Pendant Droplet Research Articles

Central spot formed in dried coffee-water-mixture droplets: Inverse coffee-ring effect

We have investigated the formation of central spot when coffee-water-mixture droplets are dried, which is a reverse effect of the famous coffee-ring effect (CRE). Typically, the central spot is unnoticeable or ignored even though it is significant. The ring-shaped stain is due to the capillary flow (CF). The CF is caused by the difference in the evaporation rates between the edge and the center of the droplet owing to a temperature gradient. The same temperature gradient, however, causes the so-called Marangoni flow (MF). The MF is routinely ignored, particularly when the solvent is water. However, from experiments, we found that, in addition to the ring-shaped stain formed by the CRE, central spot is formed. When the volume of a droplet of coffee-water mixture is ∼15 μL, the strongest central spot is formed We employed an improved enhanced heat-transfer model, in which the shape of the droplet was assumed to be spheroidal, to understand the effects of the MF on the central-spot formation. According to the model, the formation of central spot can be explained, at least, semi-quantitatively. As a result of the existence of a stagnation point, the direction of flow is changed. Furthermore, the dependence of its location on the initial geometrical parameters of the droplet is very important. In addition, the effect of gravity was investigated for pendant droplets. The central-spot formation is more prominent in pendant droplets than in sessile droplets because the gravity enhances the MF in the pendant droplets, while it hinders the MF in the sessile droplets.

Mechanism of Sunlight Damage on Drip Tape by Pendant Droplets in Mulched Drip Irrigation

Abstract. Drip irrigation under mulch has been applied in China for nearly 20 years, but sunlight damage from the lens effect through droplets beneath clear plastic mulch is always a problem that cannot be ignored. Droplet volume and mulch wettability affect the geometric parameters of the pendant droplets. Changes in geometric parameters were experimentally investigated by analyzing side-view images of droplets. Models were built to predict droplet focal length and light-gathering power based on the geometric parameters. A comparison between numerical and optical experimental results suggested that the focal length model was accurate and reliable. The effective incident area of the parallel light proposed in this study could also be used to represent the light-gathering power, which had a relationship with the drip tape burning rate. The increase in wettability of the clear mulch considerably increased the focal length of the pendant droplets, expanded the focal length range, enhanced the light-gathering power, and thus increased the risk of drip tape burning. In practice, pendant droplets with a wetting radius of 3 to 5 mm, with corresponding focal lengths of 5 to 12 mm, have a high probability of emergence. Therefore, the distance between the mulch and drip tape should be beyond this focal length range to reduce the risk of drip tape burning by pendant droplets. In addition, filming the mulch surface with hydrophobic materials to increase the contact angles of droplets can also protect the drip tape from sunlight damage. Keywords: Drip irrigation under mulch, Drip tape burning, Effective incident area of parallel light, Focal length, Pendant droplet.

Ionic solubility and solutal advection governed augmented evaporation kinetics of salt solution pendant droplets

The presence of dispersed inclusions is known to modify the interfacial characteristics in liquids by adsorption–desorption of the ions at interfaces. The present article reports the influencing role of dissolved ions in a polar fluid on its evaporation dynamics. The evaporation dynamics of pendant droplets of aqueous solutions of variant simple salts and concentrations have been experimentally studied. The presence of salts is observed to enhance the evaporation rate (obeying the classical D2 law), and the enhancement has been found to hold a direct proportionality to the concentration of the dissolved salt. Furthermore, it is observed that the degree of enhancement in the evaporation rate is also directly proportional to the solubility of the salt in question. The phenomenon is explained based on the chemical kinetics and thermodynamics of hydration of the ionic species in the polar fluid. The classical evaporation rate constant formulation is found to be inadequate in modeling the enhanced species transport. Additional probing via particle image velocimetry reveals augmented internal circulation within the evaporating salt based drops compared to pure water. Mapping the dynamic surface tension reveals that a salt concentration gradient is generated between the bulk and periphery of the droplet and it could be responsible for the internal advection cells visualized. A thermo-solutal Marangoni and Rayleigh convection based mathematical formulation has been put forward, and it is shown that the enhanced solute-thermal convection could play a major role in enhanced evaporation. The internal circulation mapped from experiments is found to be in good quantitative agreement with the model predictions. Scaling analysis further reveals that the stability of the solutal Marangoni convection surpasses the thermal counterpart with higher salt concentration and solubility. The present article sheds insight into the possible domineering role of conjugate thermohydraulic and mass transport phenomena on the evaporation kinetics aqueous droplets with ionic inclusions.

The Mass Transfer and Coalescence Time Scales in Binary Droplet Systems for Copper Extraction

In this work, we studied whether coalescence has a direct effect on mass transfer in copper extraction. The coalescence of pendant and sessile droplets containing diluted Acorga M5640 in an aqueous copper sulfate solution was recorded on video. The videos were analyzed to determine droplet rest times, sizes, and concentrations. Concentration measurements revealed that coalescence does not enhance mass transfer because coalescence is a rapid phenomenon. A comparison of the experiments performed with and without mass transfer showed that the coalescence dynamics are not affected by mass transfer. A bimodal rest time distribution was observed when the copper sulfate solution was in the continuous phase. The surface flows and cell-like structures observed on the droplet interface are presumed to be because of a Marangoni convection, which is caused by concentration changes because of extraction. The presence and absence of surface flow is anticipated to lead to a bimodal rest time distribution. The presence of surface flow improves coalescence probability because of very short binary droplet rest times.

Numerical simulation of the transition of metal transfer from globular to spray mode in gas metal arc welding using phase field method

A numerical model is constructed based on the solution of the magnetohydrodynamic equations within the framework of phase field algorithm to simulate the metal transfer process and investigate the mechanism of the transition of metal transfer from globular to spray mode. Surface tension is the strongest driving force acting on the pendent droplet in globular transfer, while the governing force shifts to the electromagnetic pinch force in spray transfer. Driving force balance in the axial direction could be the indicator of detachment in globular transfer, while that force balance doesn’t exist in spray transfer. The condition for the transition from globular to spray transfer is that the local pressure at the root of the droplet caused by the electromagnetic pinch force exceeds the surface tension pressure at the droplet tip corresponding to a droplet radius equals to the wire radius. Compared with volume of fluid method, phase field method shows a more physically realistic estimation of the current path from the drop to the arc plasma and leads to a better agreement with experimental data.

Evaporation induced natural convection inside a droplet of aqueous solution placed on a superhydrophobic surface

Numerical study has been conducted to study the fluid convection inside sessile and pendant evaporating droplets of aqueous NaCl solution placed on a superhydrophobic surface. Evaporation from the droplet surface leads to increase in the solute concentration at the evaporating liquid–air interface generating concentration gradient inside the droplet. Concentration gradient inside the droplet induces Rayleigh convection. Fluid with higher concentration in the liquid–air interface region moves downward along the interface and lighter fluid rises upward along the central region of the droplet like a plume. The average concentration, evaporation rate and the maximum velocity inside the sessile droplet on a superhydrophobic surface is higher than that on a hydrophobic surface. Both sessile and pendant droplet configurations have been investigated. Fluid near the interface moves towards the substrate in case of sessile droplet, where as the fluid moves away from the substrate along the interface for the pendant droplet configuration. Two counter rotating recirculation bubbles are observed in both sessile and pendant droplets. The magnitude of maximum convection velocity and circulation strength of the recirculation bubbles for pendant droplet is smaller than that of sessile droplet at the same evaporation conditions. This may be attributed to the stratification of higher density fluid for the pendant droplet configuration which suppresses the Rayleigh convection. The effect of initial solute concentration on the strength of convection is stronger for sessile droplet configuration compared to that of pendant droplet. The present study establishes strong influence of superhydrophobicity and orientation on the internal convection inside a droplet of aqueous solution.

Cloud Activation Potentials for Atmospheric α-Pinene and β-Caryophyllene Ozonolysis Products.

The formation of atmospheric cloud droplets due to secondary organic aerosol (SOA) particles is important for quantifying the Earth’s radiative balance under future, possibly warmer, climates, yet is only poorly understood. While cloud activation may be parametrized using the surface tension depression that coincides with surfactant partitioning to the gas–droplet interface, the extent to which cloud activation is influenced by both the chemical structure and reactivity of the individual molecules comprising this surfactant pool is largely unknown. We report herein considerable differences in the surface tension depression of aqueous pendant droplets that contain synthetically prepared ozonolysis products derived from α-pinene and β-caryophyllene, the most abundant of the monoterpenes and sesquiterpenes, respectively, that are emitted over the planet’s vast forest ecosystems. Oxidation products derived from β-caryophyllene were found to exhibit significantly higher surface activity than those prepared from α-pinene, with the critical supersaturation required for cloud droplet activation reduced by 50% for β-caryophyllene aldehyde at 1 mM. These considerable reductions in the critical supersaturation were found to coincide with free energies of adsorption that exceed ∼25 kJ/mol, or just one hydrogen bond equivalent, depending on the ammonium sulfate and oxidation product concentration in the solution. Additional experiments showed that aldehyde-containing oxidation products exist in equilibrium with hydrated forms in aqueous solution, which may modulate their bulk solubility and surface activity. Equilibration time scales on the order of 10–5 to 10–4 s calculated for micrometer-sized aerosol particles indicate instantaneous surface tension depression in the activation processes leading to cloud formation in the atmosphere. Our findings highlight the underlying importance of molecular structure and reactivity when considering cloud condensation activity in the presence of SOA particles.

Ex situ calibration technique for simultaneous velocity and temperature measurements inside water droplets using temperature-sensitive particles

Phosphorescence-based temperature measurements usually employ in situ calibration in macro-scale flow domains. However, the application of conventional in situ calibration in millimetre scales such as in 2 mm droplets is difficult because temperature probing using an intrusive technique such as thermocouple-based measurement can deform a droplet interface and even its integrity. Therefore, in this paper we propose an ex situ calibration technique for combined 2D fluid temperature and flow velocity measurements inside pendant droplets using thermographic phosphorescence and particle image velocimetry. This calibration technique has the potential to perform measurements not only inside droplets but also in other small-scale fluid domains that are sensitive to intrusive temperature probing. To develop this technique, the effect of local phosphorescence intensity on the phosphorescence decay constant (initial intensity effect) was studied and quantified. We observed that the phosphorescence light intensity of the first image among the decay image series affects the local decay constants as the coefficient of a half sigmoid function. This novel ex situ calibration technique was used to investigate high-spatial-resolution temperature and flow velocity distributions inside a pendant water droplet located in an air stream, and an anti-distortion algorithm was used to correct the optical distortion induced by the curved surface of the droplet. The measured temperature and velocity fields were found to be reasonable and consistent with those obtained in previous studies. The proposed technique is expected to be useful in conducting further investigations on the mechanisms of heat and mass transfers between droplets and carrier gases. Furthermore, it can potentially improve our understanding of the heat and mass exchange mechanisms within a droplet’s internal flow structures and temperature gradients.

Spline Based Shape Prediction and Analysis of Uniformly Rotating Sessile and Pendant Droplets.

Prediction and analysis of the shapes of liquid-vapor interface of droplets under the influence of external forces is critical for various applications. In this regard, a geometric model that can capture the macroscopic shape of the liquid-vapor interface in tandem with the subtleties near the contact line, particularly in the regime where the droplet shape deviates significantly from the idealized spherical cap geometry, is desirable. Such deviations may occur when external forces such as gravity or centrifugal dominate over the surface tension force. Here we use vector parametrized cubic spline representation for axisymmetric fluid-fluid interfaces along with a novel thermodynamic free energy minimization based heuristic to determine the shape of liquid-vapor interface of droplets. We show that the current scheme can easily predict the shapes of sessile and pendant droplets under the action of centrifugal force over a broad range of surface contact angle values and droplet sizes encountered in practical applications. Finally, we show that the cubic spline based modeling approach makes it convenient to perform the inverse analysis as well, i.e., predict interfacial properties from the shape of a droplet under the action of various types of external forces including gravity and centrifugal. We believe that this versatile modeling approach can be extended to model droplet shapes under various other external forces including electric and acoustic. In addition, the simple shape analysis approach is also promising for the development of inexpensive interfacial analysis tools such as surface tensiometers.

Intensification of mass transfer and reaction in electrically disturbed liquid-liquid systems

A new study of electrically induced disturbances and mass transfer at a liquid-liquid interface as a means of process intensification is presented. Visualization of electrically induced disturbances during mass transfer of ethanol from an aqueous phase into an extracting solvent, n-decanol is demonstrated. Mass transfer rates were measured for extraction of ethanol from an aqueous electrically charged pendant droplet into a continuous phase of n-decanol. In a second part, mass transfer rates of ethanol into n-decanol across a planar interface in the presence of a DC electrical field are presented. Thirdly, results are presented of electrostatic spraying of aqueous enzyme solutions into an immiscible triglyceride ester oil phase. The effect of electrical field on specific interfacial rate of reaction was determined. The first part of the study demonstrated the positive effect of electrical disturbance on mass transfer rate from the pendant droplet. Time dependent mass transfer was also shown, consistent with earlier mass transfer studies with uncharged pendant drops. The mass transfer study using the planar interface provided further confirmation of the positive effect of electrically induced interfacial turbulence on mass transfer. The experimental data are successfully compared with simulations based on rigorous numerical solutions of the controlling equations. The visual disturbance pattern at the interface and rates of mass transfer were accurately predicted. The reactor experiments clearly show a significant positive effect of electrical charge on the specific rate of hydrolysis. This latter finding opens up the possibility of intensification of enzymatic catalytic activity using electrical fields. The potential for electrically induced enhancement of other reaction systems involving liquid-liquid interfaces such as in the case of phase-transfer catalysis is highlighted.

Measurement of Interfacial Tension of CO2 and NaCl Aqueous Solution over Wide Temperature, Pressure, and Salinity Ranges

Interfacial tension data and models are of great importance to the storage of CO2 in deep saline aquifers. In this study, the pendant-drop method combined with axisymmetric drop shape analysis was used in the interpretation of the interfacial behavior of CO2 and brine. Extensive experimental measurements of the interfacial tension between CO2 and an NaCl solution were acquired for pressures ranging from 3.0 to 12.0 MPa, temperatures from 300 to 353 K, and NaCl molalities from 0 to 1.8 mol·kg–1, for a total of 1,254 valid data points. All experiments were conducted in a pressure cell fitted with a capillary tube to create pendant droplets in a CO2-rich atmosphere. The experimental results indicated that interfacial tension decreased with increasing pressure and increased with temperature and salinity. As pressure increased to a certain point, the interfacial tension reached a plateau. At a given temperature, the CO2–aqueous system reached a plateau for different salinities under nearly the same pressure. However, the plateau pressure increased with temperature. The plateau interfacial tension value slightly increased with temperature and salinity. We also found a linear relationship between the change in interfacial tension and the molality concentration of brine. An empirical model was also proposed based on the Parachor model for the prediction of interfacial tension. Most results of this model deviated by less than ±5% from our experimental results, indicating that the model was a good fit to our experiments.

Electrochemical Study of a Pendant Molten Alumina Droplet and Its Application for Thermodynamic Property Measurements of Al-Ir

Limited knowledge of the thermodynamic and transport properties of refractory materials in the liquid state remains a key challenge limiting their application. Using alternating current (AC) and direct current (DC) techniques, the electrochemical kinetics of oxygen evolution and metal deposition was investigated in a pendant droplet of molten alumina (Al2O3) with three iridium (Ir) electrodes in a thermal imaging furnace. For the first time, the direct electrolytic decomposition of molten Al2O3 to oxygen gas and aluminum (Al) metal (alloyed with Ir) was observed, confirming the ionic nature of molten Al2O3. The decomposition potential of molten Al2O3 was measured with high precision using AC voltammetry, and the results demonstrated remarkable sensitivity to variation in temperature enabling measurement of chemical potential and entropy of Al at the Ir-rich solid-liquid phase boundary for the first time. The results were in remarkably close agreement with the most recent thermodynamic assessment of the Al-Ir system.

Ring-Sheared Drop (RSD): Microgravity Module for Containerless Flow Studies

Microgravity is potentially a powerful tool for investigating processes that are sensitive to the presence of solid walls, since fluid containment can be achieved by surface tension. One such process is the transformation of protein in solution into amyloid fibrils; these are protein aggregates associated with neurodegenerative diseases such as Alzheimer’s and Parkinson’s. In addition to solid walls, experiments with gravity are also subject to influences from sedimentation of aggregates and buoyancy-driven convection. The ring-sheared drop (RSD) module is a flow apparatus currently under development to study formation of amyloid fibrils aboard the International Space Station (ISS). A 25 mm diameter drop of protein solution will be contained by surface tension and constrained by a pair of sharp-edged tubes, forming two contact rings. Shear can be imparted by rotating one ring with the other ring kept stationary. Here we report on parabolic flights conducted to test the growth and pinning of 10 mm diameter drops of water in under 10 s of microgravity. Finite element method (FEM) based fluid dynamics computations using a commercial package (COMSOL) assisted in the design of the parabolic flight experiments. Prior to the parabolic flights, the code was validated against experiments in the lab (1 g), on the growth of sessile and pendant droplets. The simulations show good agreement with the experiments. This modeling capability will enable the development of the RSD at the 25 mm scale for the ISS.

High-speed camera thermometry of laser droplet generation

This paper presents a high-speed thermal imaging method using a visible light camera, with application to the laser droplet generation process (LDG). In the experiment, a nickel wire-end was exposed to a collimated laser beam, and the subsequent process of wire melting, pendant droplet formation and its detachment were recorded by a high speed camera. Instantaneous temperature fields of the metal surface were calculated from the imaging data and were characterized by a very good spatial and temporal resolution (200×400 pixels at 13,837 frames per second). The droplet temperature could be accurately calculated between the melting point of nickel (1455°C) and approximately 1950°C, where image saturation started to occur. The remaining pendant droplet was shown to cool much more rapidly than the detached droplet, which is due to the heat conduction to the solid wire. Except for the time immediately after the droplet separation, the temperature distribution across the melt droplets was found to be quite uniform. Apart from the possibility of temperature field calculation, it was also demonstrated that the high-speed images of the LDG process can accurately capture contours and oscillation dynamics of melt droplets.

Smart self-cleaning lens cover for miniature cameras of automobiles

The removal of water droplets is indispensable for practical applications, such as mirrorless smart vehicles that replace side mirrors with cameras, because it is directly connected to the safety of drivers and passengers. We systematically study the removal of sessile and pendant droplets both on inclined and horizontal planes by electrowetting (EW) actuation. Based on these results, we first propose a smart self-cleaning lens cover for miniature cameras assisted by EW with transparent coplanar electrodes. This design has technological advantages, such as a rapid cleaning operation, effective energy consumption, and efficient integration into any device.

Studies on laser induced emission of microdroplets containing Rhodamine 6G solutions in water doped with TiO2 nanoparticles

Studies on the emission spectra of microdroplets containing Rh6G solutions in water doped with TiO2 nanoparticles are reported. The excitation is made by the second harmonic of a pulsed Nd:YAG laser at 532nm, pulse duration at half maximum 6ns and energy varied between 6 and 10mJ. The laser induced emission spectra are analyzed function of TiO2 concentration and pumping laser energy. Comparison between fluorescence dispersed spectra emitted by pendant droplets containing TiO2 nanoparticles with respect to Rh6G water solutions droplets pumped in the same conditions is made. The surface tension measurements of the samples show that with variation of dye and nanoparticles concentrations, surface phenomena take place and influence the behavior of the droplet fluorescence.

Effect of a Surrounding Liquid Environment on the Electrical Disruption of Pendant Droplets.

The effect of a surrounding, dielectric, liquid environment on the dynamics of a suddenly electrified liquid drop is investigated both numerically and experimentally. The onset of stability of the droplet is naturally dictated by a threshold value of the applied electric field. While below that threshold the droplet retains its integrity, reaching to a new equilibrium state through damped oscillations (subcritical regime), above it electrical disruption takes place (supercritical regime). In contrast to the oscillation regime, the dynamics of the electric droplet disruption in the supercritical regime reveals a variety of modes. Depending on the operating parameters and fluid properties, a drop in the supercritical regime may result in the well-known tip streaming mode (with and without whipping instability), in droplet splitting (splitting mode), or in the development of a steep shoulder at the elongating front of the droplet that expands radially in a sort of "splashing" (splashing mode). In both splitting and splashing modes, the sizes of the progeny droplets, generated after the breakup of the mother droplet, are comparable to that of the mother droplet. Furthermore, the development in the emission process of the shoulder leading to the splashing mode is described as a parametrical bifurcation, and the parameter governing that bifurcation has been identified. Physical analysis confirms the unexpected experimental finding that the viscosity of the dynamically active environment is absent in the governing parameter. However, the appearance of the splitting mode is determined by the viscosity of the outer environment, when that viscosity overcomes a certain large value. These facts point to the highly nonlinear character of the drop fission process as a function of the droplet volume, inner and outer liquid viscosities, and applied electric field. These observations may have direct implications in systems where precise control of the droplet size is critical, such as in analytical chemistry and "drop-on-demand" processes driven by electric fields.

Time series analysis based study of a mass-spring-like oscillation and detachment of a metal pendant droplet

The subject of this study is the vertical mass-spring-like oscillation of a pendant droplet and its resonant detachment, which was experimentally observed in the process of laser droplet generation from a metal wire. The process was characterized by various time series, which were generated from a sequence of infrared intensity images of the process. Following a visual inspection of pendant droplet images and an analysis of a wavelet based time-frequency map of the droplet’s vertical displacement time series, the pendant droplet’s oscillation is described by a time-variable mass-spring system. Based on the characteristics of the time-frequency map, the resonant nature of the pendant droplet detachment was demonstrated. Additionally, an algebraic expression was formulated, which can be used to predict the detached droplet’s diameter as a function of the laser pulse frequency.

Evaporation-rate dynamics of a hemispherical, pendant liquid droplet, influenced by resonant oscillations

An oscillating hemispherical pendant droplet has been used as an instrument to modify evaporation conditions of simple and complex liquids. The resonant droplet vibrations can influence the evaporation by different mechanisms: by induced convective flows, by periodical changes of the pressure in the vapor phase and in the liquid phase, by stretching and contraction of the interface layer etc. On the other hand the applied dc voltage can influence and manipulate the diffusion flows of charged molecules and aggregates, if present. Pure water and water-SDS surfactant mixture, with micellar concentration 10−2M, have been examined. The time dependencies of the evaporation-rate are evaluated with evaporated-volume compensation technique.

Gas-adsorption dynamics at the water–air interface, revealed by resonant droplet tensiometry

A resonant hemispherical pendant droplet tensiometry has been used to register in real time the change of surface tension of low Bond number water droplets due to evaporation of simple volatile liquids, acetone and chloroform, in a closed vessel. The contributions of the gas vapor pressure and of the gas molecules adsorption to the surface tension changes are distinguished and evaluated in time. After the initial increase of gas adsorption, a negative adsorption has been found in later time, which may be informative for the dynamics of the adsorption and desorption processes in the interface layer. The observed desorption processes are stimulated by the mechanical oscillations of the interface layer, as far as the droplet is in resonance during the measurements.