plane to a symmetry-broken state. Additionally, the shear-layer thicknesses scale closely to the expected ${\it\delta}_{vel}\propto A\mathit{E}\,^{1/4}$ and ${\it\delta}_{vort}\propto A\mathit{E}\,^{1/3}$ for shear layers that are not affected by the confinement ($A\mathit{E}\,^{1/4}\lesssim 0.34$ in this system, the ratio of tank height to shear-layer radius). The linear stability analysis reveals that the ratio of Stewartson layer radius to thickness should be greater than $45$ for the stability of the flow to be independent of aspect ratio. Thus, for sufficiently small $A\mathit{E}\,^{1/4}$ and $A\mathit{E}\,^{1/3}$, the flow characteristics remain similar and the linear stability of the flow can be described universally when the azimuthal wavelength is scaled against $A$. The analysis also recovers an asymptotic scaling for the normalized azimuthal wavelength which suggests that ${\it\lambda}_{{\it\theta},c}^{\ast }\propto (|\mathit{Ro}|/\mathit{E}\,^{2})^{-1/5}$ for geometry-independent shear layers at marginal stability.

Fuel atomization with prefilming airblast nozzles has been investigated. The present analysis is directed toward a detailed investigation of the atomization processes and the clarification of the fundamental phenomena. Two-dimensional models were utilized. High-speed films, showing the deterioration of the liquid film close to the atomizing edge, reveal the dynamics of the liquid’s deterioration and show the motion of the film during the drop formation. The liquid separation is shown to be a periodic process with the drop formation caused by momentum transfer. The frequency spectrum of the liquid separation is determined by means of an optical technique. It is seen that the main frequencies depend only on the air velocity. They are always lower than the corresponding wave frequencies. The droplet size measurements obtained by a light scattering technique emphasize the dominant role of the air velocity at the atomizing edge. A decrease in the surface tension provides an improvement in atomization quality. Other parameters such as liquid flow rate, liquid viscosity, gap height, and length of the prefilming surface within the nozzle were found not to affect directly the droplet size distribution produced, if the air velocity in each of the two ducts of the nozzle is kept constant. The pressure drop of the air, however, rises. It is shown that the droplet size distribution can be easily determined, if the arithmetic mean value of the air velocity in both ducts is known, e.g., from a calculation of the internal flow. Due to the high liquid mass flow rates of airblast nozzles, the wavy film is partly atomized within the nozzle before the liquid separates at the atomizing edge. The measurements show that the portion of the liquid mass flow atomized remains relatively small and that the droplet sizes are equivalent to those produced at the atomizing edge.

Atmospheric amino acids constitute a large fraction of water-soluble organic nitrogen compounds in aerosol particles, and have been confirmed as effective cloud condensation nuclei (CCN) materials in laboratory experiments. We present a molecular dynamics (MD) study of six amino acids with different structures and chemical properties that are relevant to the remote marine atmospheric aerosol–cloud system, with the aim of investigating the detailed mechanism of their induced changes in surface activity and surface tension, which are important properties for cloud drop activation. Distributions and orientations of the amino acid molecules are studied; these l-amino acids are serine (SER), glycine (GLY), alanine (ALA), valine (VAL), methionine (MET) and phenylalanine (PHE) and are categorised as hydrophilic and amphiphilic according to their affinities to water. The results suggest that the presence of surface-concentrated amphiphilic amino acid molecules give rise to enhanced Lennard–Jones repulsion, which in turn results in decreased surface tension of a planar interface and an increased surface tension of the spherical interface of droplets with diameters below 10 nm. The observed surface tension perturbation for the different amino acids under study not only serves as benchmark for future studies of more complex systems, but also shows that amphiphilic amino acids are surface active. The MD simulations used in this study reproduce experimental results of surface tension measurements for planar interfaces and the method is therefore applicable for spherical interfaces of nano-size for which experimental measurements are not possible to conduct.

The stability of an immiscible layer of fluid bounded by two other fluids of different viscosities and migrating through a porous medium is analysed, both theoretically and experimentally. Linear stability analyses for both one-dimensional and radial flows are presented, with particular emphasis upon the behaviour when one of the interfaces is highly stable and the other is unstable. For one-dimensional motion, it is found that owing to the unstable interface, the intermediate layer of fluid eventually breaks up into drops.However, in the case of radial flow, both surface tension and the continuous thinning of the intermediate layer as it moves outward may stabilize the system. We investigate both of these stabilization mechanisms and quantify their effects in the relevant parameter space. When the outer interface is strongly unstable, there is a window of instability for an intermediate range of radial positions of the annulus. In this region, as the basic state evolves to larger radii, the linear stability theory predicts a cascade to higher wavenumbers. If the growth of the instability is sufficient that nonlinear effects become important, the annulus will break up into a number of drops corresponding to the dominant linear mode at the time of rupture.In the laboratory, a Hele-Shaw cell was used to study these processes. New experiments show a cascade to higher-order modes and confirm quantitatively the prediction of drop formation. We also show experimentally that the radially spreading system is stabilized by surface tension at small radii and by the continual thinning of the annulus at large radii.

Free surface synthetic schlieren (FS-SS) is a liquid surface topography visualization technique relying on apparent dot pattern displacement due to liquid surface deformation. It has gained attention in the fluid visualization field due to its relatively simple and inexpensive setup. One of the most powerful features of the FS-SS technique is the 3D topography of deformed liquid surface, in which submillimeter scale changes can be readily observed in great detail. The visualization of liquid meniscus at the solid interface is proposed in this study to calculate surface tension by equating the surface tension force with weight of light, floating object with circular geometry. It was found that surface tensions of liquids are much greater than anticipated, suggesting that the effect of buoyant force of displaced liquid due to deformed interface cannot be neglected. When the buoyant force is included, the calculated surface tension of liquids are within 10% of the reference values.

Surface tension of low GWP refrigerants R1243zf, R1234ze(Z), and R1233zd(E)

The relationship between the surface tension change with time and the foam volume was investigated for a system containing anionic AOS, LAS and/or nonionic alkyl or s-alkyl poly (oxyethylene) ether with alkyl chains of the same length. Dynamic and equilibrium surface tension was measured by the vibrating jet and Wilhelmy's plate methods, respectively. The anionics showed similar foam volume and surface tension change with time. In regard to the nonionics, on increase in the number of moles of ethylene oxide per molecule was found to make the equilibrium surface tension higher and foam volume smaller. As for dynamic surface tension change, some difference was noted between the alkyl and s-alkyl poly (oxyethylene) ethers. That is, the dynamic surface tension of the s-alkyl poly (oxyethylene) ethers decreased with an increase in the number of moles of ethylene oxide per molecule (abbrev. “EOp”), but that of the alkyl poly (oxyethylene) ethers remained constant regardless of EOp. In AOS/nonionics mixed systems, a s-alkyl poly (oxyethylene) ethers having a high EOp gave lower dynamic surface tension and smaller foam volume.

An improved theoretical method for calculating the surface tension of liquid metals is proposed. A recently derived equation that allows an accurate estimate of surface tension to be made for the large number of elements, based on statistical thermodynamics, is used for a means of calculating reliable values for the surface tension of pure liquid alkali, alkaline earth, and main group metals at the melting point, In order to increase the validity of the model, the surface tension of liquid lithium was calculated in the temperature range 454 K to 1300 K (181 °C to 1027 °C), where the calculated surface tension values follow a straight line behavior given by γ = 441 – 0.15 (T-Tm) (mJ m−2). The calculated surface excess entropy of liquid Li (–dγ/dT) was found to be 0.15 mJ m−2 K−1, which agrees well with the reported experimental value (0.147 mJ/m2 K). Moreover, the relations of the calculated surface tension of alkali metals to atomic radius, heat of fusion, and specific heat capacity are described. The results are in excellent agreement with the existing experimental data.

This study investigates the aerobreakup mechanisms of a liquid droplet initially at a temperature below its critical point impacted by a shockwave in a supercritical environment, i.e. transcritical conditions, occurring in high-pressure/speed liquid-fuelled propulsion systems. Aerobreakup droplet breakup mechanisms have been extensively studied at atmospheric conditions, not considering the significant changes in fluid properties past the critical point that occur within very short breakup time scales in shock-dominated flows. Furthermore, the effects of decreased surface tension forces due to the weakening of intermolecular forces at supercritical conditions on the droplet breakup behaviour have not been resolved to date. This study aims to address these major gaps by developing a direct numerical simulation method to investigate the governing mechanism of droplet aerobreakup at transcritical conditions considering the changes in surface tension. A diffuse interface method coupled with a real-gas equation of state is developed to capture the fluid behaviour beyond the critical point. The results show that simultaneous changes in surface tension and density ratio unique to transcritical flows dictate the droplet aerobreakup mechanisms and the resultant breakup modes. This study presents the first transcritical droplet breakup regime map as a function of Weber number and density ratio compared with the classical breakup criteria commonly accepted for subcritical conditions, proving that the breakup is facilitated at supercritical conditions. The findings are expected to significantly contribute to the development of transcritical droplet aerobreakup models to enable the simulation of spray-shock interaction needed for designing new high-speed/pressure liquid fuel injection systems.