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The simulation of droplet-wall impact process based on computational fluid dynamics (CFD) is of great significance for understanding the dynamic behavior of droplets spreading on the solid wall, and can provide technical support for the design of superhydrophobic structures and the development of anti-icing coating. The difficulty lies in how to accurately describe the evolution process of the contact line and the dynamic contact angle in the model. Herein, 4 typical dynamic contact angle models were summarized, and their application ranges were analyzed theoretically. With the UDF function in FLUENT the dynamic contact angle model was applied to the wall boundary conditions, and the dynamic process of droplet impact on smooth wall was numerically simulated. The quantitative analysis of the changes of droplet shape parameters and the comparison with the experimental results show that, the Seebergh dynamic contact angle model is more suitable for simulating the motion of droplets with lower capillary numbers. The Kistler model and the Jiang model are more widely used and can accurately describe the motions of droplets with higher capillary numbers. Then, based on the Kistler dynamic contact angle model, the impact and spreading processes of droplets on the microstructure surface were simulated. It is found that, the application of the dynamic contact angle model will lead to the change of the internal flow fields of droplets with the surface tension playing a dominant role, and the simulated droplet contact angle value in equilibrium is close to the theoretical value. [ABSTRACT FROM AUTHOR]

Featured Application: This work compares the impact dynamics of ethanol/propanol and ethanol/water droplets on the heated plate and a novel unique bubble shrinkage phenomenon is observed and analyzed for ethanol/water droplets. 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. [ABSTRACT FROM AUTHOR]

In recent years, the pseudopotential multiphase lattice Boltzmann method (LBM) has been widely applied in the numerical simulations of complex multiphase flow. However, numerical stability at high Weber (We) and Reynolds (Re) numbers seriously restricts its application. In the present work, the pseudopotential multiphase LBM is developed by introducing the entropic stabilizers to the cascaded collision operator, and thus, the numerical stability is effectively enhanced. The relaxation rates for different order moments are all determined by fluid viscosities and the maximum entropy condition instead of being user-defined. Furthermore, the surface tension and contact angle can be adjusted in a wide range, which extends the application of the pseudopotential multiphase model. The accuracy and capability of the present model to simulate the complex multiphase flow are validated by reproducing the droplet impact on the flat or textured superhydrophobic surfaces. In addition, a droplet impact on the superhydrophobic surface at We = 1280 and Re = 18000 is simulated, in which the Weber and Reynolds numbers have significantly increased. This strongly demonstrates that the present model can enhance the numerical stability in the simulation of large density ratio multiphase flows at simultaneously high Weber and Reynolds numbers, which means the present model can further extend the pseudopotential multiphase LBM to more realistic scientific and technical applications. [ABSTRACT FROM AUTHOR]

A numerical investigation is conducted to study the air entrapment phenomenon when two different liquids such as water and diesel droplet are impacted on the solid surface. The beginning of the air entrapment process was observed during droplet impact on a solid substrate forming a dimple underneath the droplet. The air film thus trapped underneath the droplet started evolving into the air bubble. This journey of evolution mainly comprises phases like an inertial retraction of air film, contraction, and pinch‐off of the secondary droplet inside the air bubble for a water droplet impact case. The volume of fluid approach has been utilized to track the progress of air film evolution. The influence of surface wettability has been observed on the evolution of air film into the air bubble by taking four different values of contact angle pertaining to the hydrophilic surface (θ = 10° and 35°) and hydrophobic surface (θ = 90° and θ = 120°). The air bubble was found to get detached from the substrate for the hydrophilic surface (θ = 35°) and observed to remain attached to the substrate for the hydrophobic surface. The variation of pressure underneath the droplet was also investigated as the droplet reaches the substrate. The effect of surface tension has been studied on the evolution of air film by impacting the diesel droplet on the same substrate keeping the same wettability condition (θ = 35°). The lower surface tension of the diesel droplet as compared to the water droplet delayed the process of air film evolution and consequently decreases the retraction speed of air film. Also, the air bubble remains attached to the surface. Furthermore, the air bubble detaches from the surface for an even higher wettability condition (θ = 10°). Thus surface wettability and surface tension become two important factors governing the development of entrapped air film and bubble elimination in many practical applications. [ABSTRACT FROM AUTHOR]

• Droplet escapes initial crater at angles < 15° and remains inside it at angles > 45°. • Furrow is a chain of craters; between them, secondary entrainment may occur. • Surface tension, viscosity and reduced thickness dampen the craters inside the furrow. • Impact near wave crest leads to partial survival and detachment of the droplet. • Intensive bubble entrapment is not reproduced by the present model. In presence of a strong wind above a liquid surface, liquid droplets get accelerated and eventually hit the interface with a high speed under a small angle. Experimental studies demonstrate that such droplets may escape the initial crater and either get broken into secondary droplets in the air, or protrude along the interface, leaving behind agitated surface with entrapped bubbles. Here we aim at reproducing the observed phenomena in a numerical model based on Volume of Fluid technique using Basilisk package. On a flat interface, the impacting droplets partially escape the crater and get broken in front of it within the range of impact angles from 15° to 45°, in agreement to the experiments and simple theoretical considerations. In presence of waves, the escaping droplets fly into the air but, being adhered to the crater, get stretched and broken into secondary droplets. For smaller angles, the droplets escape the crater and glide along the interface. The gliding droplet creates a chain of small craters in its wake. The rims between the craters may grow and get scattered into secondary droplets. Large liquid viscosity and small thickness of the liquid layer suppress the growth of the craters and secondary entrainment. Bubble entrapment during such impacts most likely occurs due to crater collapse with trapping air inside. However, such air pockets are not formed systematically in the present model. This discrepancy requires further investigation. [Display omitted] [ABSTRACT FROM AUTHOR]

• Droplet impact under different roughness and vibration conditions are studied. • Higher surface roughness inhibits droplet spreading. • Vibration results in a more pronounced variation in the dynamic contact angle. • Correlation was proposed for droplet spreading with an error of ±9.5%. Droplet impingement is pivotal in several fields, such as agricultural spraying, ink printing and firefighting. Although droplet impact studies have received much attention, the combined effects of roughness and vibration on droplet dynamics still need to be explored. In this study, an in-depth analysis is carried out to address this issue, and high-speed photography is utilised to explore the droplet impact process under different roughness and vibration conditions. The results show that higher surface roughness dissipates the kinetic energy of droplet spreading, thus inhibiting droplet spreading. Conversely, vibration imparts additional inertial effects to the droplet, leading to sustained oscillations once the droplet stabilises, which in turn results in a more pronounced variation in the droplet's dynamic contact angle. Therefore, in this paper, the vibrational Weber number (W e v) is employed to characterise the interaction between the vibration-induced extra inertia force and the droplet's surface tension. Moreover, as the W e v increases, the relative velocity of the droplet impact also rises, further intensifying the droplet's spreading behaviour. At a W e v of 8.72 and a surface roughness of 0.4 μ m , droplet spreading is enhanced by 33%. While at a surface roughness of 6.3 μ m , droplet spreading was suppressed by 32% relative to a surface roughness of 0.4 μ m. Ultimately, an empirical model was proposed to predict the droplets' maximum dimensionless spreading coefficient (β m a x) under vibration conditions, with an error of ±9.5% in the model prediction. This study delves into the dynamic characteristics of droplets under the combined influence of surface roughness and vibration, offering crucial theoretical foundations and profound insights for engineering applications in the field. [ABSTRACT FROM AUTHOR]

Featured Application: This work can be used in the droplet harvest process, for droplet impact on a solid surface with a wettable gradient like rain harvest and spray collection, as well as for regulation in a microchannel by spontaneous droplet spreading and migration. The influence of apex angle and tilting angle on droplet spreading dynamics after impinging on wedge-patterned biphilic surface has been experimentally investigated. Once the droplet contacts the wedge-patterned biphilic surface, it spreads radially on the surface, with a tendency toward a more hydrophilic area. After reaching the maximum spreading diameter, the droplet contracts back. From the experimental results, the normalized diameter β ( β = D / D 0 ) was found to be related with the Weber number ( W e = ρ D V 2 / γ ) as β max ∼ W e 1 / 5 . during the first spreading process. Below 67.4°, a larger apex angle can help a droplet to spread on the surface more quickly. The maximum spreading diameter has a tendency to increase with the Weber number, and then decrease after the Weber number, beyond 2.7. Approximately, the critical Weber number is about 5, when the droplet lifts off the surface. Considering the effect of apex angle, the maximum normalized spreading diameter has a rough expression as β ∼ α τ [ABSTRACT FROM AUTHOR]

Theoretical formulation of droplet impact on elastic beams is relatively difficult, due to its transient, non-stationary, and elasto-capillarity nature. In this study, a numerical model is proposed based on the smoothed particle hydrodynamics (SPH) method to simulate the impact process of a droplet on elastic beams. Both of the liquid droplet and the elastic substrate are modeled by SPH, and this feature ensures that the fluid-solid interaction can be solved in a unified framework. In addition, the continuum surface force (CSF) method is adopted to simulate the surface tension effect on the droplet impact. Robustness, concision and validity of the model are validated by simulating a single water drop impact on elastic super-hydrophobic beams. Interesting phenomena of droplet bouncing and beam vibrations are reproduced following the experiment. These analyses may be beneficial to engineering new materials and new devices in such areas as fabrics, agriculture, petroleum, and micro/nano technology. • A fully Lagrangian SPH-based model is developed for simulation of droplet impact on elastic surface. • The robustness of the model is ensured taking care on combining the advantages of different corrective techniques. • The continuous surface force method is implemented through accurately reconstructing the geometry of the droplet surface. • The springboard effect, beam vibration, and large deformation caused by water droplets are simulated. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • The smallest doubly reentrant cavity was provided by improved fabrication methods. • Extremely low surface tension liquids can stay Cassie state on this surface. • The new surface outperforms traditional designs in room/freezing impacting tests. • Analysis on impacting pressure and dynamic/static resistance force are conducted. Abstract A bioinspired superomniphobic surface integrating doubly reentrant nanostructures with microcavities is proposed for simultaneously increasing static repellency and dynamic pressure resistance. Novel micro/nano fabrication techniques were developed for fabricating 15 μm doubly reentrant micro-cavities, which is the smallest in the world. Static and dynamic wetting experiments were conducted on pillared, doubly reentrant, cavity and the newly developed surfaces under different surface temperatures. It is found that the newly fabricated surface has the shortest contact time in comparison with other superhydrophobic surfaces, which depressed the ice nucleation on the surface below freezing temperature and, therefore, enhance the ability of icephobic. The experimental results show that the newly developed surface can not only successfully suspend the liquid with extremely low surface tension but also can repel droplets with an impact Weber number as high as 103 under a room temperature condition which is twice higher than previous research. Especially, even at −5 °C surface temperature, the newly developed surface can still repel droplets under Weber number of 335 while conventional cavity surface failed to repel droplets under the same Weber number at surface temperature −2 °C. The mechanism behind the excellent performance of the newly developed surface is analyzed utilizing "air spring effect", and micro wetting behavior of Laplace Breakthrough on nanostructures. Breakthrough pressure on the novel surface was three times larger than that of the cavity design. It is suggested that this kind nanostructured doubly reentrant cavity surface is promising which has potential applications in anti-icing and biofluid resistance. [ABSTRACT FROM AUTHOR]

• High-speed photography used to study micro-droplet ejection on super-hydrophobic surfaces. • Impact velocity is crucial for controlling micro-droplet ejection. • Initiated chemical vapor deposition method was used to change surface wettability. • Jet is caused by the blast of air-cavity collapse, verified by visualization experiment. • Ejection occurs at velocities of 0.26–1.31 m/s, classified into 5 stages. Impact velocity plays a crucial role in the control of droplet ejection when producing micro-droplets with directed diameters and velocities from millimetre-sized droplets. In this study, high-speed photography is used to experimentally investigate the characteristics of the ejection of micro-droplets after impacting a super-hydrophobic surface with different impact velocities ranging from 0.16 to 2.34 m/s. The results indicate that droplet ejection only occurs at impact velocities ranging from 0.26 to 1.31 m/s. Furthermore, it is found that the droplet ejection process can be classified into five stages based on the Weber number. In Stages 1–3, the ratio of the ejected to initial droplet diameters changes only slightly with the Weber number. In Stage 4, the ratio first increases, then decreases, and finally increases again. In Stage 5, the ratio decreases linearly. An equation describing the decrease in the ratio during Stage 5 is obtained and the correlation between the ratio of the ejection to impact velocities and the Weber number for the same stage is investigated. It is concluded that the formation of the central liquid column and the final characteristics of droplet ejection are mainly the result of the competition among inertial force, reaction force from the surface, gravity, and surface tension; and the formation of the jet is determined by the collapse of the air cavity. [ABSTRACT FROM AUTHOR]

Methods to avoid the dynamic Leidenfrost effect are of great importance for high heat flux spray cooling which needs an efficient contact of liquid and superheated surface. In this paper, a novel method of increasing dynamic Leidenfrost temperature is proposed through addition of high-alcohol surfactant (HAS). Effects of 1-Octanol and 2-ethyl-hexanol surfactants on dynamic Leidenfrost temperature and spreading dynamic of droplets impacting on superheated surface were investigated for the first time using high-speed photography. Empirical correlations of dynamic Leidenfrost temperature and maximum spreading factor were obtained based on our experimental data. A possible explanation for the dynamic Leidenfrost temperature increase caused by HAS was proposed based on bubble bursting and bubble coalescence. The results show that dynamic Leidenfrost temperature is significantly increased by addition of HAS because of surface tension reduction. The empirical correlations of dynamic Leidenfrost temperature and maximum spreading factor show good agreement with maximum error of 5% and 10% respectively. These empirical correlations could provide reference value for the future research. [ABSTRACT FROM AUTHOR]

The influence of apex angle and tilting angle on droplet spreading dynamics after impinging on wedge-patterned biphilic surface has been experimentally investigated. Once the droplet contacts the wedge-patterned biphilic surface, it spreads radially on the surface, with a tendency toward a more hydrophilic area. After reaching the maximum spreading diameter, the droplet contracts back. From the experimental results, the normalized diameter β ( β = D / D 0 ) was found to be related with the Weber number ( W e = ρ D V 2 / γ ) as β max ∼ W e 1 / 5 . during the first spreading process. Below 67.4°, a larger apex angle can help a droplet to spread on the surface more quickly. The maximum spreading diameter has a tendency to increase with the Weber number, and then decrease after the Weber number, beyond 2.7. Approximately, the critical Weber number is about 5, when the droplet lifts off the surface. Considering the effect of apex angle, the maximum normalized spreading diameter has a rough expression as β ∼ α τ

Abstract: A transient three‐dimensional model that describes physical phenomena inside a welding pool during gas–metal arc welding process is presented. The model considers such phenomena as heat‐mass transfer, electromagnetics, hydrodynamic processes and deformation of the weld pool free surface. The fluid flow in the weld pool is induced due to the presence of the mechanical impact of the droplets, thermo‐capillary surface tension, thermal buoyancy and electromagnetic forces. The weld pool surface deformation is calculated by considering arc pressure and droplet impact force. A comparative analysis of the impact of the electric current of the welding arc and different force factors causing the motion of liquid metal in the weld pool on the shape of the welded seam was carried out and discussed. [ABSTRACT FROM AUTHOR]

In this study, an Algebraic Coupled Level Set-Volume of Fluid (A-CLSVOF) method is proposed for the simulation of interfacial capillary flows. The Volume of Fluid (VOF) method is utilized to incorporate one-way coupling with the Level Set (LS) function in order to improve the accuracy of the surface tension force calculation and to reduce the presence of parasitic currents. In this method, both VOF and LS functions are transported where the new volume fraction determines the interface seed position utilized by the reinitialization procedure for the LS field. Computational efficiency is enhanced through the use of the advected LS field, serving as an initial condition for the reinitialization procedure. The Hamilton–Godunov function is used with a second order (in space and time) discretization scheme to produce a signed distance function. In order to evaluate the performance of the methodology implemented here for capillary dominant flows, four different cases were considered: 1. static droplet; 2. capillary wave relaxation; 3. Rayleigh–Taylor instability and 4. droplet impact on a liquid pool. The simulations demonstrated reduction in spurious currents, accurately predicted capillary pressure and demonstrated overall improvements in efficiency and error reduction owing to the addition of LS advection. The present methodology is tested against previously published experimental results for a droplet impact on a deep liquid pool. Simulation results demonstrate excellent agreement with measured interface height up to and beyond the formation of a Rayleigh–Jet and break-up formation of a secondary daughter drop. [ABSTRACT FROM AUTHOR]

We investigate the effect of ethanol concentration on the spreading dynamics of an ethanol-water binary droplet impact on a supercooled surface. The maximum spreading factor, comprised of the maximum internal spreading factor and dimensionless fingering length, decreases and then increases with the ethanol concentration. It is attributed to the change in ethanol concentration which varies liquid viscosity and surface tension directly, and surface cooling which lowers the droplet temperature and thus varies liquid properties that further affect droplet spreading. The maximum internal spreading factor which is also non-monotonic with the ethanol concentration dominates the maximum spreading. The heat transfer analysis on droplet spreading shows that the temperature reduction of the droplet from impact to maximum spreading is non-monotonic dependent on the ethanol concentration, while shows different trends with surface cooling at various ethanol concentration. Deviations of the predicated maximum spreading factor, considering the droplet temperature reduction, obtained by reported correlations from the experimental ones in this study could be mainly due to the difficulty in accurately predicting the temperature-dependent spreading boundary layer thickness of the droplet. The maximum spreading time decreases and then increases with the ethanol concentration, while it keeps decreasing with the surface supercooling. A new correlation of the maximum spreading time is proposed by incorporating the coefficient of surface supercooling and capillary-inertial time of the droplet which involves density and surface tension. • Phase diagram of an impact ethanol-water binary droplet on the supercooled surface is shown. • Effect of ethanol concentration and surface temperature on the droplet spreading is discussed. • Comparison of the proposed correlations of β max and t max is introduced. • A new fitting correlation of t max is proposed. [ABSTRACT FROM AUTHOR]

The numerical study of droplets impact behaviors onto a solid substrate is performed in this work. With a given impact velocity, one or two two-dimensional droplets subsequently interact with the substrate. During the process of droplet development on the substrate, the gravity is taken into account. To conduct numerical simulations, a hybrid method is adopted, in which the flow field is solved by using the lattice Boltzmann method and the interface is captured by solving the Cahn–Hilliard equation directly. The effects of Bond number (Bo, ratio of gravity to surface tension of droplet), Weber number (We, ratio of inertial force to surface tension) and droplet arrangement on the dynamic behaviors of droplets impact are systematically investigated. After a single droplet impact, a higher Weber number can lead to a longer contact length. In addition, the occurrence of bubble entrapment is determined by the Bond number. On the other hand, in the case of two droplets impact, several segments accompanying with their detachment from the surface are observed when two identical droplets are initially placed close to each other. Moreover, sparse segments, which are attributed to the oblique jet, are produced when two droplets have different sizes. [ABSTRACT FROM AUTHOR]

We studied experimentally the behavior of a single cold water droplet that falls onto a hot horizontal flat solid surface in the film boiling region. We found that when the droplet hits the surface (for the first time), three different regimes may occur. These regimes depend on the ratio of fluid's inertia and its surface tension (the Weber number, indicated as We) and on the surface temperature. For relatively low We numbers or surface temperatures, the droplet completely bounces hack from the surface and no breakup occurs. For intermediate We numbers or surface temperatures, the spreading stage is faster and the droplet undergoes spreading and partial recession before it breaks up into bouncing small secondary droplets that leap inward and successively coalesce above the surface to form a single droplet once again. For high We numbers or surface temperatures, the spreading velocity is higher, the contact area with the surface is greater, and the liquid film thickness is smaller. Thus, during the expansion of the spreading stage, the droplet breaks up into bouncing small secondary droplets that uninterruptedly leap outward and travel independently. We also present the limiting conditions differentiating between the different behaviors found. This work shows droplet film boiling behaviors that are essentially different than droplet levitation on top of a thin vapor layer, as mainly assumed in theoretical models. We also observed that when a droplet hits the surface for the second, consecutive time (and on), the droplet behaves somewhat differently due to its preheating, very low impact velocity, different shape, spin, orientation, and the surface temperature. At the second impact on the surface (and on), the droplet can continue its bounce in a unique and different manner than in the first impact or it can explode violently to small secondary droplets. Both are unique and differentiating mainly by the droplet's shape and orientation at the exact moment of impact on the surface. Additionally, a rare and unique view of droplet-droplet collision during film boiling is presented. This type of collision behaves in a different way than other droplet-droplet collisions and compared to the adiabatic case of droplet-droplet collision on a nonlieated surface. The behaviors found, presented, and discussed in this study change our view of the droplet-surface and droplet-droplet interactions that occur in spray cooling in the film boiling region. [ABSTRACT FROM AUTHOR]

This paper deals with simulation of the spreading and solidification of a fully molten particle impacting onto a preheated substrate under traditional plasma spraying conditions. The multiphase problem governing equations of mass, momentum and energy conservation taking into account heat transfer by conduction, convection, and phase change are solved by using a finite element approach. The interface between molten particle and surrounding air, is tracked using the Level Set method. The effect of the Reynolds number on the droplet spreading and solidification, using a wide range of impact velocities (40-250 m/s), is reported. A new correlation that predicts the final spread factor of splat as a function of Reynolds number is obtained. Thermal contact resistance, viscous dissipation, wettability and surface tension forces effects are taken into account. [ABSTRACT FROM AUTHOR]

In this paper, the whole dynamic process of a single drop impact onto a thin liquid surface up to the consequent formation of a thin crown is numerically studied using the smoothed particle hydrodynamics (SPH) method. Especially, the gravity, artificial viscosity, and surface tension are introduced into the model. The obtained SPH numerical results are compared with experimental results. The numerical model of the SPH method is valid for simulating the dynamic process of a single drop impact onto a liquid surface. Meanwhile, it is found that the whole dynamic process mainly depends on the depth of the liquid pool and the initial velocity of the droplet. [ABSTRACT FROM AUTHOR]

Abstract: A study on the initial wetting velocity (V w0) for a water droplet impinging on glass and parafilm surfaces was performed using a fast-speed video camera system. The silhouette images were recorded sequentially from the moment the droplet made contact with the solid surface. The profile of the droplet during spreading revealed the droplet-wetting diameter (especially in the first millisecond), then the wetting velocity was determined. The relaxation of the wetting velocity, V w(t), was investigated at five different impact velocities (V i). The value of V w0 was found to be a few meters per second; V w then decreased dramatically in a few ms to approximately 1/10 of V w0. Moreover, the V w for water on parafilm became negative (i.e., retraction started) at approximately 2–3ms (dimensionless time t*∼1). A general phenomenon was observed: (i) a higher V i results in a larger V w0; (ii) at the first millisecond, the wetting velocity was dominated primarily by V i and was nearly independent of the surface hydrophobicity; (iii) for t >2ms, the V w depends mainly on the surface hydrophobicity; and (iv) for t =1–3ms, the V w for the droplet with higher V i became smaller for both solid substrates while the droplet continued spreading. [Copyright &y& Elsevier]

We simulate the three-dimensional impact of a droplet onto a solid surface using the level contour reconstruction method (LCRM). A Navier-slip dynamic contact line model is implemented in this method and contact angle hysteresis is accounted for by fixing the contact angle limits to prescribed advancing or receding angles. Computation of a distance function directly from the tracked interface enables a straightforward implementation of the contact line dynamic model in the LCRM. More general and sophisticated contact line models are readily applicable in this front tracking approach with few modifications, since complete knowledge of the geometrical information of the interface in the vicinity of the wall contact region is available. Several validation tests are performed including 2D planar droplet, 2D axisymmetric droplet, and full three-dimensional droplet splashing problems. The results show good agreement compared with existing numerical and experimental solutions. [ABSTRACT FROM AUTHOR]

Abstract: Three major issues associated with numerical simulations of complex free-surface flows, viz. interface tracking, fragmentation and large physical jumps, are addressed by a new hybrid continuum-particle model (HyPAM). The new model consists of three parts: (1) the Polygonal Area Mapping method [Q. Zhang, P.L.-F. Liu, A new interface tracking method: the polygonal area mapping method, J. Comput. Phys. 227(8) (2008) 4063-4088]; (2) a new algorithm that decomposes the interested (water) phase into a continuum zone, a buffer zone and a particle zone, based on material topology and graph theory; (3) a ‘passive-response’ assumption, in which the air phase is assumed to respond passively to the continuum part of the water phase. The incompressible inviscid Euler equations and the equations describing the free fall of rigid bodies are used as the governing equations for the continuum-buffer zone and the particle zone, respectively, and separately. A number of examples, including water droplet impact, solitary wave propagation, and dam-break problems, are simulated for the illustration and validation of HyPAM. It is shown that HyPAM is more accurate and versatile than a continuum-based Volume-of-Fluid model. One major contribution of this work is the single-phase decomposition algorithm, useful for many other hybrid formulations. Neglecting surface tension, viscosity and particle interactions, HyPAM is currently limited to mildly-fragmented free-surface flows with high Reynolds and Weber numbers. [Copyright &y& Elsevier]

Abstract: A fixed-grid, sharp interface method is developed to simulate droplet impact and spreading on surfaces of arbitrary shape. A finite-difference technique is used to discretize the incompressible Navier–Stokes equations on a Cartesian grid. To compute flow around embedded solid boundaries, a previously developed sharp interface method for solid immersed boundaries is used. The ghost fluid method (GFM) is used for fluid–fluid interfaces. The model accounts for the effects of discontinuities such as density and viscosity jumps and singular sources such as surface tension in both bubble and droplet simulations. With a level-set representation of the propagating interface, large deformations of the boundary can be handled easily. The model successfully captures the essential features of interactions between fluid–fluid and solid–fluid phases during impact and spreading. Moving contact lines are modeled with contact angle hysteresis and contact line motion on non-planar surfaces is computed. Experimental observations and other simulation results are used to validate the calculations. [Copyright &y& Elsevier]

This study adopts the phase-field method to investigate the dynamics of droplet impact on spherical surfaces at various Reynolds numbers Re and Weber numbers We. Five liquids are studied in the present simulation, which expands the research scope of viscosity (1–970 mPa·s) and surface tension (20–500 mN/m) compared with previous works. The temporal evolution of the spreading factor β and the dimensionless center thickness h * is systematically analyzed. The results indicate that β max ∝ We a suggested by previous works does not apply to viscous fluids. Thus, we adopt the impact factor P = We / Re 0.8, which has been used to study droplet impact on flat surfaces, to decide the dominating force of β max for impact on spheres. We first find that β max ∝ Re b exists in the viscous regime (P > 1), whereas β max ∝ We a mainly exists in the capillary regime (P < 1). Although the fluid properties of incident droplets vary widely, the variation in h * with dimensionless time τ always has three distinct phases. The first phase follows h * = 1- τ , and the second phase basically conforms to h * ∝ τ −1.6. The minimum dimensionless center thickness h * min scales as Re c . Furthermore, the exponents a , b , and c are found to b e strongly related to the diameter ratio of spheres and droplets, and prediction models of the three exponents are proposed. [Display omitted] [ABSTRACT FROM AUTHOR]

• Impact and spreading dynamics of ethanol–water droplets are investigated. • Low-We ethanol–water droplet shows better spreading than high-We water droplet. • Lower surface tension and Marangoni effect affect the droplet impact. • Impact regime maps are proposed with and without ethanol additive. In the present study, the impact and spreading dynamics of a single droplet on a heated surface are experimentally investigated. Ethanol-water droplets with ethanol concentrations of 0–8 vol% are adopted as the working fluid with a wide range of surface temperature from 75 °C to 450 °C and the Weber number ranges from 7 to 63. The instantaneous droplet evolution after impact is studied via visualization. All the observed phenomena implied that ethanol additive has a significant influence on both impact dynamics and spreading characteristics. A new phenomenon is observed that the addition of ethanol can compensate for the negative influence of small Weber numbers, i.e. , some ethanol–water droplets with smaller Weber numbers show better spreading dynamics, higher breakup and atomization possibility but weaker rebound compared with water droplets with higher Weber numbers. It is speculated that droplet impact is no longer solely dependent on the Weber number for ethanol–water droplet, and lower surface tension caused by ethanol additive and Marangoni effect due to concentration gradient along the interface are mainly responsible for this difference. The result also shows that impact behavior exhibits complex dependence on the surface temperature and Weber number, including deposition, rebound, rebound with atomization, breakup with atomization and breakup, while the regime map is significantly affected by ethanol additive. [ABSTRACT FROM AUTHOR]

• Wedge-patterned biphilic surface is used for droplet transport; • Apex angle of the wedged patterns can help droplet transport on biphilic surface between 36.9° and 67.4°. • A force balance model is promoted on droplet transport on biphilic surface with wedge patterns and agrees well with experimental results. Droplet impact on biphilic surfaces with a wettability contrast has been intensively studied in recent years. In this work the effects of tilting and apex angles on droplet transport dynamics after impacting on a wedge-patterned biphilic surface at low Weber numbers were investigated experimentally. The biphilic surface was fabricated by applying a hydrophobic polymer coating on a bare silicon surface. According to the experimental results, a larger apex angle below 67.4° can accelerate the droplet effectively at first. Then the friction force controls the droplet movement and reduces the speed. The tilting angle along the hydrophilic direction activates the droplet. If the gravity component is opposite to the hydrophilic direction and the tilting angle is over 15°, the droplet can hardly move toward the hydrophilic area. By modeling the hydrodynamics of the droplet movement after impact on a biphilic surface with assumptions of no evaporation, no Marangoni effect, negligible dynamic contact angle variation and negligible rotation effect, the surface tension values versus the position at different apex angles are derived. The predicted position versus time trends agree well with the experimental data. This study aims to provide a better understanding of the mechanisms of droplet hydrodynamics on wedge-patterned biphilic surfaces at low Weber numbers. [ABSTRACT FROM AUTHOR]