Droplet Impact Research Articles

Impact of Colloidal Drug-Rich Droplet Size and Amorphous Solubility on Drug Membrane Permeability: A Comprehensive Analysis

This study aimed to investigate the impact of amorphous solubility and colloidal drug-rich droplets on drug absorption. The amorphous solubility of cilnidipine (CND) in AS-HF grade of hypromellose acetate succinate (HPMC-AS) solution was significantly reduced compared to that in non-polymer solution due to AS-HF partitioning into the CND-rich phase. In contrast, AS-LF grade of HPMC-AS has minimal effect on the amorphous solubility. The size of colloidal CND-rich droplets formed in the CND-supersaturated solution was less than 100 nm in the presence of AS-HF, while 200–450 nm in the presence of AS-LF. When the CND concentrations were near the amorphous solubility, CND membrane flux was reduced in the presence of AS-HF due to the decrease in the amorphous solubility of CND. However, the CND flux increased with the increase in CND-rich droplets, especially in the AS-HF solution. The size reduction of the CND-rich droplets led to their effective diffusion into the unstirred water layer, enhancing CND flux. In higher CND concentration regions, the CND flux became higher in the AS-HF solution than in the AS-LF solution. Thus, it is essential to elucidate the drug concentration-dependent impact of the colloidal drug-rich droplets on the drug absorption performance to optimize supersaturating formulations.

Numerical assessment of the drag force and Nusselt number during droplet impingement onto a particle

The dynamics of droplet impingement onto solid particles play a crucial role in various engineering applications, yet a fundamental understanding of the intricate momentum and heat transfer characteristics within the processes remains unclear. In this work, we numerically investigate and quantify the drag force and Nusselt (Nu) number during the process using a volume of fraction model. After model validations, it is employed to simulate the processes of molten iron ore spreading over a coke particle for demonstration. The results show that the drag force exhibits rapid initial growth, followed by significant fluctuations marked by two peaks, ultimately decreasing to a low value. The Nu number undergoes a sharp ascent to an immediate peak, followed by a two-stage decline with varying rates. Furthermore, the effect of three key operating parameters is quantified. The comparative analysis unveils that a larger droplet size significantly contributes to an augmented drag force, especially during the first peak. The Nu numbers under various droplet sizes follow a similar trajectory, rising and then decreasing until the wetter surface reaches the maximum. The larger droplets show a slower Nu number decrease. A higher initial droplet position can remarkably increase the drag force and Nu number with more rapid fluctuations. Conversely, the effect of gas velocity under the symmetrical and steady flow field is limited and can be practically disregarded. The present work reveals the fundamental characteristics of momentum and heat transfer process during droplets impact particles.

Numerical investigation on dynamic characteristics of the droplet impacting on a random rough surface

Water management is a significant problem affecting the reliability and stability of proton exchange membrane fuel cells (PEMFC), in which droplet wall collision is the critical factor affecting the liquid water transmission in the gas channel. The surface roughness directly affects the spreading deformation of the droplet after impacting. This study's influence of surface roughness on the dynamic process of a single droplet of micrometer level impacting random rough surfaces was numerically investigated. Based on the Weierstrass–Manderlbrot (W-M) fractal theory, three-dimensional random rough surfaces with five roughness levels were established, and the dynamic process of droplet impact on the random rough surface was captured. The contour features of the droplet were analyzed, and the results showed that rough peaks hinder the spreading and retracted process of droplets, resulting in a thicker liquid film deposited on the rough surface, which is not conducive to liquid water discharge. The higher roughness level makes it difficult for droplets to gather into liquid film after hitting the wall and further hinders the discharge of liquid water from the flow channel. Therefore, when micrometer-sized droplets collide with a wall velocity of about 10 m/s, the roughness Ra should be controlled below 0.4 μm, which is conducive to the formation of thin liquid film after droplet impact and the effective discharge of water, which is crucial to maintaining the performance and life of PEMFC.

On the role of surface morphology in impacting-freezing dynamics of supercooled droplets

A thorough understanding of droplet impact and freezing is vital in preventing ice accretion on many outdoor devices. This simulation-based study investigated the effect of surface morphology on the impacting-freezing process of a supercooled droplet. Also, the variations of Weber number and supercooling temperature were studied numerically. The droplet impact and freezing process were simulated with the volume of fluid method and freezing model. A more accurate simulation was achieved by modeling the supercooled droplet and the dynamic contact angle. At the given ranges of the input parameters, the main factors that guaranteed droplet rebounding after collision were determined. The supercooling temperature and the groove width should be above 266 K and less than 0.21 mm, respectively. The droplet should also maintain its cohesion and integrity during impact. Creating grooves on a surface is novel and paves a new way to understand the impact and solidification of water droplets in supercooled conditions.

Icing characteristics of the superhydrophobic surface of gas turbine fairing

Abstract In order to investigate the mechanism underlying the impact of superhydrophobic surfaces on the icing and anti-icing characteristics of fairings, this study focuses on marine gas turbine fairings as the research subject and employs numerical simulation methods to examine how droplet diameter and impact velocity influence the icing characteristics of superhydrophobic surfaces on fairings. The findings reveal that larger droplet radii are more prone to freezing onto superhydrophobic surfaces, resulting in a more stable ice sheet formation. Moreover, higher droplet velocities facilitate easier freezing on superhydrophobic surfaces, leading to larger frozen areas, thicker ice sheets, and more pronounced ice peaks. Additionally, differences in impact angles prevent droplets from freezing.

High-speed X-ray imaging of droplet-powder interaction in binder jet additive manufacturing

Binder jetting (BJ) is an additive manufacturing process that uses a powder feedstock in a layer wise process to print parts by selectively depositing a liquid binder into the powder bed using inkjet technology. This study presents findings from high-speed synchrotron imaging of binder droplet-interaction during the BJ printing process. A custom laboratory-scale BJ test platform was used for testing which enabled control of relevant process parameters including powder material, print geometry, spacing between droplets, powder bed density, and powder moisture content. Powder ejection was observed above the powder bed surface and powder relocation due to droplet impact was observed below the powder bed surface. Powder relocation was observed to be sensitive to powder material, powder bed density, powder bed moisture, droplet spacing, and print geometry. Increasing powder bed density was found to increase particle ejection velocity but reduce the total number of particles ejected. Process parameters that increase binder / moisture content in the powder bed were found to reduce powder ejection. The number of ejected powder particles was reduced for lower droplet spacings. Both powder ejection and powder relocation below the powder bed were reduced by treating the surface of the powder bed with a water/triethylene glycol (TEG) mixture before printing. Results from this study help to build understanding of the physical mechanisms in the BJ printing process that may contribute to formation of defects observed in final parts.

Dynamic Characteristics of the Droplet Impact on the Ultracold Surface under the Engine Cold Start Conditions

Dynamic Characteristics of the Droplet Impact on the Ultracold Surface under the Engine Cold Start Conditions

Maximum spreading of an impact droplet on a conical tip

Maximum spreading of an impact droplet on a conical tip

Numerical Analysis of Dual Droplet Simultaneous Oblique Impact on a Water Film

The simultaneous oblique impact of multiple droplets on a liquid film is an intricate phenomenon prevalent in diverse natural and industrial processes. However, previous studies have primarily focused on single droplet impact, while an in-depth understanding of the more complex multi-droplet scenario remains lacking. The current study aims to numerically investigate the simultaneous oblique impact of two droplets on a water film using a three-dimensional Volume of Fluid (VOF) model. The effects of the Weber number and the impact angle on the crown behavior are carefully analyzed. The results demonstrate that increasing the Weber number enhances the central uprising sheet height but has minor influences on the upstream crown radius and central sheet radius. In contrast, the increase in the impact angle leads to a decreased upstream crown radius and an increased central sheet radius, while the central sheet height remains relatively unaffected. In addition, the splashing threshold for the dual droplet impact cases is significantly lower than that of the single droplet impact cases due to the interactions between the adjacent crowns. The present results provide novel insights into the underlying physics and useful supports in developing predictive models for the intricate multi-droplet impact phenomenon.

Component Effects in Binary Droplet Impact Behaviors on the Heated Plate: Comparison Study of Ethanol/Propanol and Ethanol/Water Droplets and Observation of Novel Bubble Shrinkage Phenomenon

This work aims to investigate the effect of liquid physical properties on the behavior of binary droplets impact on the heated smooth aluminum alloy plate with a high-speed imaging system. Two groups of mixed solutions with similar boiling point differences are selected as the working liquid, in which the low-boiling-point components are both ethanol and the high-boiling point components are propanol and water, respectively. Compared to the ethanol/propanol binary droplets, the experimental results show that the ethanol/water binary droplets have diverse impact phenomena and significantly broad transition boiling regimes, as well as the reduced droplet residence time and increased Leidenfrost temperature point. With the decreasing ethanol content in ethanol/water binary droplets, these effects become more prominent. For secondary atomization, the ethanol/water binary droplet undergoes parent droplet breakup into fragment droplets with larger diameters (Ds > 0.3 mm). Both binary droplets produce satellite droplets with small diameters (Ds < 0.3 mm) by puffing and ejection. In terms of the ethanol/propanol binary droplet impact, the probability of puffing is higher and the satellite droplet diameters are small. In the ethanol/water binary droplet impact, the probability of ejection is higher and the satellite droplet diameter distribution is wider. When an ethanol/water binary droplet of 25 vol.% ethanol content impacts the heated wall at Ts = 120 °C, a novel large bubble shrinkage phenomenon occurs at the late stage of droplet evaporation. This phenomenon is proposed to be relevant to the increasing surface tension and saturation temperature with decreasing ethanol content, as well as the decreasing ambient temperature above the top surface of the bubble.

Wettability, droplet impact and anti-icing performance of micro-nano hierarchical structure on Ti6Al4V surface via integrating of chemical modification and laser-induced plasma micromachining

Superhydrophobic functional surfaces are widely used in medical treatment, pipeline transportation, and ship corrosion protection and have great potential in the field of anti-icing. Ultrafast laser-induced plasma micromachining (LIPMM) combined with a chemical modification of a fluoroalkyl low surface-energy substance (Novec) was used to fabricate superhydrophobic surfaces with periodic layered micro-nano arrays on Ti6Al4V. The wettability, droplet collision behavior and wear resistance of surfaces with different physical and chemical properties were analyzed. In terms of static anti-icing, based on the classical nucleation theory, the icing-delay performance of different surfaces was analyzed. Ice adhesion strength and frosting properties were also studied. It was found that the micro-nano structure surface fabricated by LIPMM had strong hydrophobicity (contact angle of 164°, roll-off angle of 1.0°), high icing delay time (3072 s, 4 μL of water droplet on the surface at −10 °C), low ice adhesion strength (38.2 kPa), and better durability. Additionally, the droplets bounced off this surface after colliding at different angles (0°, 5°, 10°, and 20°). This study provides a feasible solution for fabricating anti-icing surfaces on Ti6A14V.

Formation mechanism and elimination method of joint defects in lattice structures printed by metal droplet deposition manufacturing

Benefiting from the dense inner microstructure and smooth bead-like surface morphology, metal droplet deposition manufacturing (MDDM) is advantageous in manufacturing small metallic lattice structures, which have great potential in advanced aerospace, energy, and robotics applications. However, the improper top-layer droplet distance leads to joint defects in the printed lattices and deteriorates the forming accuracy. Moreover, if the substrate temperature and inclined angle increase, joint defects may occur even if the top-layer droplets are at an ideal distance due to droplet oscillation. This work proposes a novel method to eliminate joint defects by re-placing the joint region droplets to an ideal center distance. To this end, the dynamics of top-layer droplets (impact, spread, recoil, and oscillation) were investigated by combining morphology analysis and high-speed photography (Ts = 673 K, θ = 45°). A theoretical model was established to obtain the parameter range of defect-free joints through a series of bifurcate lattice printing experiments. Then, the morphology and generation mechanism of cumulative joint defects in the lattices at higher temperatures and angles (Ts = 773 K, θ = 60°) were analyzed. A parameter window of joint morphology with different values of inclined angle, substrate temperature, and top-layer droplet distance was established for predicting potential defects in the printing trace. Next, a novel method was proposed to remove redundant droplets and re-place top-layer droplet coordinates into the ideal center distance. Furthermore, the printing strategy was expanded to multi-truss lattices using three-dimensional transformation matrixes. Finally, multiple cells bifurcate, triangular, and pyramid lattices were successfully printed with perfect joints. The height deviation of joint regions is <5 % of the droplet diameter, verifying the feasibility of the proposed strategy. This work represents a further step towards MDDM printing of high-quality truss lattice structures and other complex 3D architectures.

Maximizing the energy scavenging capability of droplet triboelectric nanogenerators through surface engineering

Recent advancements in energy harvesting have led to innovative methods for converting droplet motion into electricity, such as droplet triboelectric nanogenerators (D-TENGs). However, enhancing their power generation capacity and efficiency remains a challenge. We present a novel surface engineering approach that significantly boosts the electrical outputs of the D-TENGs. By grafting perfluorodecyltrimethoxysilane (PFDTMS) onto polydimethylsiloxane (PDMS) surfaces pre-treated with sandpaper, we achieve a dual effect: fluoridation and increased contact area between droplets and PDMS. This modification, when applied to a droplet-based TENG, yields a remarkable 10–20 fold increase in power metrics such as current, charge, and voltage as compared to untreated counterparts, resulting in an energy conversion efficiency of 17.1% under a 30 MΩ load. Our enhanced D-TENG efficiently harvested energy from falling tap water droplets, producing a current of ∼2 mA. Remarkably, a single droplet impact could illuminate 400 LED lights. Furthermore, when coupled with capacitors, the device powered a hygrometer and 3 W light bulbs, demonstrating substantial potential for real-world applications. This breakthrough in surface engineering for energy harvesters represents a significant step forward in the efficient and powerful generation of electricity from droplet motions.

Numerical investigation of droplet impact and heat transfer on hot substrates under an electric field

In this study, the effects of the electric field on the impact dynamics and heat transfer of a single droplet impinging on hot substrates in the film evaporation regime were numerically investigated with phase-field method. According to the simulation results, many fancy impact behaviors of the droplets under a vertical electric field were observed. A strong electric field was found to induce upward pinch-off or even tiny jet phenomena on the hydrophilic substrates. In contrast, the bouncing droplet on hydrophobic substrate would be vertically stretched before leaving the substrates. The maximum spreading ratio of impacting droplets was always inversely proportional to the applied electric field intensity. Correlations of the maximum spreading for the charged condition were proposed by considering the effects of the electric force. In addition, the total heat transfer from hot substrates to the impacting droplet was verified as closely related to the maximum spreading area, spreading time, and instantaneous local heat flux. However, the broken droplets from the induced tiny jet would eventually fall back to disturb the sessile droplet, enhancing the droplet cooling efficiency. The modified heat transfer model of impacting droplets under the effect of an electric field on hydrophilic substrates was established. Finally, the surface charge distribution and electric force loading of the impacting droplets were also discussed. This work delved deep into the underlings of droplet spreading heat transfer under an electric field, and the main findings promised to advance high-efficiency cooling technology.

Experimental Study of Condensation Heat Transfer and Droplet Dynamics on Multiple Horizontal Copper Tubes with Superhydrophobic Characteristics

We conducted an experimental study on the condensation heat transfer and droplet dynamics on multiple horizontal copper tubes with superhydrophobic characteristics. Condensation heat transfer has various industrial applications such as power plants and air-conditioning systems. Because condensers are typically designed in multiple-tube configurations, studying the phenomenon of multiple tubes is important. We investigated the effect of a superhydrophobic surface modification, which induces dropwise condensation, on the heat transfer performance of multiple-tube condensers. The purpose of this research is to evaluate the extent to which heat transfer performance is improved by comparing superhydrophobic tubes with bare tubes and to analyze the impact of droplet dynamics on heat transfer performance. The results show that the heat transfer coefficient of the superhydrophobic tubes is improved by approximately 9.5%–44.9% compared to that of bare tubes. Droplet dynamic analysis revealed differences in droplet behavior between the superhydrophobic tubes and bare tubes, including the formation of droplets by condensation, the process of droplets falling on the tube surface, and the impact of droplets falling on other tubes in a multiple-tube configuration. Based on these results and observations, it can be concluded that the heat transfer performance of the superhydrophobic tube is superior to that of the bare tube. The droplet dynamic analysis demonstrated that the droplets formed on the superhydrophobic surface could be easily removed by the flow, leading to more efficient heat transfer. These findings highlight the potential for more efficient heat transfer in multiple tubes through superhydrophobic modifications.

Wetting permeability of surface active agent droplets impacting on a layer of coal dust

The wetting and penetration of the coal dust layer by liquid droplet is crucial for suppressing coal dust. A combination of experimental and simulation methods was employed to investigate the impact of surfactant concentration, droplet velocity, and particle size on the penetration properties and their underlying mechanisms. Droplet impact wetting experiments were employed to evaluate their dynamic wetting behavior on the coal dust layer. The experimental results show that increasing the impact velocity of droplets is advantageous for enhancing the maximum dimensionless wetting length. Increasing the surfactant concentration can expedite the droplet reaching maximum dimensionless wetting volume in the dust layer. The larger the particle size of coal dust, the shorter time required for droplet to reach maximum wetting volume. The research results provide a theoretical basis for selecting and efficiently applying surfactants in treating coal dust.

Physical and Numerical Experimentation of Water Droplet Collision on a Wall: A Comparison between PLIC and HRIC Schemes for the VOF Transport Equation with High-Speed Imaging

Liquid films are often found in engineering applications with thicknesses ranging from micrometer scales to large scales with a wide range of applications. To optimize such systems, researchers have dedicated themselves to the development of new techniques. To further contribute to this development, the objective of this work is to present the results of the collision of water droplets on a wall by means of experimentation and numerical simulations. For physical experimentation, an injector is used to generate a chain of water droplets that collide with the opposite wall, forming a liquid film. Images of the droplets were obtained using two high-speed recording cameras. The results for different droplet sizes and impact angles are presented and the relationship between the momentum parameter and non-dimensional pool size was established. Modeling such processes is a common challenge in engineering, with different techniques having their advantages and limitations. The simulations in this work were run using the volume of fluid method, which consists of solving a transport equation for the volume fraction of each considered fluid. A correlation was found between the surface tension to momentum transport ratio, Scd, and the non-dimensional pool size for different droplet sizes and impact angles. Regions where partial depositions were most likely to occur were found via physical experiments.

Droplet asymmetry bouncing on structured surfaces: A simulation based on SPH method

The impact of a liquid droplet onto a macro-structured super-hydrophobic surface, results in an asymmetric spreading-retraction process and a significant decrease in contact time. The process involves large deformation of droplets and evolution of surface morphology, so it is difficult to efficiently simulate using traditional grid-based methods. In this study, a numerical model is established using the mesh-free smoothed particle hydrodynamics (SPH) method to simulate the interaction of liquid droplets with solid surfaces exhibiting complex macro-textures. Leveraging the Lagrange nature of SPH, liquid droplets can be model using free surface boundary condition. The weakly compressible SPH formulation is employed to discretize the governing equations of liquid. Surface tension is captured by introducing an additional negative pressure term, inducing attractive forces among fluid particles. Kernel functions are carefully chosen to mitigate stress instability resulting from droplet spreading and retraction. The model is then applied to simulate the dynamic processes of droplets impact on flat and non-flat super-hydrophobic surfaces. The bouncing dynamics of droplets are investigated under varying conditions, including Weber number, size, and morphology of macro-scale surface structures. Our simulation results for contact time, maximum diameter, and droplet morphology align closely with experimental observations. The contact time of the droplet exhibits a dependency on its size and surface geometry, with a transition towards planar geometry diminishing asymmetric spreading effects. The findings highlight the significance of Weber number and cylinder diameter in determining contact time, providing insights for the design of optimized surface structures for specific droplet impact parameters. In addition, the use of a free-surface condition for modeling proved computationally efficient for 3D simulations. The model effectively reproduces nonlinear behaviors such as droplet spreading, splashing, and bouncing, highlighting the significant advantage of SPH in simulating such problems.

Pillar height regulated droplet impact dynamics on pillared superhydrophobic surfaces

Superhydrophobic surfaces that promote rapid droplet detachment have many significant engineering applications including self-cleaning, anti-icing, drag reduction. Adding macrotextures to superhydrophobic materials can markedly modify the dynamics of water impacting them, either by triggering a non-axisymmetric, center-assisted recoil or inducing pancake-like bouncing. However, the effect of pillar heights on superhydrophobic surfaces has received limited attention. Here, we have systematically investigated the role of the size ratio of pillar height-to-droplet radius (Q) on bouncing dynamics, including spreading, penetrating depth, contact time, bubble entrapment, impact pressure, and impact force, through numerical simulations. We show that droplet impact on superhydrophobic surfaces can generate two modes of bubble entrapment: one is an impinging cavity bubble, and the other is a recoiling cavity bubble, depending on Q. Furthermore, for low Weber number (We), droplet impacts may generate three peaks of impact force for superhydrophobic surfaces with high Q. For high We, only two peaks of impact force are generated during a droplet striking the superhydrophobic surface. However, the secondary peak in the impact force will weaken or may even disappear completely as Q increases, which was hitherto unknown. Interestingly, we also observe that despite lower impact force during droplet recoil compared to droplet impact, higher penetration depths are more easily achieved during the recoil stage. These findings shed light on the role of pillar heights in droplet impact dynamics, offering valuable insights for designing superhydrophobic surfaces.

In-flight anti-icing simulation of electrothermal ice protection systems with inhomogeneous thermal boundary condition

Conventional anti-icing computational solvers calculate the convective heat transfer coefficient using a homogeneous thermal boundary condition, assuming a constant temperature across the surface. However, this approach can lead to inaccuracies in regions with significant temperature variations. To address this limitation, the present study proposes a novel approach that utilizes an inhomogeneous thermal boundary condition, which updates the convective heat transfer coefficient based on the transient wall temperature distribution. We developed a unified finite volume framework that efficiently integrates various in-house solvers, including a compressible Navier-Stokes-Fourier (NSF) airflow solver, a Eulerian droplet impingement solver, a PDE-based ice solver, and a multilayer heat conduction solver. Thermal interaction between the different solvers was modeled using the conjugate heat transfer method. The effects of updating airflow on anti-icing results were investigated by comparing the results obtained by coupled and decoupled solvers. While the decoupled solver computes airflow once and remains unchanged, the coupled solver updates the airflow during the anti-icing simulation. Our findings show that the decoupled solver has the highest deviations from the coupled solver in evaporative anti-icing regimes, where dry regions form within the protection limits. Using coupled solvers in designing ice protection systems in evaporative regimes improves temperature prediction accuracy, enabling designers to reduce safety factors and save energy.