Droplet Oscillation Research Articles

Suppression strategy for metal droplet overlapping fusion defects caused by droplet impact dynamics under coaxial shielding gas

High-precision droplet overlapping under coaxial shielding gas is a prerequisite for automated and lightweight metal micro-droplet deposition manufacturing. Unfortunately, the opening shielding environment exposes metal droplets directly to the atmosphere. Droplet overlapping fusion quality would be affected due to the coupling effects of impact dynamics, thermodynamics, and oxidation. In this study, based on experiments and theoretical modeling of molten droplet impact dynamics, a strategy to suppress droplet overlapping fusion defects under coaxial shielding gas was proposed for the first time. Results show that at lower shielding gas rates, molten droplet retraction, recoil, and oscillation would weaken or vanish due to the oxide film's self-limiting effect. This limits the improved model's accuracy in predicting the droplet spreading factor in lower shielding gas supply rates. The weakened droplet dynamic behaviors at low shielding gas supply rates would magnify the length and height defects of droplet overlapping, which is particularly evident at a small printing step distance. Finally, a quality mapping for different printing parameters is established, effectively suppressing overlapping defects and ensuring fusion quality through metallurgical bonding. This work could provide a solid evidence base and theoretical guidance for high-quality metal micro-droplet deposition manufacturing under an opening shielding environment.

Probing the contact time of droplet impacts: From the Hertz collision to oscillation regimes.

Droplet rebound on nonwetting surfaces is a common phenomenon. However, the underlying physics regulating the contact time remains unclear. In this work, we investigate droplet impacts on superamphiphobic surfaces through experiments and theoretical analyses. By analyzing the spreading and retraction of droplet impinging processes over a wide range of Weber numbers (We), it is revealed that droplet impacts experience three regimes as We is varied, which are denoted as the Hertz collision (We<1), transition (1<We<10), and oscillation (We>10) regimes. In the Hertz collision regime, the droplet impinging process is temporally symmetric, i.e., the spreading time, t_{S}, and the retraction time, t_{R}, are almost the same. Furthermore, t_{S} and t_{R} decrease with increasing We and follow a power-law dependence, which is different from previous theories. In the transition regime, t_{S} remains dominated by the Hertz collision, while t_{R} is governed by droplet oscillation. In the oscillation regime, t_{S}, t_{R}, and the total contact time, t_{C}, become independent of We. These three regimes are valid for both monophase and compound droplets. The findings in this work advance the understanding and offer a clear picture of droplet impact dynamics.

Visualization and quantitative study on film boiling heat transfer of a salt droplet on the hydrophobic substrate

A droplet impacts on high temperature surface may lead to film boiling. Hydrophobic coating used for corrosion prevention is easy to cause film boiling at low temperature, which results in a remarkable decrease in evaporation efficiency and heat transfer coefficient. However, there is a lack of quantitative visual experimental data on the flow field around the droplet to understand the heat transfer characteristics during film boiling. In this study, schlieren photography combined with high-speed imaging technology is used to observe the evolution process of a droplet impact, rebound, oscillation, and stable boiling. The effects of temperature on lifetime, vapour velocity and heat transfer coefficient of a salt droplet with different concentrations are studied for aluminum and Teflon surfaces. The distribution characteristics of vapour velocity are quantitatively analyzed using cross-correlation algorithm, and the calculation formulas of heat transfer coefficient under nucleate and film boiling modes are proposed. It is found that increasing the concentration of a salt droplet can improve the heat transfer coefficient during film boiling. This work will provide a theoretical basis for the improvement of heat exchanger efficiency in areas such as sea water spray cooling.

Experimental investigation of contact time of bouncing droplet on vibrating substrates

The observation of an elastic substrate self-driving droplet to produce a “springboard effect” provides new enlightenment to the application of elastic materials in the anti-icing area. The droplet–substrate dynamic of a water drop impacting a superhydrophobic elastic substrate is experimentally investigated at different Weber (We) numbers and beam stiffness. For water drop, the spreading dynamic is not affected by the We number and beam stiffness since the inertial action is dominant, and the elastic action of the beam is relatively small, while the receding dynamic is closely related to the parameters. For elastic substrate, the vibrating deflection increases with the increase in the We number and reduction of the stiffness, while the vibrating frequency is only dependent on its stiffness. Based on this, the rebound dynamic of the droplet is discovered dependent on the scale relationship between the droplet and substrate oscillation period. Finally, a relation of the contact time of a droplet impacting elastic substrates, which is verified to hold for a large range of We numbers, beam stiffness, and droplet sizes, is established. The discoveries may contribute to the design of a droplet–elastic substrate system to achieve desirable contact time, providing a theoretical basis to forecast the performance of droplet–substrate systems by employing elastic materials.

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

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

An improved smoothed particle hydrodynamics method for modeling multiphase flows

Multiphase flows are prevalent in both natural and engineered systems. The study of multiphase flow problems using numerical simulation is challenging due to the presence of high nonlinearities and moving interfaces. In this paper, an improved multiphase smoothed particle hydrodynamics (SPH) model is proposed for simulating multiphase flows. In the improved multiphase SPH model, an improved interface repulsive force model is proposed to reduce the interpenetration of particles at the multiphase interface and make the multiphase interface smooth and clear, and an improved kernel gradient correction is introduced to optimize the computational results. In addition, the particle shifting technology is applied to make the particle distribution uniform. Five numerical examples including the Rayleigh–Taylor instability, non-Boussinesq lock-exchange problem, square droplet deformation, single bubble rise, and circular droplet oscillation are investigated to verify the correctness and effectiveness of the improved multiphase SPH model. The results demonstrate that the improved multiphase SPH approach is effective in modeling multiphase flows.

Improving polymer electrolyte membrane fuel cell performance and preventing flooding by exciting gas flow

Effective water management is necessary to prevent the performance degradation of polymer electrolyte membrane fuel cells (PEMFCs). In this study, acoustic pressure waves (AWs) are superimposed on an oxygen gas flow passing through a cathode to evaluate its potential to mitigate the flooding issue in flow channels. The goal is to expedite droplet removal by exciting droplets at frequencies close to their natural frequency. In-situ experiments are conducted to investigate the influence of AWs on two-phase flows in the cathode channel and the corresponding PEMFC performance. When AWs are applied, the frequency of water discharge from the cathode channel increases, and reduces the internal accumulated water, resulting in the pressure drop decreases. The internal flooding is also decreased, resulting in the reduction of the high frequency resistance attributed to decreased contact resistance. The external excitation improves the PEMFC performance owing to the effective and frequent water discharge induced by the increase in the local inertial force related to the droplet oscillation. The water management method propose in this study is considered to be an efficient method not only for PEMFC systems but also for other systems requiring water management.

The coalescence and oscillation of eutectic gallium indium alloy droplets

Gallium-based liquid metal droplets have excellent deformation performance, and their oscillation has huge potential in oscillator and organ-on-chip research. At present, the oscillation of gallium-based liquid metal droplets controlled by external energy (such as the application of electric fields and chemical reactions) has been thoroughly studied, while there are vacancies in the study of the oscillation due to coalescence of droplets without external energy input. A numerical simulation study on the oscillation process after the coalescence of two and three eutectic gallium indium alloy droplets is conducted. The degree of deformation of the droplet is described by the dimensionless length change in the symmetry axis direction of the line connecting the centers of the initial droplets in the top view, that is, in the y direction. The oscillation curve of the droplet is obtained by the fitting method. The results show that the oscillation of coalesced droplets has obvious periodicity and damping attenuation characteristics, and increasing the number of droplets or reducing the droplet radius will increase the damping coefficient. Furthermore, the ratio of droplet sizes and their initial distribution have an impact on the variations in kinetic energy of the three droplets in the y direction, thereby influencing the deformation of the droplets. This research enriches the theory of gallium-based liquid metal droplet deformation and plays a significant role in guiding the application of droplet oscillation in the fields of micromixers and measuring the physical parameters of solutions.

Measuring the density, viscosity, and surface tension of molten titanates using electrostatic levitation in microgravity

Rare earth and barium titanates are useful as ferroelectric, dielectric, and optical materials. Measurements of their thermophysical properties in the liquid state can help guide melt processing technologies for their manufacture and advance understanding of fragile liquids' behavior and glass formation. Here, we report the density, thermal expansion, viscosity, and surface tension of molten BaTi2O5, BaTi4O9, and 83TiO2-17RE2O3 (RE = La or Nd). Measurements were made using electrostatic levitation and droplet oscillation techniques in microgravity, which provide access to quiescent liquid droplets and deep supercooling of 510–815 K below the equilibrium melting points. Densities were measured over 900–2400 K. Viscosities were similar for all four compositions, increasing from ∼10 mPa s near 2100 K to ∼30 mPa s near 1750 K. Surface tensions were 450–490 dyn cm−1 for the rare earth titanates and 383–395 dyn cm−1 for the barium titanates; surface tensions of all compositions had small or negligible temperature dependence over 1700–2200 K. For solids recovered after melt quenching, x-ray microtomography revealed the fracture mechanics in crystalline products and minimal internal porosity in glass products, likely arising from entrapped gas bubbles. Internal microstructures were generally similar for products processed either in microgravity or in a terrestrial aerodynamic levitator.

Rebound of oscillating droplets on non-superhydrophobic surfaces

Oscillating droplets rebounding completely from non-superhydrophobic surfaces (polydimethylsiloxane, PDMS) were experimentally studied and theoretically interpreted. The new experimental finding is that, with increasing the droplet impact Weber numbers (We), the recovery coefficient of droplet velocity, which is defined as the ratio of the rebounding velocity over the impact velocity, has an overall trend of decrease but in a fluctuating manner. Physically, a sufficiently large droplet freely falling under gravity has an inevitable oscillation, which makes the impacting droplet shape slightly deviate from being spherical and in turn affects the interaction between the droplet and the surface. The fluctuating recovery coefficient is the result of the periodically varying phase of droplet oscillation with increasing We, and increasing the droplet viscosity can suppress the droplet oscillation and then the fluctuation amplitude of the recovery coefficient. A theoretical model of oscillating droplet rebound is proposed and well fits the present experiments over a wide range of We.

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.

Marangoni Convection Velocity in Nonlinear Hanging-Droplet Vibration Phenomena

The Marangoni effect involves a mass transfer along an interface between two phases owing to the gradient of the interfacial tension. The flow caused by this phenomenon is called Marangoni convection, a complex phenomenon that involves mass transfer processes, such as surfactant adsorption/desorption processes, solvent dissolution phenomena, and viscous dissipation processes. Therefore, the strength of the convection depends on the various thermodynamic and physical properties of the fluids. In this study, we experimentally investigated the relationship between the Marangoni convection generated inside a hanging oil droplet and the interfacial tension of the oil droplet in an aqueous phase by the particle image velocimetry method. This convection velocity depended on the initial value of the interfacial tension in the oil–water interfacial tension oscillation phenomenon accompanied by the expansion and contraction of the hanging drop. Additionally, the droplet oscillation frequency decreased as the Marangoni convection velocity increased. Furthermore, continuous convection, which is unlike Marangoni convection, was observed within this spontaneously expanding and contracting hanging-droplet system. This buoyant convection was caused by the mutual dissolution of the hanging-droplet oil phase and the surrounding aqueous phase.

Generation and Suppression of Pendant Droplet Oscillation in Electron Beam Directed Energy Deposition

Electron beam–directed energy deposition (EB–DED) has emerged as a promising wire-based metal additive manufacturing technique. However, the effects of EBs on pendant droplets at wire tips have not yet been determined. The aim of this study is to enhance the understanding of this action by analyzing the mechanism of droplet oscillation. The pendant droplet oscillation phenomenon hinders the stable transfer of droplets to the molten pool and limits the feasibility of manufacturing complex lattice structures by EB–DED. Hence, another aim of this study is to create an oscillation suppression method. An escalating asymmetric amplitude is the main characteristic of droplet oscillation. The primary oscillation-inducing force is the recoil force generated from the EB-acted local surface of the droplet. The physical mechanism of this force is the rapid increase and uneven distribution of the local surface temperature caused by the partial action of the EB. The prerequisites for droplet oscillation include vacuum conditions, high power densities, and bypass wire feeding processes. The proposed EB–dynamic surrounding melting (DSM) method can be applied to conveniently and effectively suppress oscillations, enable the accurate transfer of droplets to the molten pool, and achieve stable processes for preparing the strut elements of lattice structures. Lowering the temperature and improving the uniformity of its distribution are the mechanisms of oscillation suppression in EB–DSM. In this study, the physical basis for interpreting the mechanism by which EBs act on droplets and the technical basis for using EB–DED to prepare complex lattice structure parts are provided.

Investigating the dynamic characteristics of oil droplets spreading on solid surfaces in water

The use of thermoplastic-reinforced pipes for fluid recovery is becoming increasingly common because the oil field enters the high-water-cut stage in this process. Investigating frictional drag in case of oil-water flow in nonmetallic gathering pipelines is important because the dynamics of oil droplets on the inner surfaces of the pipes have a significantly influence on the drag. In this article, we experimentally and theoretically investigate the dynamic characteristics of the spreading of oil droplets with varying diameters from 600 to 900 μm and viscosities on surfaces with different degrees of wettability in water. The durations of oscillation and spreading of oil droplets on the surfaces submerged in water were found to be dependent on their diameter and viscosity. Because the prevalent equations used for calculations in this context cannot adequately describe the durations of oscillation and spreading of the oil droplets on surfaces in water, we corrected them based on experimental data. Finally, we examined the dimensionless maximum diameter of spreading of the oil droplets on the surfaces in water, and found that it was influenced by the diameter of the oil droplets and the wettability of the surface. We developed a theoretical model to represent the behavior of the oil droplets as they spread in order to predict the dimensionless maximum diameter of spreading, and verified it by using experimental data. And the results showed that the deviations between the experimental results and those of the model were generally within ±8%.

Computation of aluminum droplet ejection and flight in microgravity

Persistent and frequent space explorations are limited by real-time parts supply and it is significant to achieve space manufacture, such as the droplet-based printing. In order to study the microgravity environment effect on droplet-based printing, this paper proposed an effective method to research the effect of space station environmental g-jitter (according to NASA experimental signal) on droplet ejection and flight process. The heat transfer, transient gravity acceleration and Marangoni effect are studied based on the improved model. The results show that the g-jitter is in the order of 10−3 magnitude and the effect on aluminum droplet ejection could be ignored when nozzle diameter (dn) is smaller than 0.1 mm and so do ground case. Combined with the ground microgravity simulation of SnPb alloy lateral ejection experiments, it can be obtained that the ejected single droplet is characterized by capillary number (Ca≤0.002), the droplet flight trajectory is dependent on the Froude number (Fr) and the laminar-turbulence transition exists during the droplet flight process. The relationship formulation between the deviation along gravity direction and the deposition distance is introduced to control and adjust the droplet flight trajectory. Moreover, the temperature effect on material property, such as surface tension and so on, has effect on the droplet breakup length. The g-jitter field enhances the Marangoni effect resulting in the deviation of droplet trajectory. In microgravity field, the computational droplet oscillation period is well coincidence with theoretical equation. Improved KIC-SST based model is available for simulating droplet-based printing in microgravity.

ANALYSIS OF THE DYNAMICS AND FREEZING OF WATER DROPLETS ON METAL SURFACES

This article investigates the effects of substrate temperature, tilt angle, and droplet size on droplet impact dynamics and freezing using a Motionpro high-speed camera and a DSA-30 droplet surface analyzer. The temperature of the substrate was changed from the ambient temperature of 21&amp;deg;C to -13&amp;deg;C, and three droplet sizes (&lt;i&gt;D&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; &amp;#61; 2.57, 3.02, and 3.54 mm) were studied. The results show that some air gets trapped under the liquid film during the impact process due to insufficient escape time, resulting in the interior of the droplet being in an unstable state. Simultaneously, due to the low surface energy of the substrate, liquid droplets exhibit a rebound effect upon impact with the ambient temperature substrate, reaching their maximum height and forming a dumbbell-like shape. Furthermore, the rebound height decreases rapidly with the decrease in substrate temperature. A change in substrate temperature had no significant effect on the droplet spreading process, but decreasing substrate temperature increased the viscous forces, thereby suppressing the droplet retraction and oscillation processes, ultimately leading to longer droplet freezing times. Additionally, at low Weber numbers (&lt;i&gt;We &lt;/i&gt;&amp;#60; 250), the droplet dimensionless parameters exhibited a similar trend with respect to dimensionless time or temperature.

Dynamics of a silicone oil drop submerged in a stratified ethanol-water bath.

We analyze numerically the Marangoni flow around an immiscible droplet submerged in a stably stratified mixture of ethanol and water. The linear stability analysis shows that the base flow undergoes a supercritical Hopf bifurcation that leads to oscillations. The theoretical prediction for the critical droplet radius is consistent with previous experimental results. Ethanol diffusion in water is critical in the flow stability for both low and high droplet viscosity. Direct numerical simulations of the nonlinear oscillatory flow show that the frequency of those oscillations approximately equals that of the critical eigenmode. The nonlinear convective term of the ethanol diffusive-convective transport equationfixes the amplitude of the droplet oscillations. The viscous dissipation associated with the Marangoni flow inside the droplet considerably reduces the oscillation.

Modeling and application of droplet oscillation momentum for elucidating the development of surface roughness in wire-arc additive manufacturing

ABSTRACTIn feedback control systems of wire-arc additive manufacturing (WAAM), timely adjustments before the occurrence of deviations (feedforward control) would reduce excessive requirements on the sensitivity and accuracy of characteristic parameters of control systems. However, the search for characteristic parameters suitable for feedforward control is extremely rare in the WAAM field. Herein, based on ‘mass-spring' theory, a model of droplet oscillation momentum (DOM) is developed to describe the dynamic behavior of a pendant droplet and its influencing mechanism on surface roughness. The model combines the contribution of wire movement to droplet displacement with experimental correction of the spring/damping coefficients. The results show that the predictions of the model are in good agreement with the experimental values, and DOM is quadratically correlated with the surface roughness. Therefore, the model can be expected as a characteristic parameter to elucidate the development of surface-forming quality of WAAM-fabricated components.

Free surface tension modelling using particle-grid hybrid method without considering gas particles

In particle method, the number of particles is an important factor affecting the computational efficiency. For the free-surface flow, gas particles are usually necessary for surface tension calculation, but they have little impact to the liquid flow with a large density. If the free surface tension can be modeled without considering gas particles, it is of great significance to improve the computational efficiency. The existing potential-based surface tension model and the stress-based surface tension model don't need gas particles, but they have the problems of instability or are difficult to implement. Therefore, in this study, another free surface tension calculation method by coupling particles and grids is proposed. In the method, background mesh is applied to the entire computational domain, where the boundary of grid is extended outward by 3.1 l0 on the basis of particle boundary for curvature calculation. The level-set function is adopted to mark different phases on background mesh, whose value is set according to the normal distance between the grid and the nearest free surface particle. After obtaining the curvature and the level-set function gradient on background mesh, these variables are interpolated to corresponding particles to calculate the surface tension. Through the comparative study of area-weighted and distance-weighted interpolation schemes, it is found that the accuracy of distance-weighted interpolation scheme is higher than that of area-weighted interpolation scheme. Finally, the performance of the particle-grid hybrid method is verified by simulating four benchmark cases, including droplet oscillations, droplet spreading, capillary jet breakup and droplet impinging onto plate.

Simulation of Electrowetting-Induced Droplet Detachment: A Study of Droplet Oscillations on Solid Surfaces

The electrowetting-induced detachment of droplets from solid surfaces is important for numerous applications in the fields of heat transfer and fluid mechanics. The forced oscillations of droplets on solid surfaces and their ability to detach are studied. In this study, the process is efficiently simulated by implementing a powerful methodology developed by our team. Our results agree with experiments showing that optimal detachment, in terms of actuation energy, is achieved when the application of voltage is synchronized with the spreading time of the droplet. Under these conditions, the droplet oscillates with a period close to that of a mirrored Rayleigh droplet. The relationship between the droplet’s oscillation period and its physical properties is examined. During voltage-droplet synchronization, the droplet’s ability to detach depends mostly on its contact angle, its viscosity, and the applied voltage. An energy analysis is also conducted, revealing how energy is supplied to the droplet by electrowetting-induced detachment.