Droplet Flow Research Articles

A Literature Review on Numerical Simulation of Thermal Anti-Icing

This paper reviews the numerical simulation method for thermal anti-icing. Typically, the numerical study of an anti-icing system involves a coupled simulation of various physical processes: airflow, droplet flow, thin water film flow on the wall, and heat conduction within the solid wall. Airflow is commonly simulated using the Reynolds-Averaged Navier–Stokes method, while droplet flow can be modeled using either the Eulerian or Lagrangian approach. For simulating water film flow, there are three primary models: the Messinger model, the SWIM model, and the Myers model. The heat transfer process within the solid wall can be coupled with the external air/droplet and film flow using either a tight-coupling or a loose-coupling method. When simulating an electrothermal anti-icing system, methods such as the equivalent heat conductivity scheme or shell conduction method are employed to handle heat conduction in multi-layer thin walls. To improve the accuracy of thermal anti-icing simulations, additional research is still necessary, focusing on studies on rivulet flow, bead flow, and the heat convection coefficient on the system’s wall.

The overall‐process dynamic mass transfer research of surfactant at the three‐phase emulsions interface

AbstractSurfactant‐stabilized multiphase emulsions are widely used. However, current studies on the dynamic adsorption of emulsions during flow are mainly focused on the droplet formation stage rather than the flow stage. In this study, the mass transfer of surfactants in microchannels during the droplet formation and flow phases (the overall process) was investigated and a mass transfer diffusion model and an adsorption kinetic model for emulsions were developed, which explained the mass transfer process in microchannels for low and high surfactant concentrations, respectively. Subsequently, dynamic interfacial tension values between the two phases were calculated using two surfactants (SDS and DTAB) to validate these models and the results were in good agreement with the experimental values. This study contributes to a deeper understanding of how surfactants diffuse throughout three‐phase emulsions, thus shedding light on the mass transfer mechanisms inherent in these complex systems.

Clearing MRD positivity with blinatumomab in pediatric B-cell acute lymphoblastic leukemia: insights from droplet digital PCR and flow cytometry.

Blinatumomab has shown to improve survival outcomes in B-cell acute lymphoblastic leukemia (B-ALL) patients with measurable residual disease (MRD) detected by multiparametric flow cytometry (MFC). However, data on blinatumomab clearing MRD with high sensitivity remain scarce. This study evaluates the effectiveness of blinatumomab in eradicating low levels of MRD, as detected by droplet digital PCR (ddPCR) but undetectable by MFC, in children with B-ALL. Patients (n = 9) whose MRD was undetectable by MFC but detectable by ddPCR after chemotherapy and followed by blinatumomab consolidation were included retrospectively. After the administration of blinatumomab, 5 out of 9 patients (55.56%) successfully achieved undetectable levels of ddPCR-MRD. Notably, among the 4 patients with BCR::ABL1 gene-positive acute lymphoblastic leukemia (ALL), only one achieved gene negativity. Starting from the initiation of blinatumomab treatment, with a median follow-up of 12 months, all patients remained in complete remission. Our study was the first to demonstrate that blinatumomab could further eradicate ddPCR MRD after patients achieve MFC-MRD undetectable status in B-ALL patients.

Numerical simulation of high-concentration droplet flow in an idealized mouth–throat airway model in the influence of environmental temperature and humidity

The exchange of water vapor between high-concentration droplets and air significantly influences droplet deposition in the upper airway model during nebulizer use. This study employed a two-way coupled Eulerian–Lagrange method to quantify nebulized droplet evaporation and relative humidity (RH) variations within an idealized mouth–throat (MT) airway model, utilizing validated numerical models. The water vapor interaction between high-concentration droplets and inhaled air was computed using a multiplier based on the particle parcel method. Simulations of normal saline droplet flow inhalation in the MT airway were conducted under two environmental conditions: indoor (26.5 °C, RH = 50%) and warm and wet (30 °C, RH = 75%), with various inhalation flow rates mirroring previous experiments. Droplet deposition fractions (DFs) and deposition patterns were recorded. The results indicated that DF initially decreased and then increased with rising inhalation flow rates. The largest discrepancy between predicted and measured DFs was 10.86%. These findings support the theory that the balance between droplet evaporation and elevated air RH dictates the deposition of nebulized droplets in the airway. Additionally, simulations revealed that environmental conditions significantly affect droplet DF, with variations up to 20.78%. The deposition hotspot shifted from the anterior to the posterior pharynx.

Engineering Wettability Transitions on Laser-Textured Shark Skin-Inspired Surfaces via Chemical Post-Processing Techniques.

Surface wettability, the interaction between a liquid droplet and the surface it contacts, plays a key role in influencing droplet behavior and flow dynamics. There is a growing interest in designing surfaces with tailored wetting properties across diverse applications. Advanced fabrication techniques that create surfaces with unique wettability offer significant innovation potential. This study investigates the wettability transition of laser-textured anisotropic surfaces featuring shark skin-inspired microstructures using four post-processing methods: spray coating, isopropyl alcohol (IPA) treatment, silicone oil treatment, and silanization. The impact of each method on surface wettability was assessed through water contact angle measurements, scanning electron microscopy (SEM), and laser scanning microscopy. The results show a transition from superhydrophilic behavior on untreated laser-textured surfaces to various (super)hydrophobic states following surface treatment. Chemical treatments produced different levels of hydrophobicity and anisotropy, with silanization achieving the highest hydrophobicity and long-term stability, persisting for one year post-treatment. This enhancement is attributed to the low surface energy and chemical properties of silane compounds, which reduce surface tension and increase water repellence. In conclusion, this study demonstrates that post-processing techniques can effectively tailor surface wettability, enabling a wide range of wetting properties with significant implications for practical applications.

Fog collection using hydrophobic and hydrophilic treatments on wrinkle‐based multilayered surfaces

AbstractThis study evaluated the fog‐collection efficiency of wrinkle‐based multilayer surfaces using hydrophilic and hydrophobic treatments. The wrinkle structures were fabricated by leveraging the elastic modulus and Poisson's ratio of polydimethylsiloxane (PDMS) and ultraviolet (UV) resin. The optimal wrinkle periodicity for fog collection was determined by varying the spin‐coating rate of the UV resin. Chemical surface treatments were examined by applying hydrophilic (hyaluronic acid [HA]) and hydrophobic (perfluoropolyether [PFPE] and TiO₂‐PFPE) agents. Surfaces with perpendicular wrinkles treated with TiO₂‐PFPE demonstrated the highest fog‐collection efficiency due to increased surface roughness that promoted droplet nucleation and growth. These wrinkles further optimized efficiency by facilitating the rapid downward flow of water droplets through the combined effects of gravity and capillary action. The study highlights the significant impact of wrinkle structures and surface treatments on fog collection, with the TiO₂‐PFPE treatment showing particular effectiveness and potential for applications in arid regions.

Optimisation of a converging-diverging nozzle for the wet-to-dry expansion of the siloxane MM

Wet-to-dry expansion within the nozzle guide vane of an ORC turbine has been proposed as a means to improve the power output of ORC systems for waste-heat recovery (<250 °C). However, given the rapid fluid acceleration in the stator, the phases can develop significant velocity and temperature disparity due to density difference and finite rate of interphase heat transfer. Since these factors can significantly affect the phase-change process, wet-to-dry nozzle design techniques must account for non-equilibrium effects. The first part of this paper aims to further verify a previously developed quasi-1D inviscid non-equilibrium nozzle design tool by comparing it to non-equilibrium CFD simulations, which, unlike the design model, account for lateral flow variations, viscous and turbulence effects, along with secondary momentum forces. Within the CFD model, the interphase mass, momentum, and energy exchange models have been updated using correlations better tailored to evaporating droplet flows and a corrected drag equation. Moreover, the definition of the vapour mass fraction has been modified, while a simplified droplet breakup model has been used to predict the droplet size. The results from the CFD simulations indicate that the outlet vapour mass fraction is approximately 10 to 15% lower than that predicted by the quasi-1D tool. However, the overall flow behaviour and phase-change pattern were in satisfactory agreement, justifying the use of the design tool for 1D optimisation. As such, the quasi-1D tool is coupled to a gradient-based optimiser to optimise the nozzle pressure profile and enhance evaporation of siloxane MM for expansions with an inlet pressure ranging from 450 to 650 kPa, and inlet vapour quality of 0.3. CFD simulations of the optimised geometries indicate an increase of 3.3 to 5.7% in the outlet vapour mass fraction, which was raised from 84.9, 87.7 and 90.5% to 88.2, 93.4 and 95.7% for 450, 550 and 650 kPa inlet pressures respectively. However, a more abrupt expansion in the optimised nozzles resulted in the development of a shock and led to deterioration in nozzle efficiency compared to the baseline nozzles. Finally, a CFD-based shape optimisation was conducted, which demonstrated that it may be difficult to further enhance the vapourisation rate. However, the optimised geometry did mitigate the effect of the oblique shock that appears in the diverging section of the nozzle, raising the expansion efficiency by around 3%.

Insights into surrogate respiratory droplet behaviour on inclined surfaces: Implications for disease transmission

Disease transmission via fluid ejections from infected individuals presents a significant public health challenge. The ejected droplet frequently lands on substrates with varying orientations, including horizontal, vertical, and inclined. However, the behaviour of disease-causing droplets on inclined substrates remains unexplored. Recent research has demonstrated that droplet evaporation, flow, and colloidal deposition are significantly altered when surfaces are inclined. Changes in contact angle impact evaporative flux and induce flow between the top and bottom edges of the droplet. This study examines the behaviour of simulated respiratory droplets containing NaCl, mucin, and micrometer-sized particles as pathogen surrogates, focusing on substrate inclinations of 0°, 45°, and 90° on glass surfaces. As respiratory droplets evaporate, their solute concentration rises, altering both surface tension and viscosity. The study explores the coupled effects of solute concentration variations and asymmetric evaporative flux at varying relative humidity conditions and droplet volumes. The presence of salt and mucin induces Marangoni flow, potentially altering evaporation, flow patterns, and deposition dynamics. Additionally, sedimentation flow influences crystal nucleation sites and precipitation patterns. Results reveal unprecedented crystallization dynamics on inclined substrates, with notable differences in nucleation and growth based on the angle of inclination. Optical profilometry and confocal microscopy further show that surrogate bacterial particles accumulate excessively at the bottom edge of inclined droplets, suggesting an elevated risk of pathogen survival on inclined fomites. These findings highlight the critical importance of considering substrate orientation in understanding the transmission of disease through surface-bound droplets, offering insights that could inform public health strategies.

The Flow of Lubricant as a Mist in the Piston Assembly and Crankcase of a Fired Gasoline Engine: The Effect of Viscosity Modifier and the Link to Lubricant Degradation

Droplet flows, termed misting, are significant lubrication flow mechanisms to, in and around the piston assembly. Therefore, these are important in piston assembly tribology and engine performance. Crankcase lubricant degradation rate has been hypothesised to be influenced by lubricant droplet flows through the piston assembly and crankcase, but not previously confirmed. Lubricant was sampled from the sump, top ring zone (TRZ), and mist and aerosol from the crankcase during an extended run. The physical and chemical degradation of these samples was characterised. Droplet flows were intermediate in degradation and fuel dilution between TRZ and sump. Flows with smaller droplet sizes were more degraded that those with larger droplets. The degradation of polymers was dependent on their molecular architecture.

Dramatic droplet deformation through interfacial particles jamming

Droplets of one fluid in a second, immiscible fluid are typically spherical in shape due to the interfacial tension between the two fluids. Shear forces can lead to droplet deformation when they are subjected to flow, and these effects can be further modified when the droplet is stabilized by a surfactant due to a flow-induced gradients in the surfactant concentration. An alternative method of stabilizing droplets is through the use of colloidal particles, whose stabilization behavior is intrinsically different from molecular surfactants. Under the same flow condition, a gradient of particle concentration can result in the jamming of particles in regions with a high packing density, making the interface solid-like, albeit only under compression and not tension. However, how this asymmetry in the surfactant properties alters the droplet shape under shear is unknown. Here, we show that shear of particle-stabilized droplets can lead to a remarkable array of shape deformations as the droplets flow through a constrained microchannel. The shear-induced migration of particles on the surface results in the formation of an elastic shell at the back of the droplet, which can wrinkle and invaginate, ultimately leading to a unique core-shell structure. The shapes depend on the Peclet number of the flow, reflecting the balance of shear forces that drive the particles and diffusion that randomizes them. These findings highlight the consequences of the asymmetry in the forces between the particles and provide a unique method to controllably create droplets with a vast array of different shapes.

Characterization of the oil water two phase flow in a novel microchannel contactor equipped with helical wire static mixer

This study investigates an oil/water two-phase system to assess the potential efficacy of a novel passive mixer in enhancing the liquid-liquid interfacial area within a micro-channel contactor. In this system, two fluids are introduced into a microchannel with a diameter of 800 μm and a length of 20 cm, which is equipped with a stainless-steel helical wire measuring 250 μm in diameter. Throughout the experiments, both fluids are supplied at equal flow rates, and the dominant forces, including attachment and detachment forces, are examined. The results reveal a critical Weber number of 3.8 × 10−³, at which the first detachment occurs. A comparison between microchannels with and without the passive micromixer demonstrates that greater slug breakup occurs in the system incorporating the helical wire micromixer. This innovative configuration results in a significant reduction in slug/droplet size compared to a microchannel without a barrier, decreasing from approximately 600 μm to 390 μm at a flow rate of 0.8 mL/min. Additionally, a flow map is presented, illustrating three distinct flow regimes: flow contains long slug, Slug-droplet flow, and droplet flow regimes, with the droplet flow regime covering the largest area. The findings indicate that the implementation of this innovative passive mixer substantially increases the interfacial area, providing significant advantages for mass transfer applications.

Minimizing movements for forced anisotropic curvature flow of droplets

We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in Bellettini and Kholmatov [J. Math. Pures Appl. 117 (2018), 1–58], we establish the existence of smooth flow, starting from a regular droplet and satisfying the prescribed anisotropic Young’s law, and also the existence of a 1/2 -Hölder continuous in time minimizing movement solution starting from a set of finite perimeter. Furthermore, we investigate various properties of minimizing movements, including comparison principles, uniform boundedness, and the consistency with the smooth flow.

Computational fluid dynamics investigation of pesticide spraying by agricultural drones

Precise control over pesticide spraying by agricultural drones requires fundamental research of multiphase flow, heat and mass transfer of liquid droplets in downwash flow. In this study, water was used as a carrier agent in pesticide formulations, in which the liquid droplets exhibit a Newtonian fluid behavior. A general computational fluid dynamics (CFD) model that characterizes propeller motion coupled with droplet evaporation and deposition was developed. The downwash flow generated by the propeller rotation was simulated using a multiple reference frame method along with the SST-k-ω turbulence model. Spraying of liquid droplets was simulated using a discrete phase model. The flow model validation was conducted by comparing the simulated velocities with experimental data, and the spray model validation was completed by a comparison of droplet depositions from CFD predictions and experiments. The results indicated that the droplet deposition fluctuates with an increase of propeller speed, and that both temperature and relative humidity affect the droplet deposition. In addition, the relation between the number of particles and the impact velocity was identified quantitatively, impact velocity with respect to particle diameter was predicted, and the effects of surface inclination, surface roughness, and crosswind speed on droplet deposition were analyzed. Moreover, an in-depth discussion about the intrinsic relation between downwash flow and droplet spraying was conducted.

Experimental framework to examine turbulent puffs generated by human coughing

Respiratory infections spread through pathogen-laden droplets and aerosols exhaled by humans as part of turbulent puffs. Understanding the dynamics of these puffs is essential for assessing risks and implementing effective infection control measures. This study introduces an innovative experimental framework that employs neutrally buoyant helium-filled soap bubbles to visualize and quantitatively analyze puffs expelled during respiratory exhalations. This approach allows for the exploration of flow and turbulence statistics in exhalation puffs, an area that has not been previously examined. The experimental setup employs a high-speed camera coupled with light sheet illumination in a controlled environment. This framework can measure puff trajectory and radius directly from the raw images captured by the camera or from the velocity fields obtained through particle image velocimetry. The framework was subsequently applied to 15 coughs from three subjects. Our observations of maximum and mean velocities within the puff align with previous studies on droplet flow statistics. Additionally, based on the vorticity distribution of the exhalation, we observed a two-stage evolution of the puff with an initial jet-like phase where the trajectory scales with t1/2, followed by a puff-like phase with t1/4 scaling. Furthermore, we observed an entrainment coefficient (α) of 0.32 ± 0.06 for the initial jet-like phase and 0.17 ± 0.08 for the puff-like phase. Overall, this framework offers improved insight into the transport mechanisms of respiratory aerosols by enabling the quantification of different flow statistics of turbulent puffs.

Immiscible non-Newtonian displacement flows in stationary and axially rotating pipes

We examine immiscible displacement flows in stationary and rotating pipes, at a fixed inclination angle in a density-unstable configuration, using a viscoplastic fluid to displace a less viscous Newtonian fluid. We employ non-intrusive experimental methods, such as camera imaging, planar laser-induced fluorescence (PLIF), and ultrasound Doppler velocimetry (UDV). We analyze the impact of key dimensionless numbers, including the imposed Reynolds numbers (Re, Re*), rotational Reynolds number (Rer), capillary number (Ca), and viscosity ratio (M), on flow patterns, regime classifications, regime transition boundaries, interfacial instabilities, and displacement efficiency. Our experiments demonstrate distinct immiscible displacement flow patterns in stationary and rotating pipes. In stationary pipes, heavier fluids slump underneath lighter ones, resulting in lift-head and wavy interface stratified flows, driven by gravity. Decreasing M slows the interface evolution and reduces its front velocity, while increasing Re* shortens the thin layer of the interface tail. In rotating pipes, the interplay between viscous, rotational, and capillary forces generates swirling slug flows with stable, elongated, and chaotic sub-regimes. Progressively, decreasing M leads to swirling dispersed droplet flow, swirling fragmented flow, and, eventually, swirling bulk flow. The interface dynamics, such as wave formations and velocity profiles, is influenced by rotational forces and inertial effects, with Fourier analysis showing the dependence of the interfacial front velocity's dominant frequency on Re and Rer. Finally, UDV measurements reveal the existence/absence of countercurrent flows in stationary/rotating pipes, while PLIF results provide further insight into droplet formation and concentration field behavior at the pipe center plane.

Numerical simulations of polymer devolatilization in a steam contactor: Correlating particle distribution with volatile content removal

Abstract The focus of the current study is on a polymer devolatilization process in a device called a contactor, that involves the use of superheated steam to eliminate volatile cyclohexane, through evaporation, from the polymer mixture, also known as cement. The primary objective is to analyze the cement particle distribution and how it relates to the cyclohexane content at the exit or the devolatilization efficiency. The study develops a computational fluid dynamics (CFD) model that solves for the turbulent steam flow as a continuous phase and the the flow of cement droplets as a discrete phase. Following validation of the CFD model by comparing cement particle size distribution at the exit of the contactor to experimental data, a detailed examination of the same is conducted through a series of 69 CFD different calculations to understand its influence on the evaporation of the volatile in the polymer mixture. Two metrics are developed here: a cluster distribution index (CDI) based on the actual particle pairwise distances and a new mass-CDI based on the the radial distribution of masses. It is demonstrated that by relating the CDI and mass-CDI to the reduction in the cyclohexane content in the contactor, these metrics can be utilized to achieve the desirable input conditions in this polymer processing operation. Through a detailed examination of the particle dynamics in a steam contactor under various conditions, this study assists the polymer manufacturing industry in optimizing the devolatilization process for better steam savings and improved product quality.

Investigation of smoothed particle hydrodynamics (SPH) method for modeling of two-phase flow through porous medium: application for drainage and imbibition processes

The drainage and imbibition processes are critical mechanisms in petroleum engineering. These processes in a porous medium are controlled by surface forces and pressure gradients. The study of these processes in the pore scale by common simulators always has limitations in multiphase flow modeling. Also, obtaining relative permeability curves through laboratory analysis requires expensive equipment. Additionally, these laboratory experiments are quite expensive and may introduce significant uncertainties. For this purpose, this study investigated the creation of relative permeability curves and their effect on oil production. Initially, single-phase fluid and two-phase droplet flow within a fracture with both soft and rough surfaces were utilized to validate the formulation of the Smoothed Particle Hydrodynamics (SPH) method. Then, by using three randomly constructed porous medium models, the imbibition and drainage processes have been studied. Finally, sensitivity study has been carried out on critical parameters related to fluid flow dynamics in the porous environment, including pressure changes, wettability, and heterogeneity in drainage and imbibition processes. The simulation results were consistent with current theories; therefore, it is reasonable to consider SPH to characterize the fluid flow dynamic during the drainage and imbibition processes. According to sensitivity studies, pressure gradient (residual saturation of displaced fluid is about 5.65% and 8.44%) and heterogeneity (the residual saturation of the displaced fluid was 4.04% and 2.98%) have the largest impact on flow modeling in both drainage and imbibition processes and wettability (the residual saturation became 36.62% and 5.12%) has significant effect on the drainage process through porous medium. In general, fluid flow dynamic studies can be performed using the SPH method to model fluid flow in simple and complex porous medium under various flow conditions. The SPH method can also be used as an applicable tool to investigate the hydrocarbon fluids flow within larger geometries in the future.

Evaporation from thin porous Coatings: Pore size effects and predictive equation for homogeneous coatings

Evaporation of small water droplets on solids is hindered because surface tension pulls the droplet into a spherical cap that has a small perimeter. Our solution is to coat a solid with a very thin, porous layer into which the droplet flows to create a large-area disk with concomitant high rate of evaporation. We investigate evaporation by varying factors that have not been previously considered: pore size and distribution, contact angle, temperature, and relative humidity (RH).A larger pore size resulted in faster evaporation, which we explain through faster transport within the coating. Even faster evaporation occurred for a bilayer structure with small particles on the air side and larger particles on the solid side. The water advancing contact angle had an insignificant effect in the range from < 10° through to 60°.Our results for different pore sizes, temperature, humidity, and contact angle all collapse onto a single curve when appropriately normalized. This validates an equation that can be used for the evaporation from a homogeneous coating that depends only one empirical factor and the droplet volume. Since the volume is often user-controlled, we envisage that this equation can be used to predict evaporation and guide design of fast-drying coatings.

Resonant oscillation of droplets under an alternating electric field to enhance solute diffusion

This study investigates a novel microfluidic mixing technique that uses the resonant oscillation of coalescent droplets. During the vertical contact-separation process, solutes are initially separated as a result of the combined effects of diffusion and gravity. We show that the application of alternating current (AC) voltage to microelectrodes below the droplets causes a resonant oscillation, which enhances the even distribution of the solute. The difference in concentration between the top and bottom droplets exhibits frequency dependence and indicates the existence of a particular AC frequency that results in a homogeneous concentration. This frequency corresponds to the resonance frequency of the droplet oscillation that is determined using particle tracking velocimetry. To understand the mixing process, a phenomenological model based on the equilibrium between surface tension, viscosity, and electrostatic force was developed. This model accurately predicted the resonance frequency of droplet flow and was consistent with the experimental results. These results suggest that the resonant oscillation of droplets driven by AC voltage significantly enhances the diffusion of solutes, which is an effective approach to microfluid mixing.

Droplet motions directed by an expansion section in the T-junctions

The controlled motion of droplets in microfluidic chips is a preliminary requirement to realize their functions. The influence of the expansion section on the droplet motion is mainly investigated in the T-junction. The droplet dynamic characteristics are analyzed at the junction and the applicable flow rate of the expansion section is explored. The expansion section can reduce the entered length and motion time of the droplet when droplets flow into the channel with it, and finally avoid the possibility of droplet splitting. Even under a large difference of the branch flow rate, the expansion section can direct the droplet into its located channel. It is found that with the increase in continuous phase flow rate, the effect of the expansion section on the droplet motion behavior is gradually weakened until it disappears. Moreover, the critical conditions of it can be obtained by theoretical calculation. The expansion section can direct droplet motion in both symmetric and asymmetric junctions. However, it is mainly achieved by influencing the interfacial tension of the droplets in the symmetric junction, while the key force is related to the droplet motion in the asymmetric junction. Specifically, the expansion section influences the differential pressure force to direct the droplet in the flow into the side branch (with expansion section) mode, but it varies the interfacial tension of the droplet in the flow into the main branch mode.