Droplet Geometry Research Articles

Modeling of spatial growth of SnO2 nanowires on silicon substrates by VLS technique

The growth of SnO2 nanowires on silicon substrates using a vapor-liquid-solid (VLS) technique has been theoretically modeled. Since VLS is a catalyst-based method, we have initially modeled the gold droplet using a modified Young’s equation to be more suitable for SnO2 nanowires. Apart from the droplet geometry, the flow profile of the source vapor can also affect the overall formation of nanowires. This effect is more predominant for solid sources of SnO vapor where highly variable density and length of nanowires are observed. To understand this complex phenomenon, we describe a spatial growth model to predict the observed profile of SnO2 nanowires at different locations on silicon substrates. The model is based on gas transportation over the nanosized catalyst droplets, leading to a gradual reduction in both the length and density of the grown wires. This theoretical model is applied to a randomly patterned distribution of gold catalysts, and the results are consistent with the experimental findings. Since gold is used as the growth catalyst for tin oxide nanowires, the parameters of gold droplets atop silicon nanowire and Young’s angle are extracted.

Tunable magnetism of a hexagonal Anderson droplet on the triangular lattice

Motivated by recent progress on quantum engineered Kondo lattices, we numerically investigated the local magnetic properties of a hexagonal Anderson droplet consisting of multiple rings of magnetic atoms periodically arrayed on a triangular lattice. We demonstrated the tunability of the magnetic properties via their evolution with the droplet geometry for two types of systems with distinct local orbital occupancy profile. We found that the local susceptibility of the droplet center of some types of droplets can be remarkably enhanced in contrast to the conventionally rapid decrease due to spin correlations of surrounding droplet rings. The tunability of the magnetic properties is attributed to the charge redistribution with varying the droplet geometry enforced by the confined lattice with open boundary. Our simulations complements the exploration of the novel artificial tunability of engineered lattice systems.

Electrocoalescence Criterion of Conducting Droplets Suspended in a Viscous Fluid

Coalescence of conducting droplets dispersed in an immiscible medium can be facilitated by an electric field. However, droplets recoil promptly after contact in sufficiently high electric fields if the cone angle between droplets exceeds a critical value. To elucidate the critical condition for droplet coalescence, the behavior of two suspended droplets after contact with a direct current electric field is studied. It is shown that the critical angle is determined not only by the droplet geometry but also conductivity, surfactant concentration, and size. As the droplet conductivity increases, more identical ions accumulate on the adjacent interfaces of two droplets due to the faster ionic migration, which results in Coulombic repulsion between droplets and a reduced critical angle. For surfactant-laden droplets, film drainage induces a surfactant concentration gradient on the leading edges of droplets, and then Marangoni stress is formed to reduce the critical angle. In the case of large droplets, the bri...

A thermodynamic description for the hygroscopic growth of atmospheric aerosol particles

Abstract. The phase state of atmospheric particulate is important to atmospheric processes, and aerosol radiative forcing remains a large uncertainty in climate predictions. That said, precise atmospheric phase behavior is difficult to quantify and observations have shown that “precondensation” of water below predicted saturation values can occur. We propose a revised approach to understanding the transition from solid soluble particles to liquid droplets, typically described as cloud condensation nucleation – a process that is traditionally captured by Köhler theory, which describes a modified equilibrium saturation vapor pressure due to (i) mixing entropy (Raoult's law) and (ii) droplet geometry (Kelvin effect). Given that observations of precondensation are not predicted by Köhler theory, we devise a more complete model that includes interfacial forces giving rise to predeliquescence, i.e., the formation of a brine layer wetting a salt particle at relative humidities well below the deliquescence point.

Sessile drop evaporation under an electric field

In this study, for the first time, the natural (diffusion-limited) evaporation of a sessile drop under an electric field was experimentally examined. A sessile drop natural evaporation is affected by the geometry of the drop, e.g. baseline, contact angle, and surface area, which all can be changed in the presence of an electric field. As such, first, the effect of electric field on sessile water droplet geometry was studied, together with how it differs for surfaces with various contact angle and contact angle hysteresis (for both hydrophilic and hydrophobic surfaces). Then, the dynamics (evaporation time and mode) of natural evaporation of sessile droplet under an electric field was studied by measuring the evaporation rate, surface area, contact angle, and baseline of the droplet. It is found that compare to when there is no electric field, the evaporation time of a sessile droplet increases when there is an electric field. This was statistically shown to be significant for drops placed on surfaces with contact angle hysteresis lower than 32°. For droplets that evaporate in constant baseline mode initially and then by evaporation in constant contact angle mode, the presence of the electric field resulted in a decrease in the duration of constant baseline mode when the surface had a low contact angle hysteresis.

Oblate spheroidal droplet evaporation in an acoustic levitator

The modelling of evaporation in which droplet geometry deviates from sphericity, i.e., oblate spheroid, when the droplet experiences high dynamic stresses or a high Weber number, is important in many applications. The validation of such theoretical models is often difficult to achieve experimentally. The acoustic levitation technique was used to investigate the evaporation of an oblate spheroid for different liquids. Evaporation of oblate droplet at constant aspect ratio is realized through the course of evaporation in the acoustic levitator by continuously adjusting the applied acoustic force on the droplet. A Two-dimensional axisymmetric computational model in oblate coordinate system is presented to predict droplet evaporation driven by the acoustic boundary layer, the model calculates the vapor flux at each grid point on droplet surface. The evaporation follows the d2-law and a good agreement between model prediction and experiments is demonstrated. The acoustic levitator allows for the study of the evaporation of freely suspended deformed droplets and validates the theoretical model of oblate droplet evaporation.

Image analysis of axisymmetric droplets in wetting experiments: A new tool for the study of 3D droplet geometry and droplet shape reconstruction

A new software tool is developed for droplet image analysis for the study of wetting of solid substrates. The tool extracts information exclusively from images and does not require the use of any properties of the system. Moreover, its applicability covers both axisymmetric and non-axisymmetric droplets. The developed software processes independently droplet images taken from side and top perspectives. Processing of side-view images is made by polynomial fitting to the droplet shape and provides important 2D geometrical features such as contact angles, length, height, contact point coordinates and contour outline. The analysis of top-view images is achieved through active contours (snakes) and yields droplet dimensions, centroid position and contour outline. The combination of synchronized side and top images provides the reconstruction of the droplet 3D shape by means of slices of circular arc shape, which allows estimation of droplet volume and of the distribution of contact angles along its perimeter. The above is an important feature that has not been delivered by other software tools. Experimental results to support the applicability of the new tool are presented for two distinct substrates having different surface properties (glass and Teflon).

Control-oriented models for ink-jet 3D printing

This paper proposes two control-oriented models to describe the layer-to-layer height evolution of the ink-jet 3D printing process. While the process has found wide applicability, as with many industrial 3D printing systems, ink-jet 3D printers operated in open loop, even when sensor measurements are available. One of the primary reasons for this is the lack of suitable control-oriented models of the process. To address this issue, two control-oriented models are proposed in this paper, the first is based on droplet geometry superposition, while the other is based on a graph-based characterization of local flow dynamics. The superposition model ignores the flow of the deposited liquid material, while the graph-based dynamic model is able to capture this phenomenon. These two models are compared with an existing flow-based empirical model and validated with experimental results, with the graph-based dynamic model demonstrating between 5 and 14% improvement in layer height prediction. Both the superposition model and the graph-based dynamic model are suitable for closed-loop control algorithm design (as they are discrete layer-to-layer state-space models). We envision that these control-oriented models will ultimately enable the design of model-based closed-loop control for high resolution ink-jet 3D printing.

Multicomponent fuel droplet combustion investigation using magnified high speed backlighting and shadowgraph imaging

The liquid-phase processes occurring during fuel droplet combustion are important in deciding the behaviour of the overall combustion process, especially, for the multicomponent fuel droplets. Hence, understanding these processes is essential for explaining the combustion of the multicomponent fuel droplet. However, the very fast combustion of the too small fuel droplet makes experimental investigation of these processes uneasily affordable. In the present work, a high speed backlighting and shadowgraph imaging of the multicomponent fuel droplet combustion including liquid-phase dynamics are performed. Two categories of multicomponent fuels – in which diesel is the base fuel – are prepared and utilized. The first category is biodiesel/diesel and bioethanol/diesel blends, while the second category is the water-in-diesel and diesel-in-water emulsions. Specific optical setups are developed and used for tracking droplet combustion. The first setup is associated with the backlighting imaging with the resulting magnification of the droplet images being 30 times the real size. The second optical setup is used for shadowgraph imaging, with the resulting magnification being 10 times the real size. Using these setups, spatial and temporal tracking of nucleation, bubble generation, internal circulation, puffing, microexplosion, and secondary atomization during the combustion of isolated multicomponent fuel droplets are performed. Spatial and temporal tracking of the sub-droplets generated by secondary atomization, and their subsequent combustion, in addition to their overall lifetimes have also been performed. Accordingly, a comparison of the burning rate constant between the parent droplet and the resulting sub-droplets is carried out. The rate of droplet secondary atomization is higher than those obtained by relatively low imaging rate. Additionally, it is shown that during a large portion of its entire lifetime, the droplet geometry has been affected by combustion significantly.

Droplets wetting and evaporating on ethanol-philic micro-structured surfaces

Four hydrophobic micro-structured surfaces and a polished silicon wafer were tested. First, wettability on different surface morphologies was evaluated. Initial and temporal contact angles were measured. Then, the droplet geometry evolution was monitored. Four evaporation stages were identified. Besides, an evaporation critical time (ECT) was defined. The effects of surface morphology and surface temperature on droplet wetting and evaporating were discussed.

Going beyond the standard line tension: Size-dependent contact angles of water nanodroplets

The dependence of the contact angle on the size of a nanoscopic droplet residing on a flat substrate is traditionally ascribed solely to line tension. Other contributions, stemming from the droplet geometry dependence of the surface tension and line tension, are typically ignored. Here, we perform molecular dynamics simulations of water droplets of cylindrical morphology on surfaces of a wide range of polarities. In the cylindrical geometry, where the line tension is not operative directly, we find significant contact angle dependence on the droplet size. The effect is most pronounced on hydrophilic surfaces, with the contact angle increase of up to 10° with a decreasing droplet size. On hydrophobic surfaces, the trend is reversed and considerably weaker. Our analysis suggests that these effects can be attributed to the Tolman correction due to the curved water-vapor interface and to a generalized line tension that possesses a contact angle dependence. The latter is operative also in the cylindrical geometry and yields a comparable contribution to the contact angle as the line tension itself in case of spherical droplets.

Diffusion coefficients of water and propylene glycol in supercritical CO2 from pendant drop tensiometry

New optimized experimental setup based on pendant drop tensiometry was developed, and a mathematical model designed to fit the experimental data was used to determine the diffusion coefficients of binary systems at elevated pressures and temperatures. For the first time, the diffusion coefficients of propylene glycol in supercritical CO2 were determined at temperatures of 398.2 and 423.2K and at pressures from 5MPa, up to 17.5MPa.Experimental procedure was validated by a comparison of the experimental data for the mixture water-CO2 with data from the literature. For this purpose, the diffusivity of water in CO2 was measured at 298.15K in the pressure range from 5MPa, up to 60MPa. Accuracy of results was certified by measuring more than 1000 points of equivalent drop diameter. Droplet geometry was examined by using a precise computer algorithm that fits Young–Laplace equation to the axisymmetric shape of a drop.

Droplet evaporation on a solid surface exposed to forced convection: Experiments, simulation and dimensional analysis

Experiments were carried out in order to study the evolution of the mass and wetted surface during evaporation of pure water droplets on stainless steel and PVC plates exposed to forced air convection. The numerical model developed takes into account both coupled heat and mass transfer phenomena and the change in droplet geometry during both pinning and receding periods. The comparison between experimental results and simulation shows good agreement. The model is able to reproduce the influence of the plate properties and that of relative humidity. Dimensional analysis was performed and dimensionless diagrams were developed to predict the drying time for water droplets on stainless steel under a broad range of operating conditions.

A viscous‐to‐brittle transition in eruptions through clay suspensions

AbstractVolcanic lakes are often associated with active geothermal circulation, mineral alteration, and precipitation, each of which can complicate the analysis of shallow magma physics, geophysical signals, and chemical signals. The rheology of the lake and associated hydrothermal system affects the eruptive activity as bubbles ascend and burst through the lake producing distinct ejection behavior. We investigate such phenomena by conducting scaled experiments in which heated water‐clay suspensions are decompressed rapidly from relevant pressures. After a jet phase of expanding vapor, the suspensions break up into ejecta that are either angular or droplet geometry. We parameterize these regimes and find a universal clay volume fraction of 0.28 below which the ejecta are form droplets and above which the ejecta are angular. We propose a regime diagram for optical observations of active lakes, which allows rheological characterization and informs volcanic monitoring.

Amphiphilic nanoparticles suppress droplet break-up in a concentrated emulsion flowing through a narrow constriction.

This paper describes the break-up behavior of a concentrated emulsion comprising drops stabilized by amphiphilic silica nanoparticles flowing in a tapered microchannel. Such geometry is often used in serial droplet interrogation and sorting processes in droplet microfluidics applications. When exposed to high viscous stresses, drops can undergo break-up and compromise their physical integrity. As these drops are used as micro-reactors, such compromise leads to a loss in the accuracy of droplet-based assays. Here, we show droplet break-up is suppressed by replacing the fluoro-surfactant similar to the one commonly used in current droplet microfluidics applications with amphiphilic nanoparticles as droplet stabilizer. We identify parameters that influence the break-up of these drops and demonstrate that break-up probability increases with increasing capillary number and confinement, decreasing nanoparticle size, and is insensitive to viscosity ratio within the range tested. Practically, our results reveal two key advantages of nanoparticles with direct applications to droplet microfluidics. First, replacing surfactants with nanoparticles suppresses break-up and increases the throughput of the serial interrogation process to 3 times higher than that in surfactant system under similar flow conditions. Second, the insensitivity of break-up to droplet viscosity makes it possible to process samples having different composition and viscosities without having to change the channel and droplet geometry in order to maintain the same degree of break-up and corresponding assay accuracy.

Modelling of radiolytic production of HNO3 relevant to corrosion of a used fuel container in deep geologic repository environments

ABSTRACTCopper-coated steel containers are part of the engineered barrier system to permanently store Canadian nuclear fuel waste in a deep geological repository. This work models the dose rates (DRs) at the container surfaces as a function of fuel age. It also utilises a humid-air radiolysis model to study the effects of DR and humidity on radiolytic oxidant production for conditions where unexpected early water intrusion reaches clay seal materials. Radiolysis of humid air produces HNO3. The HNO3 production rate in a condensed water droplet formed on a container surface was conservatively estimated by assuming that every •OH produced by primary radiolytic processes was immediately converted to HNO3 in the gas phase and that all of the HNO3 was absorbed in the water droplet. Also assuming that all of the nitric acid absorbed in the water droplet is consumed in corroding copper and using a hemispherical water droplet geometry, the corrosion depth of the copper coating induced by humid-air radiolysis is conservatively estimated to be 9.4 μm over the permanent storage time.This paper is part of a supplement on the 6th International Workshop on Long-Term Prediction of Corrosion Damage in Nuclear Waste Systems.

Flow Field Inside a Sessile Droplet on a Hydrophobic Surface in Relation to Self Cleaning Applications of Dust Particles

Internal fluidity of a sessile droplet on a hydrophobic surface and dynamics of fine size dust particles in the droplet interior are examined for various droplet contact angles. The geometric features of the droplet incorporated in the simulations resemble the actual droplet geometry of the experiments, and simulation conditions are set in line with the experimental conditions. The dust particles are analyzed, and the surface tension of the fluid, which composes of the dust particles and water, is measured and incorporated in the analysis. Particle tracking method is adopted experimentally to validate the numerical predictions of the flow field. It is found that heat transfer from the hydrophobic surface to the droplet gives rise to the formation of two counter rotating cells inside the droplet. The Nusselt and the Bond numbers increase with increasing droplet contact angle. The number of dust particles crossing over the horizontal rake, which corresponds to the top surface of the dust particles settled in the droplet bottom, toward the droplet interior increases as the particle density reduces, which is more pronounced in the early period. Experimental findings of flow velocity well agree with its counterparts obtained from the simulations.

Statistical Modeling Applied to Deformation-Relaxation Processes in a Composite Biopolymer Network Induced by Magnetic Field

This study investigated a methodology based on image processing and statistics to characterize and model the deformation upon controlled and uniform magnetic field and the relaxation under zero field of droplets observed in aqueous solutions of sodium alginate incorporating magnetic maghemite nanoparticles stabilized by adsorption of citrate ions. The changes of droplet geometry were statistically analyzed using a new approach based on the data obtained from optical microscopy, image processing, nonlinear regression, evolutionary optimization, analysis of variance and resampling. Image enhancement and then image segmentation (Gaussian mixture modeling) processes were applied to extract features with reliable information of droplets dimensions from optical micrographs. The droplets deformation and relaxation trends were accurately adjusted by the Kohlrausch-Williams-Watts (KWW) function and a mean relaxation time was obtained by fitting the time evolution of geometry parameters. It was found to be proportional to the initial radius of the spherical droplets and was associated to interfacial tension.

An experimental note on the deformation and breakup of viscoelastic droplets rising in non-Newtonian fluids

The deformation of viscoelastic droplets rising in non-Newtonian fluids is examined experimentally. Similarly to the case of bubbles and Newtonian droplets traveling in viscoelastic fluids, a critical volume exists but there is no jump in velocity nor a drastic change in droplet geometry. Nevertheless, a tail appears as well as a negative wake. For large-enough volumes, the thickness of the tail is much larger than that for the Newtonian droplets; this is also true for the magnitude of the negative wake and for the extension of the tail. The head of the droplet is subjected to a bi-axial elongation which deforms the spherical part of the droplet converting it into an elongated shape. This elongated shape blends into a tail and the droplet is converted into a viscous elongated teardrop. The tail is then subjected to a uniaxial extensional flow under the action of elongational stresses along the length of the tail. This extensional flow is counteracted by the shear stresses acting on the interface between the tail and the outer surrounding fluid. This interaction will determine the tail breakup. The influence of the elastic properties of the surrounding fluid and the extensional viscosity of the droplet will be responsible for the length and thickness of the tail as well as for its breakup mechanism.

Exact Short-Time Height Distribution in the One-Dimensional Kardar-Parisi-Zhang Equation and Edge Fermions at High Temperature.

We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions in curved (or droplet) geometry. We show that for short time t, the probability distribution P(H,t) of the height H at a given point x takes the scaling form P(H,t)∼exp[-Φ_{drop}(H)/sqrt[t]] where the rate function Φ_{drop}(H) is computed exactly for all H. While it is Gaussian in the center, i.e., for small H, the probability distribution function has highly asymmetric non-Gaussian tails that we characterize in detail. This function Φ_{drop}(H) is surprisingly reminiscent of the large deviation function describing the stationary fluctuations of finite-size models belonging to the KPZ universality class. Thanks to a recently discovered connection between the KPZ equation and free fermions, our results have interesting implications for the fluctuations of the rightmost fermion in a harmonic trap at high temperature and the full counting statistics at the edge.