Critical Droplet Size Research Articles

Spontaneous process of dispersed salt water droplets in lubricant oil establishing wetted areas: Settling, spreading, coalescing and de-wetting

Main shaft bearings determine aircraft engine's reliability and performance benchmark. Corrosion induced by salt water contamination in lubricant oil (SWCLO) is a big threat to bearing especially in coastal aircraft's engine. The recent progress in harm, purification and monitoring of SWCLO mixture contrasts the inadequate understanding about the critical process how droplet in SWCLO mixture is settled and distributed on bearing steel surface before corrosion occurrence. In present work, the complete processes towards reaching equilibrium states of single and multiple droplets were investigated. Hydrodynamic pressure involved model well predicts the overall falling of droplet over several millimeters. Smaller droplet has longer resting while faster spreading processes. Statistically, smaller droplet takes more time to be deposited accompanied by less probability, further smaller droplet keeps resting or drifting. There is a critical droplet size for deposition. Spreading induced coalescing causes droplet reshaping or de-wetting depending on causal and sessile droplet sizes. De-wetting indicates weakened corrosion. Spatial distribution of eventual sessile droplets is determined by deposition and coalescence at early stage of standing. These results are crucial for understanding, predicting and preventing aircraft engine's bearing corrosion from SWCLO mixture.

Jumping droplets

AbstractWhen microdroplets with quasi‐spherical contact angles coalesce together on a low‐adhesion substrate, the capillary‐inertial expansion of the liquid bridge induces a dramatic out‐of‐plane jumping event due to symmetry breaking. From the onset of merging, droplet jumping initiates after a capillary‐inertial time scale of μs with characteristic jumping speeds of order m/s. This coalescence‐induced jumping‐droplet effect is most commonly observed among a population of growing dew droplets on a superhydrophobic condenser, but can also occur by colliding deposited droplets together or during droplet sliding on fog harvesters. In this review, we cover the historical development of capillary‐inertial jumping droplets, summarize the decade‐long effort to rationalize the ultra‐low energy conversion efficiency and critical droplet size of the phenomenon, and then present 15 variations on a theme of jumping. Capillary‐inertial jumping droplets are not only a visceral illustration of the surprising power of surface tension at the microscale but they also have the potential to enhance phase‐change heat transfer, enable self‐cleaning surfaces, combat frost formation, harvest energy, and govern the rate of disease spread for wheat crops.

High efficiency separation of fine coke powders by the novel jet-swirl scrubber: Characteristics and mechanisms

The deep removal of fine coke powders is an urgent need and remains a great challenge for the stable operation of the delayed coke system. Herein, a novel jet-swirl scrubber was developed. A combined approach utilizing CFD and DPM was employed to investigate the mechanism of droplet fragmentation. The results indicated that droplets underwent two stages of fragmentation in the convergent and throat sections under the influence of turbulent vortex structures. This leaded to a rapid reduction in droplet size and an effective dispersion. Thorough mixing with the gas phase occurred in the divergent section, facilitating enhanced capture of coke powders. Cold model experiments were conducted to examine the relationship between droplet size, coke powders capture efficiency, and gas-liquid separation efficiency. Under the condition of optimized critical droplet size 0.106 mm by adjusting the flow rate, the removal efficient of coke powders was up to 99.57 %. This work provides valuable technical support for further development and process optimization of the decoking powder unit in delayed coking system.

Investigating airborne transmission risks: A mathematical model of evaporating droplets with solid residue

The COVID-19 pandemic has spotlit the scientific field of fluid dynamics governing airborne transmission through virus-laden mucosal-salivary droplets. In this work, a mathematical model for airborne droplet dispersion and viral transmission centered on evaporating droplets containing solid residue was proposed. Droplet dynamics are influenced by factors such as initial velocity, relative humidity (RH), and solid residue, in agreement with analytical and experimental results. Interestingly, the maximum droplet dispersion distance depends strongly on initial droplet size and RH, such as 0.8-mm-diameter droplet at 0.3 RH, 1.0 mm at 0.6 RH, and 1.75 mm at 0.9 RH, but only weakly on initial projected velocity. Under realistic conditions, an evaporating sputum droplet can cover a dispersion distance at least three times than that of a pure water droplet. Based on Wells falling curves, the critical droplet size, the largest droplet that can remain suspended in air without settling due to gravity, ranges from 120 μm at 0.3 RH to 75 μm at 0.9 RH. Together, our results highlight the role of evaporation on droplet lifetime, dispersion distance, and transmission risks.

Performance of the frosting characteristics of fin-and-tube heat exchanger subject to superhydrophobic coating

The condensation and freezing processes of fin-and-tube heat exchangers with a bare surface and coated with a superhydrophobic substance were experimentally studied for various air velocities, relative humidity (RH) values, and fin spacings. The performance of the fin-and-tube heat exchangers in terms of dynamic pressure drop and heat transfer rate were reported in details. The frosting characteristics of these exchangers were visually characterized microscopically. It is found that for a superhydrophobic exchanger with 1-mm fin spacings, water bridges were likely to form, causing droplets to stick between the fins instead of slipping off the surface. At a low RH and a maximum air velocity of 1.0 m s−1, the heat transfer rate of the superhydrophobic exchanger was 12% lower than that of the surface without superhydrophobic coating. For a fin spacing of 3.0 mm, the critical droplet size was smaller than the fin spacing, hence the droplets can easily slip or jump off the fins. At a velocity of 0.6 m s−1, the steady-state pressure drop at low humidity of the superhydrophobic exchanger was 14% lower than that of the bare surface because of the differences in frosting characteristics. The results of this study indicate that the adopted superhydrophobic coating can delay frosting at high humidity and air velocity.

Limitations of Atomistic Molecular Dynamics to Reveal Ejection of Proteins from Charged Nanodroplets.

Atomistic molecular dynamics (MD) is frequently used to unravel the mechanisms of macroion release from electrosprayed droplets. However, atomistic MD is currently feasible for only the smallest window of droplet sizes appearing at the end steps of a droplet's lifetime. The relevance of the observations made to the actual droplet evolution, which is much longer than the simulated sizes, has not been addressed yet in the literature. Here, we perform a systematic study of the desolvation mechanisms of poly(ethylene glycol) (PEG), protonated peptides of different compositions, and proteins, to (a) obtain insight into the charging mechanism of macromolecules in larger droplets than those that are currently amenable to atomistic MD and (b) examine whether currently used atomistic MD modeling can establish the extrusion mechanism of proteins from droplets. To mimic larger droplets that are not amenable to MD modeling, we scale down the systems, by simulating a large droplet size relative to the macromolecule. MD of PEG charging reveals that, above a critical droplet size, ions are available near the backbone of the macromolecule, but charging occurs only transiently by transfer of ions from the solvent to the macroion, while below the critical size, the capture of the ion from PEG has a lifetime sufficiently long for the extrusion of a charged PEG from the aqueous droplet. This is the first report of the role of droplet curvature in the relation between macroion conformation and charging. Simulations of protonated peptides with a high degree of hydrophobicity show that partial extrusion of a peptide from the droplet surface is rare relative to desolvation by drying-out. Different from what has been presented in the literature, we argue that atomistic MD simulations have not sufficiently established the extrusion mechanism of proteins from droplets and their charging mechanism. We also argue that release of highly charged proteins can occur at an earlier stage of a droplet's lifetime than predicted by atomistic MD. In this earlier stage, we emphasize the key role of jets emanating from a droplet at the point of charge-induced instability in the release of proteins.

Properties and microstructural evolution of a ternary Cu–Co–Fe immiscible alloy solidified under high magnetic fields

In this study, ternary Cu52Co24Fe24 immiscible alloys are prepared with varying undercoolings and under a high magnetic field. The microstructure evolution and properties of the alloys are investigated. The temperature range of the immiscible gap is determined using CALPHAD. According to the excess Gibbs free energy of liquid, the addition of Fe promotes the demixing tendency of the Cu–Co–Fe ternary system during solidification. With the application of a magnetic field, the (Fe, Co)-rich phases transform from a globular shape to an elongated form along the direction of the magnetic field during solidification, which is due to the existence of the counteracting behavior of the interparticle magnetic dipole-dipole force at the critical droplet size. Under a high magnetic field, the obtained samples had a more dispersed minority phase, higher microhardness and better conductivity. However, the saturation magnetization of the samples with large undercooling decreases with increasing magnetic field due to the suppression of the phase separation behavior under a high magnetic field. This study proposes a novel technology for preparing immiscible alloys with excellent properties by applying a superimposed magnetic field during solidification.

Analysis of the characteristics of the gas–liquid mixed artificial snow-making

This study investigates the heat and mass transfer of liquid droplets freezing in the process of artificial snow-making, and emphatically analyses the effects of droplet size, ambient temperature and relative humidity on the evaporative cooling and freezing of liquid droplets by establishing a theoretical model. On this basis, the critical droplet size for snow-making under different environmental conditions is obtained, and the accuracy of the droplet freezing model was verified by artificial snow-making experiments. Finally, by analyzing the density of artificial snow under different environmental conditions, the optimum gas-liquid mixing mass ratio (GLR) suitable for snow-making is obtained. The results show that the liquid droplets could be frozen under the action of self-evaporation and convection heat transfer with ambient. The time required for the droplet to be frozen completely shows a positive correlation with ambient temperature, relative humidity and droplet size. In the evaporation cooling stage, the droplet cooling rate increases with the decrease of ambient temperature, and in the phase transition stage, the time for the droplet resists the latent heat of phase transition increases with the increase of the droplet size. When the droplet size is smaller than the critical size for snow-making, the artificial snow can be achieved at a maximum temperature of 3 °C. The snow density decreases with the increase of GLR. And when the GLR is greater than 0.15, the snow density tends to be stable.

Predominance of inhalation route in short-range transmission of respiratory viruses: Investigation based on computational fluid dynamics.

the Supplementary Materials are available in the online version of this article at 10.1007/s12273-022-0968-y.

Fingering instability of active nematic droplets

From the mitotic spindle up to tissues and biofilms, many biological systems behave as active droplets, which often break symmetry and change shape spontaneously. Here, I show that active nematic droplets can experience a fingering instability. I consider an active fluid that acquires nematic order through anchoring at the droplet interface, and I predict its morphological stability in terms of three dimensionless parameters: the anchoring angle, the penetration length of nematic order compared to droplet size, and an active capillary number. Droplets with extensile (contractile) stresses and planar (homeotropic) anchoring are unstable above a critical activity or droplet size. This instability is interfacial in nature: it arises through the coupling of active flows with interface motion, even when the bulk instability of active nematics cannot take place. In contrast to the dynamic states characteristic of active matter, the instability could produce static fingering patterns. The number of fingers increases with activity but varies non-monotonically with the nematic penetration length. Overall, these results pave the way towards understanding the self-organized shapes of biological systems, and towards designing patterns in active materials.

Effect of Flow Rate on the Corrosion Behavior of API 5L X80 Steel in Water-Saturated Supercritical CO2 Environments

The effect of the water-saturated supercritical carbon dioxide (scCO2) flow rate on the corrosion behavior of API 5L X80 steel at a temperature of 35°C and pressure of 80 bar was investigated. Tests were performed with the samples attached to a rotating shaft inside an autoclave. Results indicate that increasing the scCO2 flow rate had no significant influence on the general/localized corrosion rate under the various dynamic conditions considered. The average general corrosion rate was 0.064 mm/y, while the average measured pitting penetration rates were one order of magnitude higher. The size of the corrosion features on the surface of the samples, which were believed to provide an indication as to the size of the condensed water droplets, was much smaller than the calculated critical droplet size needed to be displaced by the flow, supporting the theory as to why flow rate had little effect on the corrosion response.

Destabilising persistent coal froth using silicone oil

Persistent froth is becoming more and more common in coal and mineral flotation plants and presents safety and operational challenges. No effective method has been developed to destabilise persistent froth. As a new initiative, this study examined the structural difference between persistent foam and coal froth, based on which a solution was developed to maximumly destabilise coal froth. Destabilisation test, oscillatory rheology measurement and scanning electron microscopy (SEM) analysis indicated that the coal froth was more stable than the foam due to the formation of thin capillaries and tightly arranged coal particles on bubble surfaces. Although 107 µm silicone oil droplet could completely destabilise the foam at 2 mmol/L concentration, it only destabilised less than 50% coal froth even at 6 mmol/L concentration. To maximumly destabilise the coal froth formed by −38 and −20 µm particles, 24 and 18 µm silicone oil droplets were required to pass through the thin capillaries and enter the bubble films, respectively. However, smaller silicone oil droplets could not bridge the bubble films to destabilise coal froth and therefore a critical droplet size occurred depending on the size of particles stabilising the froth.

Droplet shedding characteristics on metal fibers with different wettability and inclined angles

Critical size of droplet on metal fiber is an important parameter during the dehumidifying process, as it determines the drainage performance of metal foam heat exchangers. In the present study, the droplet shedding characteristics on metal fibers with various fiber diameters, surface wettability and inclined angles were investigated experimentally. The results show that, the critical size of droplet on metal fibers is increased by 69%-213% as the receding contact angle reduces from 132.8° to 17.2°, and it is increased by 93%-292% as the fiber diameter increases from 0.3 mm to 2.0 mm. As the inclined angle of metal fiber increases from 0° to 90°, the critical droplet size is decreased by 78%-86%. Based on the equilibrium of gravity and capillary force, a predictive correlation for the critical droplet size on metal fibers with different wettability and inclined angles was developed, and it agrees with 90% of the experimental data within a deviation of ±15%.

Optimization of Brinzolamide Loaded Microemulsion using Formulation by Design Approach: Characterization and <l>In-vitro</i> Evaluation

Background: The clinical application of Brinzolamide, a drug used in the treatment of glaucoma is limited due its poor aqueous solubility. Microemulsion based ocular delivery can be an effective means to improve its solubility and in turn the bioavailability. Objective: The main objective of the present work was optimization and characterization of Brinzolamide loaded microemulsion for the treatment of glaucoma. Method: The solubility of Brinzolamide in various oils and surfactants was checked in order to identify components of microemulsion. Pseudo-ternary phase diagram using Prosim software was plotted to identify microemulsion existence area. D-optimal mixture design was used for optimization of microemulsion. The optimized formulation consisted of Isopropyl myristate, Tween-80 and Transcutol-P as surfactant and co-surfactant respectively, and water. The chosen critical responses were droplet size, zeta potential, nepheloturbidimetric unit, and viscosity. Results: The selected optimal composition shows favorable features, such as droplet size (41.69 nm), Zeta potential (-9.496 mV), Viscosity (170.8 cps), Transparency (1.483 NTU) and pH (7.646) that are suitable for ocular delivery. Moreover, a prolonged drug release (78.08 % within 7 hour) was found in in-vitro experiments. By and large the formulation was found to be safe and nonirritant as proven by the ocular irritation study. Conclusion: Our study illustrated potential of Brinzolamide loaded microemulsion for ocular delivery for the treatment of glaucoma.

Experimental Investigation on Metallic Droplet Behavior in Molten BOF Slag

In order to better understand the metallic droplet behavior during a slag treatment process, a physical modeling based on the similarity principle was performed in a transparent scaled-down vessel at room temperature. Paraffin oil, 20 wt pct copper sulfate solution, and compressed air were used to simulate the molten slag, metallic droplet, and carrier gas, respectively. The droplets injected into paraffin oil during the experiment were captured by a high speed camera and were analyzed by Image Pro Plus software to obtain the droplet size distribution. The critical droplet size in the physical modeling and slag treatment process is quantitatively correlated. The results show that droplet breakage phenomenon is dominant over its coalescence in the current industrial practice, and droplet breakage is enhanced with increasing gas flow rate and/or lance depth. No significant effect of the nozzle configuration was found on the droplet breakage and coalescence. The droplet size distribution varies with the lance position. Gas flow rate and lance depth are the most important factors for droplet breakage, the extent of which can be reduced through a proper selection of the operational conditions. A linear relationship between the droplet size and the input energy flux is obtained.

Coalescence-induced droplet detachment on low-adhesion surfaces: A three-phase system study.

Coalescing water droplets on superhydrophobic surfaces can detach from the surface without the aid of any external forces. This self-propelled droplet detachment mechanism is useful in many applications, such as phase change heat transfer enhancement, self-cleaning surfaces, and anti-icing and antidew coatings. In this article, the coalescence-induced droplet jumping in a three-phase system is numerically investigated. The gaps between the surface structures are filled with a liquid that is immiscible with water, e.g., lubricant. A mass-conserving lattice Boltzmann method is implemented to study the effects of several parameters, such as interfacial tensions, droplet size, and surface wettability on the jumping process. The numerical results show that for relatively high values of lubricant-water interfacial tensions and large surface-water contact angles (>150^{∘}) the water droplets are capable of detaching. The critical droplet size for jumping is also highly dependent on the lubricant-water interfacial properties. The results of this study provide insights into the fluid-fluid and fluid-solid interactions and shed light on the underlying mechanisms involved in the droplet coalescence process on such surfaces.

WETTING AND PREWETTING PHENOMENA IN NEMATIC LIQUID CRYSTAL DISK-LIKE DROPLET

We present a theoretical investigation of wetting and prewetting phenomena in a nematic-disk like droplet under a concentric anchoring configuration. Our theoretical model is based on Landau–de Gennes free energy together with a quadratic surface energy. By using the Maxwell construction, we numerically solve the Euler–Lagrange differential equation. The occurrence of boundary layer transition is summarized in the phase diagram scanned by temperature and surface potential. We find that prewetting phenomenon disappear below a critical droplet size and critical temperature.

Influence of the Homogenization Pressure on the Rheology of Biopolymer-Stabilized Emulsions Formulated with Thyme Oil

Different continuous phases formulated with ecofriendly ingredients such as AMIDET® N, an ecological surfactant, as well as welan and rhamsan gums were developed. An experimental design strategy was been in order to study the influence of the ratio of these two polysaccharides and the homogenization pressure applied in a microfluidizer on the critical shear stress for the continuous phases developed. A pure rhamsan gum solution was selected as the starting point for further study based on the production of thyme oil-in-water emulsions. The effect of the homogenization pressure on the physical stability, critical shear stress and droplet size distribution was analyzed for emulsions with optimized values of the rhamsan–welan ratio. These bioactive thyme oil-in-water emulgels could be considered as delivery systems with potential applications in the food industry.

Effect of protein type, concentration and oil droplet size on the formation of repulsively jammed elastic nanoemulsion gels.

Rheology of sodium caseinate (SC) and whey protein isolate (WPI)-stabilized nanoemulsions (NEs) was investigated as a function of protein (1-5 wt%) and oil (30 and 40 wt%) concentration and storage time. For SC NEs, gel strength increased with an increase in protein and oil concentration and a decrease in droplet size and below a critical size transformed into a strong elastic gel that did not flow under gravity. Surprisingly, WPI NEs, although stable and had similar droplet size to SC NEs, did not form elastic gels. The stability of the NEs was studied for 3 months, and no significant change was observed. Considerable higher storage modulus (G') of SC NEs compared to WPI NEs was attributed to an increased effective droplet volume fraction (φeff) due to a thicker steric barrier of SC compared to WPI. The DLVO interdroplet potential was used to calculate the thickness of the charge cloud at an overall repulsive interaction of 1 kBT, which was added to the steric barrier to calculate the effective droplet size and φeff. At the highest φeff (0.79) for 5% SC NEs with 40% oil, the nanodroplets and associated repulsive barrier randomly jammed, leading to the formation of a strong elastic gel. For WPI NEs, maximum φeff was 0.57, leading to a lack of jamming and viscous fluid-like behaviour. Re-plotting G' with φeff for SC NEs with different protein concentration showed a linear trend followed by a rapid increase in G' at a critical φeff, confirming the transition from weak glassy region to strong randomly jammed structure. SC-stabilized repulsively jammed NE-gels could be used as a novel soft material where a lower oil volume fraction and long-term stability is required.

Aspects of nucleation on curved and flat surfaces.

We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calculations in the plane and on the sphere. Using an isoperimetric inequality from the differential geometry literature and a theorem on the inequality's saturation, we show how geometry informs the critical droplet size and shape. This inequality establishes a "mean field" result for nucleated droplets. We then study the effects of fluctuations on the interfaces of droplets in two dimensions, treating the droplet interface as a fluctuating line. We emphasize that care is needed in deriving the line curvature energy from the Landau-Ginzburg energy functional and in interpreting the scalings of the nucleation rate with the size of the droplet. We end with a comparison of nucleation in the plane and on a sphere.