Macroscopic Droplet Research Articles

The spray characteristics of a pressure-swirl injector with various exit plane tilts

The gasoline spray characteristics of a pressure-swirl injector were investigated with various exit plane tilts. The analysis focused on the correlation between tilt angle and flow angle. Mie-scattering technique and phase Doppler anemometry were employed to analyze the macroscopic spray development and droplet size distribution of the spray. An analytical method for mass flux estimation was applied to understand the velocity distribution at the nozzle exit. The results showed that the spray shape and velocity distribution of the spray were more asymmetrical at high tilt angles. In particular, an opened hollow cone spray was formed when the tilt angle is greater than the complementary flow angle. The pressure drop inside the spray, one of the crucial factors for the swirl spray collapse at various surrounding conditions, was attenuated in this opened hollow cone spray since the pressure inside the spray was assimilated to the surrounding air pressure. The spray collapse at high fuel temperature and back pressure conditions did not appear when the tilt angle is larger than the complementary flow angle due to the reduced pressure drop inside the spray. However, tilt angle should be optimized to fulfill the requirements of spray robustness and avoid the locally rich area. The droplet size of 70° tilted nozzle spray shows a value similar to that of the original swirl spray in the plane that includes nozzle axis and the major axis of exit surface ellipse (Major axis plane) while it shows an increased value in the plane that includes nozzle axis and the minor axis of exit surface ellipse (Minor axis plane).

Interfacial Oil Droplets

Very small, discrete oil droplets can form at the solid-liquid interface. We demonstrate this effect through formation of decane droplets at the interface between an aqueous ethanol solution and silicon wafers that have been made hydrophobic through self-assembly of octadecyltrichlorosilane (OTS). The droplets have a lens-like shape; the shape is approximately a spherical cap with a contact angle < 25 degrees. The heights of the droplets are about 2-50 nm, and diameters at the three-phase boundary are about 100-600 nm in 25% ethanol solution. The size and contact angle can be varied by changing the ethanol concentration. The contact angle of the very small droplets (height < 20 nm) is similar to the contact angle of macroscopic droplets (height approximately equal to 1 mm), so the line tension is very small. The droplets are only stable for a few hours: they gradually lose mass, presumably through Ostwald ripening. The drop perimeter is not pinned during ripening but retreats across the solid. We form the droplets by direct adsorption from an emulsion; evidence for adsorption is obtained by comparing the drop volumes in bulk to the volumes at the interface. The droplet sizes are obtained by dynamic light scattering and atomic force microscopy.

Transient Interfacial Patterns and Instabilities Associated with Liquid Film Adhesion and Spreading

A surface force apparatus was used to study surface shape changes during the adhesion and spreading of a polymer melt on a bare mica surface. Transient fingers were observed during the initial, rapid spreading process, pointing radially out from the initial adhesive contact point. The fingers had microscopic widths and lengths but submicroscopic thicknesses. They eventually disappeared, leaving a more slowly growing circular neck with a smooth, featureless polymer-air surface. The mean radius of the spreading meniscus (neck) was found to follow a scaling relationship with time of the form (ri + ro)/2 proportional, variant tn, with n = 0.128, while the ends of the fingers grew according to ro proportional, variant tn, with n = 0.10. These rates agree with the values of n = 0.100-0.125 predicted by classical wetting theories for circular macroscopic droplets (i.e., radially symmetric, without fingers) spreading on a solid surface. The lifetime of the transient fingering patterns increases with the polymer viscosity as tau proportional, variant etan, with n = 2.1 +/- 0.2. A circular trough or depression in the film was observed just beyond where the fingers ended, which appears to be a source of the material for the advancing fingers. In addition, beyond the trough, circular ripples/waves were observed on the polymer melt film surface. Such patterns may arise quite generally whenever a perturbation occurs that changes the local forces, thereby inducing a bulge or depression in a liquid film or surface. Thus, we observe similar fingers and ripples/waves during the spreading of liquid polybutadiene on (the immiscible and more viscous) liquid poly(dimethylsiloxane), suggesting that the phenomenon may exist in various liquid adhesion and spreading situations. For low viscosity liquids such as water and low molecular weight oils, our scaling relations suggest that the transient patterns will exist for only a few microseconds; this is likely the reason for why they have not yet been observed.

Collision dynamics of nanoscale Lennard-Jones clusters

An investigation of collision dynamics of nanoparticles for a broad range of impact factors and collision speeds is presented. The investigation is based on molecular dynamics simulations in conjunction with the Lennard-Jones interaction potential thus making the results applicable for a broad range of material properties. Identification criteria are used to classify the collision dynamics into different collision modes and submodes. Detailed analysis of the collision processes reveals the existence of coalescence and stretching separation modes, which are further classified according to their dynamics into sticking; slide-and-locking; droplet; normal stretching separation; stretching separation with satellite droplets; and shearing-off modes. Qualitative and quantitative comparisons with previous molecular dynamic studies and analytical prediction models derived for macroscopic droplet collisions are also discussed. The investigation reveals that the reflexive separation mode, which has been observed in macroscopic droplet collisions, does not occur for nanoparticles consisting of 10 000 (or less) atoms.

Quadrupole mass spectrometry desorption analysis of Ga adsorbate on AlN (0001)

The authors have investigated the adsorption and subsequent desorption of Ga on AlN (0001) with line-of-sight quadrupole mass spectrometry (QMS). The authors present desorption data consistent with a continuous Ga-flux dependent accumulation of a laterally contracted Ga bilayer on AlN (0001) from 0 to 2.7±0.3 ML GaN equivalent coverage, and further Ga accumulation in macroscopic Ga droplets. The temperature dependence of Ga-adsorbate QMS desorption transients was investigated and the authors determined that the desorption activation energies for individual monolayers of the Ga adsorbate on AlN (0001) were similar to Ga desorption from GaN (0001). For the (first) pseudomorphic Ga-adsorbate monolayer on AlN, the authors measured a maximum Ga coverage of 1.0±0.1 ML and desorption activation energy of 6.2±0.3eV. For the (second) laterally contracted Ga monolayer (1.7±0.3 ML) the desorption activation energy was 3.8±0.1eV.

Removal of Induced Nanobubbles from Water/Graphite Interfaces by Partial Degassing

Nanobubbles at an interface between a hydrophobic solid and water have a wide range of implications, but the evidence for their existence is still being debated. Here we artificially induced nanobubbles on freshly cleaved HOPG substrates in water using the protocol developed previously and subjected the system to moderate levels of degassing (approximately 0.1 atm for 0.5 to 3 h). The AFM images after the partial degassing revealed that some nanobubbles had coalesced and detached from the substrate because of buoyancy, whereas others apparently remained unaffected. The size and spatial distributions of the nanobubbles after the partial degassing suggest that there is a critical size for a nanobubble above which it may grow. The contact angle of water next to nanobubbles (approximately 160 degrees) is much larger than the advancing contact angle of a macroscopic water droplet on the same substrate (approximately 80 degrees) both before and after the partial degassing and concomitant growth and shrinkage of the nanobubbles. The contact angle of a nanobubble also remained unchanged as the nanobubble was moved along the substrate by the AFM tip. The apparent lack of contact angle hysteresis in the nanobubble systems may suggest that the very large contact angle may correspond to a local minimum of the free-energy landscape.

Liquid droplet spreading with line tension effect

For a macroscopic liquid droplet, we applied the fluid mechanics to predict its dynamicspreading where the energies associated with volume are dominant (e.g. Shikhmurzaev 1997J. Fluid Mech. 334 211). When the droplet size is reduced to the sub-millimetre level, thesurface energy becomes the dominant factor. If the droplet size is further reduced to themicrometre or sub-micrometre level, the line tension should be included in our theoreticalformulation for predicting droplet spreading. In the present paper, we extend thenon-equilibrium thermodynamics (Gao et al 2000 Acta Mater. 48 863–74) to describe themicrometre or nanometre size droplet spreading on a solid substrate with the line tensioneffect. Discussion of the stable and unstable equilibrium states is made based on thethermodynamic force expression.

Condensation on Ultrahydrophobic Surfaces and Its Effect on Droplet Mobility: Ultrahydrophobic Surfaces Are Not Always Water Repellant

The condensation of water was studied on topography-based ultrahydrophobic surfaces containing hydrophobized silicon pillars. Optical microscopy showed that water nucleated and grew both on top of and between the pillars. As condensation progressed, water between the pillars became unstable and was forced upward to the surface. Macroscopic water droplets on top of the pillars coalesced with condensed water that remained between the pillars, pinning the droplets at their three-phase contact line. Dynamic contact angle measurements on ultrahydrophobic surfaces wet with condensation revealed a dramatic increase in hysteresis compared to that on dry surfaces, leading to a corresponding decrease in water drop mobility.

Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model. First, the apparent contact angle of a droplet on a heterogeneous surface under the condition of constant volume is considered. By assuming a cylindrical liquid–vapor surface (meniscus) and minimizing the total free energy, we derive an equation for the apparent contact angle, which is similar but different from the well-known Cassie's law. Next, using this modified Cassie's law as a guide to predict the behavior of a droplet on a heterogeneous striped surface, we examine several scenarios of contact angle hysteresis using a periodically striped surface model. By changing the volume of the droplet, we predict a sudden jump of the droplet edge, and a continuous change of the apparent contact angle at the edge of two stripes. Our results suggest that as drop volume is increased (advancing contact lines), the predominant drop configuration observed is the one whose contact angle is large; whereas, decreasing drop volume from a large value (receding contact lines) yields drop configuration that predominantly exhibit the smaller contact angle.

The validity of Cassie's law: A simple exercise using a simplified model

The contact angle of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model which can lead to the augmented Young–Laplace equation. Droplets under the condition of constant volume as well as constant vapor pressure are considered. By assuming a cylindrical liquid–vapor surface (meniscus) and minimizing the total free energy of the interface displacement model, we derive an equation which is similar but different from the well-known Cassie's law. Our modified Cassie's law is essentially the same as the formula obtained previously by Marmur [J. Colloid Interface Sci. 168 (1994) 40]. A few consequences from this modified Cassie's law are briefly described in the following sections of this paper. Several sets of recent experimental results seem to support the validity of our modified Cassie's law.

Comparative Study of the Thermodynamics and Kinetics of the Ion Transfer Across the Liquid|Liquid Interface by Means of Three-Phase Electrodes

A comparative study of the behavior of different sorts of three-phase electrodes applied for assessing the thermodynamics and kinetics of the ion transfer across the liquid/liquid (L/L) interface is presented. Two types of three-phase electrodes are compared, that is, a paraffin-impregnated graphite electrode at the surface of which a macroscopic droplet of an organic solvent is attached and an edge pyrolytic graphite electrode partly covered with a very thin film of the organic solvent. The organic solvent contains either decamethylferrocene or lutetium bis(tetra-tert-butylphthalocyaninato) as a redox probe. The role of the redox probe, the type of the electrode material, the mass transfer regime, and the effect of the uncompensated resistance are discussed. The overall electrochemical process at both three-phase electrodes proceeds as a coupled electron-ion transfer reaction. The ion transfer across the L/L interface, driven by the electrode reaction of the redox compound at the electrode/organic solvent interface, is independent of the type of redox probe. The ion transfer proceeds without involving any chemical coupling between the transferring ion and the redox probe. Both types of three-phase electrodes provide consistent results when applied for measuring the energy of the ion transfer. Under conditions of square-wave voltammetry, the coupled electron-ion transfer at the three-phase electrode is a quasireversible process, exhibiting the property known as "quasireversible maximum". The overall electron-ion transfer process at the three-phase electrode is controlled by the rate of the ion transfer. It is demonstrated for the first time that the three-phase electrode in combination with the quasireversible maximum is a new tool for assessing the kinetics of the ion transfer across the L/L interface.

A macroscopic solids-stabilized emulsion droplet model in reduced gravity

The presence of solid nano-scale particles affects the stability of emulsions but it is difficult to make direct observations of these particles because of their dimensions. By reducing the gravitational force exerted on the droplets and particles, it is possible to enlarge the emulsion droplet system and optically observe the particles on the interface. Such a macroscopic model of a solidsstabilized emulsion droplet has been developed using silicone oil, water and glass beads. The macroscopic system behaved similarly to colloidal scale emulsion systems in that beads protruding from the interface prevented coalescence. The behavior observed in the model system helps explain some previously published nanoscale solids-stabilized emulsion results and is consistent with the location of particles at fluid interfaces being influenced by: hydrophobicity, starting phase, line tension and van der Waals attraction.

Continuous evolution of Ga adlayer coverages during plasma-assisted molecular-beam epitaxy of (0001) GaN

We present a study of the evolution of the Ga adlayer during plasma-assisted molecular-beam epitaxy of (0001) GaN as a function of both Ga flux and growth temperature. In situ quadrupole mass spectrometry was used to quantitatively determine the adsorbed Ga coverage by monitoring its subsequent desorption after GaN growth. Independent of the growth time, the Ga adlayer was found to form steady-state coverages that increase continuously from 0 to 2.5 monolayers when raising the Ga flux from N-rich to moderate Ga-rich growth conditions. At higher Ga fluxes or lower growth temperatures, macroscopic Ga droplets form on top of the Ga adlayer (Ga droplet regime). Based on the temperature dependency for the transition between the Ga adlayer and Ga droplet regime, we determined an apparent activation energy of 3.4eV, which is discussed with respect to previously reported values.

Macroscopic-Wetting Anisotropy on the Line-Patterned Surface of Fluoroalkylsilane Monolayers

Micropatterned fluoroalkylsilane monolayer surfaces with liquidphilic/liquidphobic area (line width 1-20 microm) were prepared with few defects by vacuum ultraviolet (VUV) photolithography. The anisotropic wetting of a macroscopic droplet with a 0.5-5 mm diameter on the micropatterned surfaces was investigated. The strong anisotropy of the contact angle and the sliding angle and droplet distortion for fluoroalkylsilane/silanol patterned surfaces was attributed to the difference in the energy barrier of wetting between parallel and orthogonal lines. The wetting anisotropy decreased with decreases in the liquidphilic area. Fluoroalkylsilane/alkylsilane patterned surfaces with small differences in the surface free energies of the components showed anisotropic wetting only for the low-surface-tension liquids.

Nanobubbles give evidence of incomplete wetting at a hydrophobic interface

The appearance of a hydrophobic surface, namely a crystalline (111) Si wafer coated with a thick soft polystyrene film, and the morphological changes along this interface depending on the polarity of an adjoining liquid phase were studied with magnetic tapping mode atomic force microscopy. Interfacially associated nanobubbles of decreasing size and number are observed as the hydrophobicity of the subphase increases. The disturbance of the water structure in the contact region induces the formation of nanobubbles. The topology of the interface is visualized, starting with the dry polymer under normal atmosphere conditions and observing the changes as air is replaced by a series of liquids. With water, the surface coverage of the substrate with bubbles is almost a close-packed configuration. The bubble shape is well approximated by spherical caps of a rather low aspect ratio. The Gaussian size distributions of bubble shape parameters are discussed. The contact angle of the nanobubbles is substantially smaller than the corresponding number measured for a macroscopic droplet. This apparent discrepancy might be resolved if the nanobubbles were assumed to exist along the interface as a connecting sublayer between a depleted water film at the hydrophobic polymer surface and an adsorbed macrodroplet.

Influences of support fibers on shapes of heptane/hexadecane droplets in reduced gravity

This paper describes analytical and experimental results related to the effects of support fibers on shapes of heptane/hexadecane mixture droplets (both burning and evaporating) in reduced gravity. The experimental results were obtained from large droplets (a few mm) investigated during the MSL-1 Flight of Spacelab. Theoretical (asymptotic) analyses are developed to predict droplet shapes. These analyses, which predict droplet shapes very well, illustrate important aspects of droplet shapes in a transparent fashion. The asymptotic theory shows that for small droplet-fiber contact angles, two spatial zones exist where droplet shapes behave differently. Away from a fiber, a droplet is essentially spherical. As the fiber is approached, however, deviations from spherical symmetry are significant. Previously developed analytical theory to predict macroscopic droplet shapes also compares well with experimental results. In addition, the experiments indicate that thin liquid films can form on support fibers. In the present experiments, these films apparently lead to transient formation of small droplets/bubbles on the support fibers at locations near the surface of a droplet.

Nanobubbles: the big picture

Nanobubbles, whose existence on hydrophobic surfaces immersed in water has previously been inferred from measurements of long-ranged attractions between such surfaces, are directly imaged by tapping mode atomic force microscopy. It is found that the nanobubbles cover the surfaces in an irregular, interconnected or close-packed network whose morphology is dependent on pH and whose lifetimes are at least of the order of hours. Their height is of the order of 30 nm and their radius of curvature is of the order of 100– 300 nm . It appears that the nanobubbles form from a solution supersaturated with air. A thermodynamic and statistical mechanical analysis of the homogeneous nucleation of liquid droplets from a supersaturated vapour shows that although a single droplet can be in equilibrium with a finite volume of gas, for a gas reservoir the equilibrium state is represented by a single macroscopic droplet, which grows by collisions and by Ostwald ripening. It is concluded that the electric double-layer repulsion between neighbouring nanobubbles on the hydrophobic surface plays a role in their stabilisation.

Plasma–lithium interaction in the CDX-U spherical torus

Results on the interaction between plasma in the current drive experiment-upgrade (CDX-U) spherical torus and a liquid lithium limiter are reported. It is observed that macroscopic lithium droplets detach from the limiter head and fall towards the plasma core. However, no disruptions occurred during these discharges despite the fact that relatively large-scale blobs are observed entering the confined plasma. A multi-tip Langmuir probe measures the edge plasma properties. It is found that the average density and temperature and their fluctuations are unaffected by the presence of lithium within experimental error.

Instability and Reconstruction of Thin Liquid Layer Under Inversed Gravitation Conditions

Evolution of shape of thin liquid layer covering a solid substrate under conditions of inversed gravitation (the van der Waals's and gravitation forces have opposite directions) with increasing the layer thickness is studied numerically. It is shown that at thickness higher than the critical value ∼10−4 cm flat surface of neutral liquid layer becomes unstable, and the stationary solitary wave of surface deformation is formed, i.e. the reconstruction transition takes place at the surface. With increasing the layer thickness amplitude of the wave grows gradually, and at amplitudes much higher than the critical thickness shape of the wave is close to shape of single macroscopic droplet. Influence of external electric field on charged droplet's shape is evaluated, also. The obtained theoretical dependencies are used for treatment of results of the experiments with charged liquid hydrogen droplets.

Thermal Induced Instability of Thin Polymer Films: A Study by Atomic Force Microscopy

Systematic studies of thin-film stabilities of random copolymers consisting of decyl methacrylate (DMA)/methyl methacrylate (MMA) units on a polystyrene (PS) layer tethered to silicon wafer have been carried out by atomic force microscopy (AFM) as functions of molecular weight and chemical composition. Upon annealing at an elevated temperature above the glass transition temperature ( Tg), the initially flat polymer films break up into small holes, and finally form macroscopic droplets. The tethered PS layer was found to be dense enough to inhibit penetration of the copolymers into the lower layer during the annealing process. AFM studies at an early stage showed that the velocity of the hole growth was dependent upon both the molecular weights and chemical compositions of the copolymers. However, the equilibrium contact angles of the copolymer droplets formed on the PS layer were more dependent on the chemical compositions than on the molecular weights.