Drop Growth Research Articles

Effect of Surface Renewal on the Drop Size Distribution in Dropwise Condensation within a Hybrid Surface

The description of liquid drop growth and drop distribution are two key models in evaluating the thermal performance of dropwise condensation (DWC) heat transfer. The drop size distribution describes the growth process of small drops by direct condensation and large drops by coalescence. The present work investigates the effect of surface renewal and coalescence intensities of DWC within a hybrid surface. Additionally, it examines the validity of the current empirical expression of the drop size distribution that is developed for DWC without considering surface renewal and coalescence intensities. The simulation work illustrates the drop growth process and surface renewal as drops depart and merge with neighboring film regions. The simulation results show that in hybrid DWC, the area fraction occupied by drops (f) lies between 0.28 to 0.296 for the ratio of maximum drop diameter to DWC region width (RD) from 0.125 to 1 and a total temperature drop (∆T) of 2, 4, and 8 ℃. Thus, the drop population is less sensitive to RD, and an average f of 0.288 is generalized. On the other hand, the surface renewal for DWC within the hybrid surface shows improvement for RD > 0.5 with the highest enhancement of 64 to 85% taking place at RD = 1, mainly due to the merging effect. In addition, results for drop size distribution profiles of DWC within the hybrid surface are characterized by a lower population of large drops and a higher population of small drops than full DWC. Additionally, the constant exponent (n) in the literature’s empirical expression is replaced by a polynomial series as a function of drop effective and maximum radii. The impact of surface renewal on coalescence intensity is presented in a relatively steeper slope on the logarithmic scale.

Exploration of laser-induced drop transfer modes from wire for AM

Laser-induced ablation of drops from a metal wire enables the sequential deposition of voxels, for additive manufacturing. Striving for the goal of controlled, reproducible drop transfer, for this new technique, further trends and phenomena have been studied. Different modes of drop growth along with necking have been observed. Rather reproducible was a growing pending drop underneath the wire tip until separation for a certain size. In contrast, initial transients from the laser-induced recoil pressure can lead to a quick separation of a smaller drop. Initiation of a swinging cycle can also cause drop ablation after one cycle. For too fast wire feeding, the wire underpins the melt for a while in a spoon-like manner. Apart from the drop size, the different modes affect the scatter of the flight trajectory and landing position, as important optimization criteria, for controlled 3D-printing.

Nuclear viscosity estimated by dynamics of neck formation in the early stage of nuclear collision

The very early stage of the coalescence of two nuclei is studied and used to estimate the nuclear viscosity. The time evolution of the neck region has been simulated by the unified Langevin equation method, which is used in the analysis of heavy-ion collisions from the approaching stage to the fusion-fission stage. It is found that the transition from viscous to inertial coalescence that appeared in the neck growth of macroscopic drops can also be seen in the present simulation in nucleus–nucleus collisions. The dynamics of neck growth is analyzed in terms of the hydrodynamical formula and the viscosity coefficient of nuclear matter is estimated using the analogy of macroscopic drops.

Effect of water droplet growth dynamics on electrode current in fuel-cell catalyst layers

Fuel cells are a promising next-generation energy-conversion technology designed to replace internal combustion engines in transportation applications. However, much work remains to optimize them. Operation at high humidities causes liquid water droplet formation on Pt catalyst particles during oxygen reduction, potentially impeding reactant arrival to the reactive electrode. In this work, four different cases of water droplet growth in fuel-cell catalyst layers are considered: pinned or advancing droplets on a bare Pt surface, advancing droplets on a Nafion film, and water-layer growth in carbon nanopores. Transient drop growth is captured with a combination of mass, species mass, and momentum balances, and the subsequent limiting current is determined via oxygen diffusion and Tafel kinetics. Water droplets are found not to be mass-transfer limiting due to the relatively large liquid-gas area compared to the Pt nanoparticle. Mass-transfer-limited behavior is calculated in carbon nanopores.

Development of Drop Size Distribution Model for Dropwise Condensation on a Superhydrophobic Surface

This study presents a mathematical model of drop size distribution during dropwise condensation on a superhydrophobic surface. The model is developed by combining a power law growth model, an exponentially decaying population model, and a Gaussian probability model for growth variations. The model is validated against experiment data, with correlations ranging from 88% to 94%. The growth model is shown to sufficiently describe the growth of drops from 0.02 mm to 0.1 mm but may be extrapolated to describe the growth of even smaller drops. The experiment data show that drop size distribution or frequency distribution of drops of different sizes varies significantly with time and may be considered pseudo-cyclic. The developed model, together with the sweep rate of drops, sufficiently describes this behavior and, consequently, may also be used to better estimate the heat transfer rate due to dropwise condensation.

Binary Collisions of Water Drops in Presence of Horizontal Electric Fields: A Wind Tunnel Study

AbstractCoalescence/breakup characteristics of binary collisions of small water drops (dS = 0.4–1.8 mm diameter) with large drops (dL = 3–3.5 mm diameter) occurring in the absence/presence of horizontal electric field (EH) = 0, 100, and 300 kVm−1 have been investigated in a small vertical wind tunnel using a high‐speed digital camera. The coalescence efficiency (EC) of 0.299 observed for average diameters (dL = 3.2 mm, dS = 1.2 mm) in EH = 0 decreased to 0.244/0.211 when EH is increased to 100/300 kVm−1. The increase in the electric field reduces the probability of coalescence when Weber number (We) < 1. However, when We ≥ 1, an increase in We restricts the probability of coalescence. Our data, when plotted in the regime diagram in the We*‐p plane, delineates the collision outcomes in all‐electric field values but does show the overlapping of some data points in the adjacent categories. After a binary collision, the relaxation time for coalescence is higher than that for the breakup. Further, the relaxation time increases from the filament to sheet to disk mode of breakup in all‐electric field values. Fragment size distributions after the filament and sheet types of breakups differ and are differently affected by the applied electric field. Higher collision kinetic energy has a tendency to increase the number of fragments of the sizes between dL and dS. It is concluded therefore that, the effect of the electric field needs to be included in the estimation of drop growth and precipitation in clouds.

Investigation of airflow onto uncooled and cooled perpendicular substrates for bioaerosol sampling

A better understanding of the mechanics of condensation is needed to devise active bioaerosol samplers. Here, dropwise water condensation produced by directing humid air flow perpendicularly on ambient (25 °C) and cooled (4 °C) copper plate substrates was studied. Numerical data obtained from solving the two-dimensional incompressible Navier-Stokes equations with low Reynolds numbers (= 40) showed significant vorticity strength developing at the edges of the copper plate. This resulted in a higher degree of aerosol deposition and an increased likelihood of drop nucleation at the impaction zone. When a drop is already present at the edge, simulations predicted that the high vorticity region shifted to the apexes of drops with concomitant increase in the magnitude of vorticity strength. These results explained the experimentally-observed dropwise condensation of larger drops at the edges of the ambient substrate. Analyses of drop size distributions at the center and edges of ambient and cooled substrates showed that drop growth was enhanced by improved condensation on the cooled substrate surface in addition to the flow vorticity effect. Preliminary findings indicate that the recovery of viable aerosolized Escherichia coli from ambient and cooled substrate was found to be invariant, portending its utility for sampling when the electrical power available for cooling is limited.

Multiplexed Viability Assays for High-Throughput Screening of Spheroids of Multiple Sizes.

High-throughput (HT) drug screening is in high demand for successful drug discovery and personalized medicine. Spheroids act as a promising preclinical model for HT drug screening, which may decrease drug failures in clinical trials. Numerous spheroid-forming technological platforms are currently under development, which include synchronous, jumbo-sized, hanging drop, rotary, and nonadherent surface spheroid growth. Initial cell seeding concentration and time of culture play a vital role for spheroids to mimic the extracellular microenvironment of natural tissue, especially for HT preclinical evaluation. Hence microfluidic platforms become a potential technology to provide a confined space for the oxygen and nutrient gradients within the tissues while controlling the cell count and spheroid size in an HT manner. We describe here a microfluidic platform capable of generating spheroids of multiple sizes in a controlled manner with a predefined cell concentration for HT drug screening. Ovarian cancer spheroids grown on this microfluidic platform were evaluated for viability using a confocal microscope and flow cytometer. In addition, screening of the HT chemotherapeutic drug carboplatin was carried out on-chip to evaluate the impact of spheroid size on drug toxicity. This chapter summarizes a detailed protocol on microfluidic platform fabrication for spheroid growth, on-chip multi-sized spheroid analysis, and chemotherapeutic drug screening.

Ophthalmic Solution of Smart Supramolecular Peptides to Capture Semaphorin 4D against Diabetic Retinopathy (Adv. Sci. 3/2023)

Smart Supramolecular Peptides In article number 2203351, Lei Wang, Hao Wang, Bo Hu, and co-workers report the formulation of a smart supramolecular peptide (SSP) eye drop for diabetic retinopathy treatment that is effective via specifically identifying and capturing Semaphorin4D (Sema 4D), a strongly pro-angiogenesis and exudates factor. The combination of SSP eye drop and anti-vascular endothelial growth factor (VEGF) injection showed approximately two times better therapeutic effect over anti-VEGF treatment alone. This work provides an alternative and effective method for noninvasive treatment for diabetic retinopathy.

Experimental validation of a coupling concept for drop formation and growth onto porous materials by high-resolution X-ray imaging technique

Droplets formed on the hydrophobic surface of a porous medium exposed to a cross-flowing gas stream have a strong influence on the mass, momentum, and energy exchange across the porous interface, being of importance in several physical systems and engineering applications, like fuel cells. However, the fluid displacement front is highly complex at the pore-scale, since it is characterized by the surface wettability and a contact angle variation along the triple line. Furthermore, the droplet formation is affected by the pore geometry and the surface wettability. These result in a challenging multi-phase scenario with controversial literature, and few studies consider the detailed mechanism of droplet formation on the surface of the porous medium. In this work, two multi-scale simulations for the emerging water droplet from a single hydrophobic capillary pore opening into the gas phase are validated by a benchmark experiment with the help of a high-resolution X-ray imaging technique to characterize the droplet growing. A three-domain approach (gaseous free flow, interface and porous medium, FIP) was compared with a two-domain approach (based on a free-flow and the porous medium, FP). Whereas the three-domain approach introduces two sets of coupling conditions, one for the free flow-interface and one for the interface-porous medium, the two-domain approach introduces only one set of coupling connections for describing the interaction between the domains. In both approaches, droplet formation and growth alter the coupling conditions between the domains. While the FIP approach treats the porous medium as a continuous matter, it is resolved discretely with the help of a pore network in the FP approach. Both approaches show good agreements with the experimental observations and high correspondences for the drop volume, radii and contact angle evolution. The proposed models provide a base for future developments and help to gain a better insight about the impact of the droplet formation on the interface in a coupled free flow-porous medium system.

Assessing Raindrop Breakup Parameterizations Using Disdrometer Observations

Abstract An intercomparison of raindrop mean diameter frequency distribution (RDFD) is performed for numerical simulations of precipitating cloud systems using an array of models and microphysics schemes. This includes results from the Regional Atmospheric Modeling System (RAMS) double-moment microphysics, the Hebrew University Cloud Model bin microphysics (HUCM) interfaced to the RAMS parent model, and the Weather Research and Forecasting (WRF) Model with the Thompson, Morrison, double-moment 6-class (WDM6), and National Severe Storms Laboratory (NSSL) double-moment schemes. Simulations are examined with respect to the raindrop size distribution (DSD) volume-number mean diameter (Dm) and intercept parameter (Nw). When compared to a suite of disdrometer observations, the RDFD resulting from each microphysics scheme exhibits varying degrees of mean drop size constraints and peaks in the frequency distribution of Dm. A more detailed investigation of the peaked RDFD from the RAMS simulations suggests that the parameterization of raindrop collisional breakup can impose strong limitations on the evolution of simulated drop growth. As such, a summary and comparison of the drop breakup parameterizations among the aforementioned microphysics schemes is presented. While some drop breakup parameterizations are adjusted toward the observations by modifying the threshold diameter for the onset of breakup, this study explores the use of a modified maximum breakup efficiency. This method permits the parameterization to retain its threshold breakup diameter, while limiting the strength of drop breakup and permitting a broader range of drop sizes. As a result, the simulated mean drop sizes are in better agreement with observations.

Unique Radar Observations of Large Raindrops in Tropical Warm Rain during PISTON

Abstract Isolated warm-rain cells are an important feature over the tropical oceans. Although warm rain is typically associated with relatively small raindrops, large raindrops (>4.5 mm in diameter) have been observed in some cases. Previous studies have examined warm rain cells with large drops on a case-study basis, but they have yet to be investigated in a broader, statistical sense. During the recent Propagation of Intraseasonal Oscillations (PISTON) field campaign, a C-band polarimetric radar routinely measured extreme values of differential reflectivity in small, isolated convection, indicating the presence of large drops. Using an objective feature identification and tracking algorithm, this study offers new insights to the structure and frequency of cells containing large drops. Cells with high differential reflectivity (>3.5 dB) were present in 24% of all radar scans. The cells were typically small (8-km2 mean area), short lived (usually <10 min), and shallow (3.7-km mean height). High differential reflectivity was more often found on the upwind side of the cells, suggesting a size sorting mechanism was operating establishing a low concentration of large drops on the upwind side. Differential reflectivity also tended to increase at lower altitudes, which is hypothesized to be due to continued drop growth and increasing temperature (increasing the dielectric constant of water). Rapid vertical cross-section radar scans, as well as transects made by a Learjet aircraft with onboard particle probes, are also used to analyze these cells, and support the conclusions drawn from statistical analysis.

Effect of the Interactions between Oppositely Charged Cellulose Nanocrystals (CNCs) and Chitin Nanocrystals (ChNCs) on the Enhanced Stability of Soybean Oil-in-Water Emulsions.

Chitin nanocrystals (ChNCs) and cellulose nanocrystals (CNCs) have been recently used to stabilize emulsions; however, they generally require significant amounts of salt, limiting their applicability in food products. In this study, we developed nanoconjugates by mixing positively charged ChNCs and negatively charged CNCs at various ChNC:CNC mass ratios (2:1, 1:1, and 1:2), and utilized them in stabilizing soybean oil–water Pickering emulsions with minimal use of NaCl salt (20 mM) and nanoparticle (NP) concentrations below 1 wt%. The nanoconjugates stabilized the emulsions better than individual CNC or ChNC in terms of a reduced drop growth and less creaming. Oppositely charged CNC and ChNC neutralized each other when their mass ratio was 1:1, leading to significant flocculation in the absence of salt at pH 6. Raman spectroscopy provided evidence for electrostatic interactions between the ChNCs and CNCs, and generated maps suggesting an assembly of ChNC bundles of micron-scale lengths intercalated by similar-size areas predominantly composed of CNC. The previous measurements, in combination with contact angles on nanoparticle films, suggested that the conjugates preferentially exposed the hydrophobic crystalline planes of CNCs and ChNCs at a 1:1 mass ratio, which was also the best ratio at stabilizing soybean oil–water Pickering emulsions.

Comparison of Lagrangian Superdroplet and Eulerian Double-Moment Spectral Microphysics Schemes in Large-Eddy Simulations of an Isolated Cumulus Congestus Cloud

Abstract Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

A mechanistic model for the prediction of flow pattern transitions during separation of liquid-liquid pipe flows

A one-dimensional mechanistic model that predicts the flow pattern transitions during the separation of dispersed liquid-liquid flows in horizontal pipes was developed. The model is able to capture the evolution along the pipe of the four characteristic layers that develop from initially dispersed flows of either oil-in-water or water-in-oil at a range of mixture velocities: a pure water layer at the bottom, a settling (flotation/sedimentation) layer, a dense-packed zone, and a pure oil layer on the top. Coalescence correlations from literature were included in the model to predict the drop growth due to binary drop coalescence and the coalescence rate of drops with their corresponding interface. The model predictions on the evolution of the heights of the different layers were partly compared against available experimental data obtained in a pilot scale two-phase flow facility in a test section of 0.037 m inner diameter using tap water and an oil of density 828 kg m−3 and viscosity 5.5 mPa s as test fluids, and in a 0.1 m inner diameter test section using water and an oil of density 857 kg m−3 and viscosity 13.6 mPa s. It was shown that the evolution of the four characteristic layers depends on the rates of drop settling and drop-interface coalescence. Oil-in-water dispersions separated faster than water-in-oil ones, while dispersions with smaller drop-sizes were more likely to exhibit depletion of the dense-packed zone.

Multiscale Interactions Contributing to Enhanced Orographic Precipitation in Landfalling Frontal Systems over the Olympic Peninsula

Abstract Orographic precipitation results from complex interactions between terrain, large-scale flow, turbulent motions, and microphysical processes. This study appeals to polarimetric radar data in conjunction with surface-based disdrometer observations, airborne particle probes, and reanalysis data to study these processes and their interactions as observed during the Olympic Mountain Experiment (OLYMPEX). Radar and disdrometer observations from OLYMPEX, which was conducted over the Olympic Peninsula in the winter of 2015, revealed 3 times as much rain fell over elevated sites compared to those along the ocean and coast. Several events were marked by significant water vapor transport and strong onshore flow. Detailed analysis of four cases demonstrated that the warm sector, which previous authors noted to be a period of strong orographic enhancement over the terrain, is associated not only with deeper warm cloud regions, but also deeper cold cloud regions, with the latter supporting the growth of dendritic ice crystals between 4 and 6 km. This dendritic growth promotes enhanced aggregation just above the melting layer, which then seeds the warm cloud layer below, allowing additional drop growth via coalescence. Periods of subsynoptic variability associated with mesoscale boundaries and low-level jets are shown to locally modify both the ice microphysics as well as surface drop-size distributions. This study explores the spatial and temporal variability of precipitation, cloud microphysics, and their relationship over the complex terrain of the Olympic Peninsula. Significance Statement This study appeals to polarimetric radar, aircraft particle probes, disdrometer data, and reanalysis to investigate the complex interactions between large frontal systems, terrain, and microphysical processes contributing to precipitation characteristics at the surface over the Olympic Peninsula. The study finds that the precipitation is a complex function of the synoptic regime, distance inland, and terrain height. Ice microphysical processes aloft act to modulate the surface rain drop size distributions, and are more important in contributing to higher rain accumulations inland during the later phases of the warm sector, particularly over the middle terrain heights (100–500 m).

Analytical solution for large-deposit non-linear reactive flows in porous media

We discuss reactive flows in porous media that exhibit an irreversible chemical reaction between two components, resulting in large solid-product deposition. Previous works used the analytical solution for the linear problem with low deposition to determine model parameters from the reactant breakthrough concentrations and pressure drop growth across the core during laboratory coreflood. The present work derives an exact analytical solution for the non-linear problem with large solid-product deposition. We use the solution for interpretation of the laboratory data, and determination of the type curves for the measured values. Seven sets of experimental data are shown to closely match the data from the analytical model, which validates the analytical model.

Drops on the Underside of a Slightly Inclined Wet Substrate Move Too Fast to Grow

Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate over an otherwise uniform horizontal film. Here we show that this scenario is surprisingly reversed when the substrate is slightly tilted (≈2°); drops become too fast to grow and shrink over the course of their motion. Combining experiments and numerical simulations, we rationalize the transition between the conventional growth regime and the previously unknown decay regime we report. Using an analytical treatment of the Landau-Levich meniscus that connects the drop to the film, we quantitatively predict the drop dynamics in the two flow regimes and the value of the critical inclination angle where the transition between them occurs.

Heat transfer calculation under film and drop condensation on tube with heat intensifiers

This article discusses well-known models and equations for calculating the heat transfer gain during film and drop condensation on a pipe, which need to be improved. Film condensation heat transfer on horizontal pipe made from brass with knurling is analyzed. The heat transfer data for investigated steam mixture condensation on horizontal tube with spikes heat intensifiers is analyzed. It is noted that the functions of drop growth for various conditions and their distribution must be known for calculating heat transfer during drop condensation. The maximum droplet radius, droplet size distribution, and then condensation heat transfer performance could be adjusted with special condensing surfaces, such as gradient, superhydrophobic, grooved, hydrophobic-hydrophilic patterned and hybrid surfaces. Now the nanoscale structures can by nanotechnologies.

Multi-scale three-domain approach for coupling free flow and flow in porous media including droplet-related interface processes

Drops on a free-flow/porous-medium-flow interface have a strong influence on the exchange of mass, momentum and energy between the two macroscopic flow regimes. Modeling droplet-related pore-scale processes in a macro-scale context is challenging due to the scale gap, but might be rewarding due to relatively low computational costs. We develop a three-domain approach to model drop formation, growth, detachment and film flow in a lower-dimensional interface domain. A simple upscaling technique allows to compute the drop-covered interface area fraction which affects the coupling fluxes. In a first scenario, only drop formation, growth and detachment are taken into account. Then, spreading and merging due to lateral fluxes are considered as well. The simulation results show that the impact of these droplet-related processes can be captured. However, extensions are necessary to represent the influence on the free flow more precisely.