Droplet Diameter Research Articles

Application of modified corn starch in stabilization of ultrasonic-assisted pickering oil in water emulsion

Starch is a sustainable and cheap raw material claimed as a good emulsion stabilizer for edible products either in food or pharmaceutical industry. To produce an emulsion stabilized by food based edible stabilizer, this study focused on the non-chemical starch modification for oil in water (O/W) emulsion stabilization produced by ultrasonic emulsification. The results showed that the finest emulsion was obtained at power rate of 500 W for 7 mins of sonication. The stability of the emulsion was investigated by turbidity, centrifugal stability values and droplet size. Pre-gelatinized corn starch (PCS) stabilizer showed better emulsion stability compared to gelatinized corn starch (GCS) due to the different polysaccharide components of the two modified cornstarch. GCS mainly contained amylose while the PCS contained both amylose and amylopectin. The emulsion, stabilized by 6 wt.% of PCS and addition of 3 wt.% of tween-80 exhibited excellent storage stability, along the 30 days storage. The results showed the lowest turbidity of 1.01 cm-1 , centrifugal stability value of 36.85% and average droplet diameter of 14.27 µm.

Study on stabilized mechanism of high internal phase Pickering emulsions based on commercial yeast proteins: Modulating the characteristics of Pickering particle via sonication

The primary significance of this work is that the commercial yeast proteins particles were successfully used to characterize the high internal phase Pickering emulsions (HIPPEs). The different sonication time (0,3,7,11,15 min) was used to modulate the structure and interface characteristics of yeast proteins (YPs) that as Pickering particles. Immediately afterward, the influence of YPs particles prepared at different sonication time on the rheological behavior and coalescence mechanism of HIPPEs was investigated. The results indicate that the YPs sonicated for 7 min exhibited a more relaxed molecular structures and conformation, the smallest particle size, the highest H0 and optimal amphiphilicity (the three-phase contact (θ) was 88.91°). The transition from extended to compact conformations of YPs occurred when the sonication time exceeded 7 min, resulting in an augmentation of size of YPs particles, a reduction in surface hydrophobicity (H0), and an elevation in hydrophilicity. The HIPPEs stabilized by YPs particles sonicated for 7 min exhibited the highest adsorption interface protein percentage and a more homogeneous three-dimensional (3D) protein network, resulting in the smallest droplet size and the highest storage (G′). The HIPPEs sample that stabilized by YPs particles sonicated for 15 min showed the lowest adsorption protein percentage. This caused a reduction in the thickness of its interface protein layer and an enlargement in the droplet diameter (D [3,2]). It was prone to droplet coalescence according to the equation used to evaluate the coalescence probability of droplets (Eq (2)). And the non-adsorbed YPs particles form larger aggregation structures in the continuous phase and act as “structural agents” in 3D protein network. Therefore, mechanistically, the interface protein layer formed by YPs particles sonicated 7 min contributed more to HIPPEs stability. Whereas the “structural agents” contributed more to HIPPEs stability when the sonication time exceeded 7 min. The present results shed important new light on the application of commercial YPs in the functional food fields, acting as an available and effective alternative protein.

Liquid-liquid two phase-system stabilized by tween 40 and 80 surfactants: multiparametric study

Abstract The purpose of this study was to investigate the impact of process parameters such as interfacial tension, type of surfactants, and their concentration on simple oil-in-water dispersion. Explored systems were prepared with 5% liquid paraffin oil and aqueous phase with emulsifiers Tween 40 of concentrations from 0.008325 mM to 0.025 mM and Tween 80 with concentrations ranging from 0.00375 mM to 0.011 mM. All systems were characterized in terms of their density and interfacial tension. In the next step analysis of droplet size distributions and mean droplet diameter was performed. The results showed that the size of paraffin droplets decreased as the concentration of surfactants grew. This trend is accompanied by decrease in the interfacial tension between phases. The correlation between mean drop size and the energy input and physical properties of both liquids was developed. The last step provides scientific evidence for the formulation of stable droplets of liquid paraffin.

Gas–liquid twin-fluid atomization from non-circular orifices

Passive control of twin-fluid atomization can be achieved by changing the orifice shape of the injector. In this study, the characteristics of twin-fluid atomization in the outside-in-liquid injector with circular, square, and rectangular orifices at various aspect ratios were investigated experimentally and computationally. The morphology of the spray was captured by shadowgraph, the diameter and velocity of the droplets were measured by the phase Doppler particle analyzer, and numerical simulations were performed for the central gaseous core. Comparing the sprays with square and circular orifices, droplets from the non-circular orifice are generally smaller with less disparities in droplet sizes due to the more intensive turbulent disturbances and corner effect. Furthermore, the non-circular orifice also results in better spatial distribution of the spray. The droplet diameters of the spray with a square orifice do not satisfy the log-normal distribution near the orifice along the centerline of the spray, which may be attributed to the different entrainment of spray droplets by the central gas flow for the sprays with circular and non-circular orifices. The twin-fluid sprays produced by the rectangular orifice also exhibit the same axial switching effect as in the high-pressure gaseous jet flow, in which the spray diffusion in the minor axis is more extensive than that in the major axis. Moreover, the droplets' Sauter mean diameter produced by the rectangular orifice is more sensitive to the size in the minor axis of the orifice and decreases as the aspect ratio of the orifice increases given the same cross-sectional area.

Manufacturing nearly monodispersed complex coacervate microcapsules by membrane emulsification and spray drying

Complex coacervation is a phase separation process in which two oppositely charged polymers or macromolecules in a solution come together at the liquid-liquid interface to form a dense coacervate shell. The process can be employed to encapsulate oil droplets, creating stable microcapsules that protect and control the release of oil while achieving a high encapsulation efficiency of active ingredients. In this work dry coacervate microcapsules of different size and shell thickness were manufactured combining a continuous single pass cross-flow membrane emulsification system and spray drying to obtain a dry powder. A single-pass crossflow membrane emulsification system with a single cylindrical 10 × 100 mm membrane module with 10 μm pore produced emulsion droplets between 71 μm and 114 μm with a dispersed phase (oil content) in the final emulsion between 3.3 and 6.2 vol/vol% and a total emulsion output mass rate between 25.68 kg h−1 – 49.68 kg h−1. Emulsions manufactured by membrane emulsification were nearly monodispersed with the highest span not exceeding 0.68. Addition of maltodextrin to the emulsion prior to spray drying increased the viscosity and prevented the capsules breakage. Microcapsules up to a mean droplet diameter of 113.19 ± 0.81 μm preserved the shell and had a yield up to 78.43 ± 0.97 wt%, a surface oil as low as 9.35 ± 0.88 wt% and an encapsulation efficiency of 71.09 ± 0.87 wt%.

Enhanced mixing efficiency and reduced droplet size with novel droplet generators

Nowadays, droplet microfluidics has become widely utilized for high-throughput assays. Efficient mixing is crucial for initiating biochemical reactions in many applications. Rapid mixing during droplet formation eliminates the need for incorporating micromixers, which can complicate the chip design. Furthermore, immediate mixing of substances upon contact can significantly improve the consistency of chemical reactions and resulting products. This study introduces three innovative designs for droplet generators that achieve efficient mixing and produce small droplets. The T-cross and cross-T geometries combine cross and T junction mixing mechanisms, resulting in improved mixing efficiency. Numerical simulations were conducted to compare these novel geometries with traditional T and cross junctions in terms of mixing index, droplet diameter, and eccentricity. The cross-T geometry exhibited the highest mixing index and produced the smallest droplets. For the flow rate ratio of 0.5, this geometry offered a 10% increase in the mixing index and a decrease in the droplet diameter by 10% compared to the T junction. While the T junction has the best mixing efficiency among traditional droplet generators, it produces larger droplets, which can increase the risk of contamination due to contact with the microchannel walls. Therefore, the cross-T geometry is highly desirable in most applications due to its production of considerably smaller droplets. The asymmetric cross junction offered a 8% increase in mixing index and around 2% decrease in droplet diameter compared to the conventional cross junction in flow rate ratio of 0.5. All novel geometries demonstrated comparable mixing efficiency to the T junction. The cross junction exhibited the lowest mixing efficiency and produced larger droplets compared to the cross-T geometry (around 1%). Thus, the novel geometries, particularly the cross-T geometry, are a favorable choice for applications where both high mixing efficiency and small droplet sizes are important.

Research on the influence of initial parameters of water droplets on the performance of counter-rotating axial-flow compressor

This paper employs a numerical simulation method to investigate the wet compression working characteristics of a counter-rotating axial-flow compressor (CRAC) in an air-inlet, water-containing environment under different water droplet parameters at a designed rotational speed. The influence of initial water droplet parameters on the overall performance of the CRAC and the variations in the flow field characteristics under different wet compression conditions was investigated. The initial diameter of water droplets exhibited the most significant impact on the wet compression effect. Under an appropriate inlet water content, water droplets with smaller diameters effectively reduced the temperature of the CRAC’s internal flow field, increasing the air density. Consequently, the axial velocity decreased, altering the velocity triangle and increasing the rotor working capacity, which enhanced the performance of the CRAC. Additionally, wet compression influenced the flow field of the rear rotor stronger than that of the front rotor. When the initial diameter of water droplets is too large, the evaporative cooling effect cannot be fully exploited so wet compression only slightly improved the compressor performance. These findings may help understand the working characteristics of the CRAC in water-containing environments better, offering guidance for CRAC design using wet compression technology.

Comparative Study of Droplet Diameter Distribution: Insights from Experimental Imaging and Computational Fluid Dynamics Simulations

The interfacial area between two phases plays a crucial role in the mass transfer rate of gas–liquid processes such as absorption. In this context, the droplet size distribution within the flow field of a droplet-based absorber significantly affects the surface area, thereby influencing the absorption efficiency. This study focuses on developing a computational fluid dynamics (CFD) model to predict the size and distribution of water droplets free-falling in a transparent square tube. This model serves as a digital twin of our experimental setup, enabling a comparative analysis of experimental and computational results. For the accurate measurement of droplet size and distribution, specialized experimental equipment was developed, and a high-speed camera along with Fiji software was used for the capturing and processing of droplet images. At the point of injection and at two different heights, the sizes and distributions of falling droplets were measured using this setup. The interaction between the liquid water droplets and the gas phase within the square tube was modeled using the Eulerian–Lagrangian (E-L) framework in the STAR-CCM+ software. The E-L multiphase CFD model yielded approximations with errors ranging from 11 to 27% for various average mean diameters, including d10, d20, d30, and d32, of the liquid droplets at two distinct heights (200 mm and 400 mm) for both nozzle plates. This comprehensive approach provides valuable insights into the dynamics of droplet-based absorption processes.

Structural characteristics and stability analysis of coconut oil body and its application for loading β-carotene

In this work, we investigated structural characteristics and stability analysis of the coconut oil body (COB) and its application for loading β-carotene (β-CA). The COB contained neutral lipids (81.1 ± 2.1 %), membrane proteins (0.6 ± 0.0 %), and moistures (18.3 ± 3.2 %), in which the molecular weights of membrane proteins ranged from 12 kDa to 40 kDa, as analyzed by the SDS-PAGE. The COB exhibited a small droplet diameter (5.1 ± 0.3 µm) with a monomodal diameter distribution, as reflected by the dynamic light scattering. The COB showed stable states at alkaline pH values (pH 8–10) and instability against ionic strengths (50–200 mmol/L) and thermal treatment (30-90℃) after analyzing the instability indexes. COB-based emulsions were favorable for the loading and retention of β-CA, as reflected by free fatty acids release rates and bioaccessibility in the simulated gastrointestinal digestion. This study will contribute to using the coconut oil bodies for loading bioactive nutraceuticals to enhance their bioaccessibility.

Cricket Protein as an Innovative Emulsifier for Avocado Oil: Formulation and Characterization of Sustainable Emulsions

The use of cricket protein in emulsions is in line with the growing interest in sustainable food sources, as crickets require minimal resources and produce lower greenhouse gas emissions than traditional livestock. Research in this area suggests that incorporating cricket protein into emulsions not only improves their nutritional value but also contributes to the development of environmentally friendly and functional food products. This study proposes the use of cricket protein for the stabilization of emulsions formulated with avocado oil as a dispersed phase. This oil is rich in monounsaturated fats, particularly oleic acid, and a variety of bioactive compounds. In the first part of this study, we assessed the influence of the emulsifier concentration and found that 2 wt.% is the optimum because a depletion flocculation effect was produced. Subsequently, processing was optimized using ultrasonication so that the higher energy input produced emulsions with a droplet diameter of less than 700 nm. Finally, rhamsan gum was added to the formulation, producing emulgels with improved pseudoplastic behavior and physical stability. This study demonstrates that cricket protein in combination with rhamsan gum is capable of forming stable, low-droplet-size emulgels with potential applications in encapsulation systems.

Study and fabrication of rain triboelectric nanogenerator based on laser-induced graphene interdigital electrode

In this work, a rain triboelectric nanogenerator (R-TENG) based on a laser-induced graphene (LIG) interdigital electrode was developed to harvest rain energy. The R-TENG comprises a LIG interdigital electrode on a polymer substrate with a hydrophobic Polydimethylsiloxane (PDMS) layer as a protective layer. When raindrops fall onto the surface of the PDMS layer and move between two adjacent interdigital electrodes, the accumulated charges move back and forth, resulting in the generation of alternating current. The LIG pattern design and the energy collection efficiency were studied by altering the production parameters of the LIG electrode and measuring the droplet diameter on the PDMS surface. A R-TENG with an electrode width of 3 mm produces a laser power of 2.1 W, and an output voltage of 2.46 V is generated. The R-TENG could be applied as an additional energy source to harvest rain energy for agricultural IoT sensors.

3D analysis of spray effect on long-term depressurization of VVER-1000 containment during LB-LOCA

Containment as the last barrier of defence in depth strategy plays the most important role in protecting the environment and public from the release of radioactive material. As a result, analysing its performance in nuclear accidents and the reliability and effectiveness of its engineering safety features (ESFs) in the depressurization of containment is a key step in safety assessment. This study demonstrates the effect of the spray system as one of the ESFs in long-term depressurization of VVER-1000 containment during an LB-LOCA accident by using GOTHIC code. In the first step toward this goal, the as-built 3D structure of VVER-1000/V446 containment has been prepared in AutoCAD and used as GOTHIC geometry input by applying the input preparation process. Long-term 3D profiles of temperature and pressure were simulated in GOTHIC without spray actuation. The next step deals with considering the effects of spray and sensitivity analysis of spray temperature and droplet diameter on long-term depressurization. 3D profiles of thermal-hydraulic parameters during long-term depressurization of containment have been presented as research outcomes and validated against FSAR data and finally, the effects of spray on profiles were concluded. Results can obviously prove the effect of spray on the long-term depressurization of containment. The required time to achieve half of the peak pressure of the containment was calculated as 1380 s which is completely in agreement with NRC safety criteria. Research outcomes confirm the success of the spray system to support the integrity of containment which could be jeopardized without spray system intervention.

Combustion Behavior of Fuel Droplets with Metallic, Non-Metallic and Organo-Metallic Boron Additives

ABSTRACT There is considerable interest in the utilization of fuels derived from boron materials, with their high calorific value, in various applications ranging from propellants to pyrotechnics. Conversely, their impact on the combustion behavior of conventional hydrocarbon fuels remains largely unclear. In this study, ignition, combustion, micro-explosion and simultaneous atomization behaviors of gasoline-based alternative fuels containing metallic (28–35 µm MgB2), nonmetallic (1 µm amorphous boron, 10 µm AlB12 with 86–88% and 95–97% purity) and organo-metallic boron derivatives (triethyl borate (TEB) containing C2H5 groups and trimethyl borate (TMB) containing CH3 groups) were investigated. The experiments were carried out at droplet scale and recorded using a high-speed camera and a thermal camera. The findings revealed a systematic reduction in ignition delay for each gasoline fuel enriched with boron derivatives. 2.5%AlB12/G and pure TMB droplets were the fastest extincting fuel droplets (0.9678 s and 1.245 s, respectively). The highest maximum flame temperature was recorded as 626 K and 610 K for pure TMB and 80%TEB/G, respectively. Droplet diameter regression analyses showed that the diameters of fuel droplets containing predominantly metallic and nonmetallic boron derivatives decreased in accordance with the d 2 -law. This study demonstrated that cost-effective and easily producible amorphous boron and organometallic boron derivatives are promising energy carriers for hydrocarbon fuels.

Numerical simulation of spray atomization in crossflow using an empirical primary atomization model

The hybrid Eulerian-Lagrangian approach is used to simulate the atomization process of spray jet in subsonic crossflow. A coupled Volume of Fluid (VOF) - Lagrangian Particle Tracking (LPT) solver is implemented in the open-source platform OpenFOAM to solve the governing equations for the continuous and discrete phase respectively. An empirical model for primary atomization is proposed, in which the aerodynamic effect is taken into account, along with the turbulence effect. Thus, it is suitable for the flow at a low liquid-gas density ratio, i.e., less than 500. The performance of the presented model is evaluated and verified by comparisons of the simulated results with the experimental data. The flow characteristics of flow fields and distribution of droplet diameters are analyzed in detail. It is revealed that the vortex structures have a direct impact on the distribution of the droplets. The effects of the empirical constants in the atomization model are also examined. Finally, it is shown that the model performs better for the flow at a higher Weber number, in which the aerodynamic effect is more significant.

Tracking protein aggregation behaviour and emulsifying properties induced by structural alterations in common carp (Cyprinus carpio) myofibrillar protein during long-term frozen storage

The effect of ultrasound-assisted immersion freezing (UIF), air freezing (AF), and immersion freezing (IF) on the protein structure, aggregation, and emulsifying properties of common carp (Cyprinus carpio) myofibrillar protein during frozen storage were evaluated in the present study. The result showed that, compared with AF and IF samples, UIF sample had higher reactive/total sulfhydryl, protein solubility, and lower protein turbidity (P < 0.05), indicating that UIF was beneficial to inhibit protein oxidation and aggregation induced by frozen storage. UIF inhibited the alteration of secondary structure and tertiary structure during frozen storage. Meanwhile, UIF sample had higher emulsifying activity index, and smaller emulsion droplet diameter than AF and IF samples (P < 0.05), suggesting that UIF was beneficial for maintaining the emulsifying properties of protein during storage. In general, UIF is a potential and effective method to suppress the decrease in protein emulsifying properties during long-term frozen storage.

Plant-Based Oil-in-Water Food Emulsions: Exploring the Influence of Different Formulations on Their Physicochemical Properties.

The global focus on incorporating natural ingredients into the diet for health improvement encompasses ω-3 polyunsaturated fatty acids (PUFAs) derived from plant sources, such as flaxseed oil. ω-3 PUFAs are susceptible to oxidation, but oil-in-water (O/W) emulsions can serve to protect PUFAs from this phenomenon. This study aimed to create O/W emulsions using flaxseed oil and either soy lecithin or Quillaja saponins, thickened with modified starch, while assessing their physical properties (oil droplet size, ζ-potential, and rheology) and physical stability. Emulsions with different oil concentrations (25% and 30% w/w) and oil-to-surfactant ratio (5:1 and 10:1) were fabricated using high-pressure homogenization (800 bar, five cycles). Moreover, emulsions were thickened with modified starch and their rheological properties were measured. The physical stability of all emulsions was assessed over a 7-day storage period using the TSI (Turbiscan Stability Index). Saponin-stabilized emulsions exhibited smaller droplet diameters (0.11-0.19 µm) compared to lecithin (0.40-1.30 µm), and an increase in surfactant concentration led to a reduction in droplet diameter. Both surfactants generated droplets with a high negative charge (-63 to -72 mV), but lecithin-stabilized emulsions showed greater negative charge, resulting in more intense electrostatic repulsion. Saponin-stabilized emulsions showed higher apparent viscosity (3.9-11.6 mPa·s) when compared to lecithin-stabilized ones (1.19-4.36 mPa·s). The addition of starch significantly increased the apparent viscosity of saponin-stabilized emulsions, rising from 11.6 mPa s to 2117 mPa s. Emulsions stabilized by saponin exhibited higher stability than those stabilized by lecithin. This study confirms that plant-based ingredients, particularly saponins and lecithin, effectively produce stable O/W emulsions with flaxseed oil, offering opportunities for creating natural ingredient-based food emulsions.

Droplet deposition of agrochemical spraying: Comparison of results from a random‐walk model and CFD simulations

AbstractThe effectiveness of agricultural spraying processes depends considerably on the ability of the atomized droplets to reach the target site in the desired amount. In this work, two mathematical models to study the trajectories and deposition of atomized droplets are implemented and compared. On the one hand, a computational fluid dynamics (CFD) coupled with discrete phase model (DPM) is implemented to calculate the trajectories of atomized droplets and determine distances at which the droplets are deposited. The continuous phase (atmospheric air) is modelled by continuity, momentum, and energy equations. On the other hand, a Lagrangian random‐walk (LRW) model based on force and energy balances to predict the pulverization process of a nozzle is formulated and implemented in Python. Both models take into account the effects of drag, gravity, buoyancy, and evaporation on individual droplets, as well as the impact of atmospheric stability and dispersion. By tracking a large number of trajectories, meaningful estimates of dispersal statistics can be obtained. The LRW model accurately replicated the trajectories, deposition distances, and final diameters of atomized droplets for three atmospheric stability cases, compared with CFD simulation results. The results of both models agreed that 100 μm droplets were most susceptible to wind‐induced spray drift, depositing at the furthest distances from the nozzle. In addition, 50 μm droplets exhibited a significant tendency to evaporate entirely before reaching the ground. The LRW model is found to be a cost‐effective alternative for estimating spray drift compared to the computationally intensive CFD approach.

Numerical Investigation of Supercooled Large Droplets Impingement Characteristics of the Rotating Spinner

Aircraft engine icing caused by supercooled large droplets (SLD) poses a significant threat to flight safety. In this paper, the SLD impingement characteristics of the rotating spinner were investigated using FLUENT UDS and the governing equations for water droplet motion were solved based on the Eulerian method. The droplet breakup was simulated using the number density equation, while the droplet rebound and splashing were simulated using a semiempirical model. The effects of rotational speed, droplet diameter, and inflow velocity on the SLD impingement characteristics of the rotating spinner were studied. Some new valuable insights have been found for the SLD impingement. The results indicated that as the rotational speed increases, the local collection efficiency of the rotating spinner decreases. Higher rotational speed results in reduced droplet impingement angle and stronger droplet rebound and splashing. For the droplets with diameters smaller than 111 μm, the local collection efficiency increases with the increase of the droplet diameter. However, when the droplet diameter exceeds 111 μm, the local collection efficiency decreases near the leading edge of the rotating spinner. Additionally, the local collection efficiency decreases as the inflow velocity increases near the leading edge of the rotating spinner. However, higher inflow velocities lead to larger droplet impingement angles, resulting in higher local collection efficiency near the tail of the rotating spinner. The critical impingement angle increases with the increase of the inflow velocity, leading to a more pronounced rebound and splashing of SLD. The research in this paper provides useful help for ice shape prediction and anti-icing system design of rotating spinner in SLD environment.

A method for the prediction of the atomization diameter distribution of the spray generated by swirl nozzles

Atomization is an indispensable process for achieving high-efficiency conversion in various energy applications. This study proposes a novel and simplified method to predict the droplet diameter distribution along the spray direction during atomization by swirl nozzles. The method considers the droplet breakup and coalescence and consists of three sub-models, i.e., the primary breakup model, the secondary breakup model, and the velocity model. The prediction method is verified by droplet sizing experiments using typical swirl nozzles. Combining the experimental results, the atomization process from fluid to droplets is analyzed in-depth. Results show that the present method can predict the droplet diameter distribution along the spray direction, with an average error of droplet diameter of approximately 7.7%. The effects of the orifice diameter and water supply pressure of nozzles on droplet diameter distribution are discussed. The droplet diameter decreases in the whole spray field as the water supply pressure rises. When the orifice diameter increases, the mass flow rate and Sauter mean diameter increase in the near-orifice region. However, the droplet diameter difference in nozzles reduces as the position is far away from the orifice. The proposed method can aid the design of some critical energy devices containing the atomization process.

Probability model for gas–liquid annular flow in dynamic equilibrium among the processes of atomization, deposition, breakup, and coalescence

In this paper, an improved probability model is introduced to provide a more comprehensive prediction of annular flow. Unlike previous work, which did not consider atomization and deposition, as well as breakup and coalescence, simultaneously, the improved model integrates all four processes into its framework. The mechanisms of these processes are described in detail by the present model. When annular flow is fully developed, the four processes reach dynamic equilibrium. A numerical program is compiled based on the influence of the four processes on the droplets. Five important parameters, including the droplet-diameter probability density distribution, characteristic droplet diameters, entrainment ratio, liquid film thickness, and interfacial shear-stress coefficient, are calculated when the annular flow is in dynamic equilibrium. The validity and accuracy of the improved model are assessed by comparison with 377 cases from 12 experiments. For most cases used to validate the predicted droplet-diameter probability density distribution, the prediction curves closely match the experimental data. The mean absolute percentage errors (MAPEs) for the two experiments used to validate the predicted characteristic droplet diameters are 20.74% and 24.04%, respectively. Additionally, the mean MAPEs of the entrainment ratio, liquid film thickness, and interfacial shear-stress coefficient are found to be 34.11%, 20.60%, and 27.28%, respectively. This demonstrates the effectiveness and reliability of the improved probability model in predicting annular flow.