Droplet Oscillation Research Articles

The dynamics of a droplet in a capillary constriction underwave excitation

The frequency dependence of the amplitude of the wave excitation mobilizing a droplet trapped in a capillary constriction is determined. The effect of droplet viscosity is analyzed. The problem of free longitudinal oscillations of a viscous-fluid droplet in a capillary constriction is considered. The influence of the surface tension, the droplet volume, and the constriction shape on the natural frequency of droplet longitudinal oscillations is studied. A formula for calculating the droplet natural frequency in the conical constriction is obtained and analyzed.

Hydrodynamics of passing-over motion during binary droplet collision in shear flow**Project supported by the NSAF (Grants No. U1530260), the National Natural Science Foundation of China (Grant No. 51306158), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130621), and the Special Program for Applied Research on Super Computation of the NSFC–Guangdong Joint Fund (the second phase).

A combined experimental and numerical study is undertaken to investigate the hydrodynamic characteristics of single-phase droplet collision in a shear flow. The passing-over motion of interactive droplets is observed, and the underlying hydrodynamic mechanisms are elucidated by the analysis of the motion trajectory, transient droplet deformation and detailed hydrodynamic information (e.g., pressure and flow fields). The results indicate that the hydrodynamic interaction process under shear could be divided into three stages: approaching, colliding, and separating. With the increasing confinement, the interaction time for the passing-over process is shorter and the droplet processes one higher curvature tip and more stretched profile. Furthermore, the lateral separation Δy/R1 exhibits larger decrease in the approaching stage and the thickness of the lubrication film is decreased during the interaction. As the initial lateral separation increases, the maximum trajectory shift by the collision interaction is getting smaller. During the collision between two droplets with different sizes, the amplitude of the deformation oscillation of the larger droplet is decreased by reducing the size ratio of the smaller droplet to the bigger one.

Linear dynamics modelling of droplet deformation in a pulsatile electric field

A linear dynamic model of water droplet deformation in the presence of an electric field has been developed. Analytical solutions of the differential equation of motion are provided with different waveforms as forcing terms, namely in the case of half-sinusoidal, square and sawtooth waves. The main dimensionless groups are identified as a result of this analysis. The predictions of the model are compared with some data of droplet deformation available in the literature. The calculations based on this model show that the waveform affects the response of the droplet to the electric field stimulus. Resonance is possible only when the droplets are sufficiently large (i.e. for Ohnesorge number less than 1). The oscillation amplitude decreases rapidly with the electric field frequency. A qualitative comparison with some experiments of droplet-interface coalescence available in the literature has also been addressed, suggesting a correlation between the formation of secondary droplets and the amplitude of oscillation of the mother droplet. The outcomes of this analysis can be useful for the selection of the best operating conditions to improve the electrocoalescence process efficiency, as they can provide guidelines to the choice of the most suitable electric field parameters.

Enhanced SO2 removal by using charged water droplets

This paper reports preliminary results on the absorption of SO2 from water charged droplets, produced by an electrospray operated in dripping mode. Our results show that the water charging allows a ≈50% increase of the SO2 absorption rate. Since the SO2 mass transfer coefficient depends mainly on the liquid-side mass transfer coefficient, we envisage that the increase of SO2 absorption rate is ascribable to the occurrence of droplet deformation and oscillation, driven by the reduction of surface tension caused by the presence of excess charge on the droplet surface. Experiments were successfully interpreted in light of an absorption model that specifically address the droplet formation and fall and considered the model of Matteson and Giardina (1974) to account the droplet charge effect.

Adsorption and rheological behavior of an amphiphilic protein at oil/water interfaces

Hydrophobins are highly surface active proteins which self-assemble at hydrophilic-hydrophobic interfaces into amphipathic membranes. We investigate hydrophobin self-assembly at oil/water interfaces to deepen the understanding of protein behavior in order to improve our biomimetic synthesis. Therefore, we carried out pendant drop measurements of hydrophobin stabilized oil/water systems determining the time-dependent IFT and the dilatational rheology with additional adaptation to the Serrien protein model. We show that the class I hydrophobin H∗Protein B adsorbs at an oil/water interface where it forms a densely-packed interfacial protein layer, which dissipates energy during droplet oscillation. Furthermore, the interfacial protein layer exhibits shear thinning behavior.

In situ experimental measurement of temperature field and surface tension during pulsed GMAW

In this paper, non-contact measurements are presented to observe droplet oscillations and to measure surface temperature during Pulsed GMAW. The techniques enable to investigate in situ the behavior of mild steel liquid metal surrounded by Ar + 8%CO2 plasma and then to measure temperature dependence of surface tension. Different temperatures are obtained by changing the process parameters. Surface tension values are a little higher than values found in the literature but the results demonstrate the interest of the developed setup. To conclude, a non-dimensional analysis is carried out, based on experimental results, to investigate the relative importance of the different phenomena acting during the transfer.

Numerical study of multiphase droplet dynamics and contact angles by smoothed particle hydrodynamics

In this paper, an efficient method is developed for droplet simulation with high density ratios using smoothed particle hydrodynamics (SPH). The new approach is straightforward compared to previous studies and is applied to both static and dynamic droplet problems. Regarding the continuum surface force method which needs the normal vector and surface curvature in surface tension calculation, a color function formulation is introduced for tracking and correcting color function of boundary particles. This leads to a stable and accurate droplet simulation which reflects the reality of surface-tension force and droplet profile without the need for setting the desired unit normal vectors directly. The developed model is validated for droplet oscillation, static contact angles, liquid droplet evolution, dynamic wetting angles on inclined surfaces and droplets collision. The results demonstrates that the developed formulation can capture the equilibrium contact angle and handle droplets motion over inclined surfaces with different inclination angles and gravitational accelerations accurately.

Time series analysis based study of a mass-spring-like oscillation and detachment of a metal pendant droplet

The subject of this study is the vertical mass-spring-like oscillation of a pendant droplet and its resonant detachment, which was experimentally observed in the process of laser droplet generation from a metal wire. The process was characterized by various time series, which were generated from a sequence of infrared intensity images of the process. Following a visual inspection of pendant droplet images and an analysis of a wavelet based time-frequency map of the droplet’s vertical displacement time series, the pendant droplet’s oscillation is described by a time-variable mass-spring system. Based on the characteristics of the time-frequency map, the resonant nature of the pendant droplet detachment was demonstrated. Additionally, an algebraic expression was formulated, which can be used to predict the detached droplet’s diameter as a function of the laser pulse frequency.

On the application of the PFEM to droplet dynamics modeling in fuel cells

The Particle Finite Element Method (PFEM) is used to develop a model to study two-phase flow in fuel cell gas channels. First, the PFEM is used to develop the model of free and sessile droplets. The droplet model is then coupled to an Eulerian, fixed-grid, model for the airflow. The resulting coupled PFEM-Eulerian algorithm is used to study droplet oscillations in an air flow and droplet growth in a low-temperature fuel cell gas channel. Numerical results show good agreement with predicted frequencies of oscillation, contact angle, and deformation of injected droplets in gas channels. The PFEM-based approach provides a novel strategy to study droplet dynamics in fuel cells.

Measurements of Submicron Particle Adsorption and Particle Film Elasticity at Oil-Water Interfaces.

The influence of particle adsorption on liquid/liquid interfacial tension is not well understood, and much previous research has suggested conflicting behaviors. In this paper we investigate the surface activity and adsorption kinetics of charge stabilized and pH-responsive polymer stabilized colloids at oil/water interfaces using two tensiometry techniques: (i) pendant drop and (ii) microtensiometer. We found, using both techniques, that charge stabilized particles had little or no influence on the (dynamic) interfacial tension, although dense silica particles affected the "apparent" measured tension in the pendent drop, due to gravity driven elongation of the droplet profile. Nevertheless, this apparent change additionally allowed the study of adsorption kinetics, which was related qualitatively between particle systems by estimated diffusion coefficients. Significant and real interfacial tension responses were measured using ∼53 nm core-shell latex particles with a pH-responsive polymer stabilizer of poly(methyl methacrylate)-b-poly(2-(dimethylamino)ethyl methacrylate) (pMMA-b-pDMAEMA) diblock copolymer. At pH 2, where the polymer is strongly charged, behavior was similar to that of the bare charge-stabilized particles, showing little change in the interfacial tension. At pH 10, where the polymer is discharged and poorly soluble in water, a significant decrease in the measured interfacial tension commensurate with strong adsorption at the oil-water interface was seen, which was similar in magnitude to the surface activity of the free polymer. These results were both confirmed through droplet profile and microtensiometry experiments. Dilational elasticity measurements were also performed by oscillation of the droplet; again, changes in interfacial tension with droplet oscillation were only seen with the responsive particles at pH 10. Frequency sweeps were performed to ascertain the dilational elasticity modulus, with measured values being significantly higher than previously reported for nanoparticle and surfactant systems, and similar in magnitude to protein stabilized droplets.

Droplet Departure Characteristics and Dropwise Condensation Heat Transfer at Low Steam Pressure

Dropwise condensation has received significant attention due to its great potential to enhance heat transfer by the rapid droplet removal. In this work, droplet departure characteristics on a vertical surface, especially the droplet departure retention at low steam pressure and its effect on the heat transfer performance are investigated experimentally. The energy dissipation increases during droplet movement due to the increased viscosity at low pressure. Droplet oscillation caused by excess kinetic energy weakens and the dynamic contact angle (CA) hysteresis becomes apparent, which is not beneficial to droplet departure. Condensed droplets grow larger and fall more slowly at low pressure compared to that at atmospheric pressure. The droplet moves smoothly downward once it grows to departure size at atmospheric pressure while the droplet exhibits an intermittent motion at low pressure. Based on the droplet departure characteristics, a unified heat transfer model for dropwise condensation is developed by introducing the pressure-dependent departure velocity. The modified model very well predicts heat transfer performances at various pressures and the nonlinearity of heat flux varying with surface subcooling is quantitatively explained. This work provides insights into the heat transfer mechanism of dropwise condensation and offers a new avenue to further enhance heat transfer at low steam pressure.

Alternating electric field actuated oscillating behavior of liquid metal and its application

As a class of newly emerging functional material, Gallium based liquid metals have attracted increasing attentions in many fields, such as chip cooling, printed electronics and microfluidics, etc. Particularly, the motion control of liquid metal droplet has been recently tried for its importance in microelectromechanical system (MEMS), microfluidics and potential use in micro-machine or reconfigurable soft robot. This paper is dedicated to explore the motion behavior of liquid metal droplet under AC electric field. The quickly induced oscillation phenomena of liquid metal droplet and surrounding electrolyte solution were observed and the major factors to influence such behaviors are theoretically interpreted and experimentally investigated, including the size of the liquid metal droplet, electrode voltage, electrolyte solution concentration and AC signal frequency etc. Moreover, some typical features to distinguish AC filed actuation with DC field are observed, such as intensive fluid waving induced by the resonance stimulation, and the efficient inhibition of solution electrolysis. Finally, two important applications of adopting AC induced surface oscillation of liquid metal droplet to develop solution mixer as well as fluidic pump were demonstrated which successfully avoid gas generation inside electrolyte environment. The bulk oscillation effects of liquid metal as clarified here could be very useful in a variety of areas such as solution disturbance and mixing, and fluid oscillator or pump etc.

Magnetic droplet microfluidic system incorporated with acoustic excitation for mixing enhancement

This paper describes a new type of magnetic droplet microfluidic system incorporated with acoustic excitation for the enhancement of mixing performance. The oscillation amplitudes of acoustically oscillating droplets with different volumes (6μl and 8μl) in different frequencies are measured by high-speed images. When a droplet is acoustically excited, it only strongly responds to the droplet’s natural frequency. Internal flow inside an acoustically oscillating droplet is visualized using fluorescent particles (15μm diameter). Mixing performance is investigated using a methylene blue and glycerol (5wt%) mixture droplet. The mixture droplet (6μl) is completely mixed within 60s with acoustic excitation; whereas, the mixture droplet remains unmixed without the excitation. The mixing efficiency is quantitatively evaluated through mixing indexes obtained by image analysis. The transportation of a magnetic droplet (6μl) containing magnetic particles (500nm dia.) is separately demonstrated using a neodymium magnet beneath a chip. The maximum manipulation speeds of magnetic droplets (approximately 25mm/s for 6μl droplet and 20mm/s for 8μl droplet) are measured by the magnetic droplet rotation test. As proof of concept, the manipulation of four magnetic droplets with two different volumes (3μl and 4μl) and colors (red and blue) is experimentally achieved by incorporating magnetic actuation for the transportation of droplets and acoustic excitation for the oscillation of droplets. This result shows the highly reliable manipulation of magnetic droplets with high mixing performance.

Instability of a charged droplet in an inhomogeneous electrostatic field of a thin rod

The problem of stability of oscillations of a charged droplet in an inhomogeneous electrostatic field of a thin charged rod is investigated in the nonlinear formulation using the asymptotic expansion in two small parameters, namely, the dimensionless equilibrium droplet strain and the ratio of the droplet oscillation amplitude to the droplet radius. It is shown that, when the droplet charge is less than the Rayleigh critical charge, in the inhomogeneous electrostatic field the droplet instability implementation mechanism remains the same as for the charged droplet in the field of a point charge. As the oscillation mode number increases, the critical field parameter reaches saturation tending to the horizontal asymptotics. The longer the rod, the higher the level of the asymptotics. As the rod length increases, the amplitudes of the related droplet oscillations and the increments of the unstable droplet oscillations in the electrostatic field of the rod decrease.

Simulation of Dynamic Behavior and Prediction of Optimal Welding Current for Short-Circuiting Transfer Mode in GMAW

An improved “mass–spring” model to analyze the entire short-circuiting transfer (SCT) dynamic process based on the association between the arcing and circuiting phases has been proposed. This paper analyses the basic characteristics of displacement of the droplet mass center and oscillation velocity of droplet variation. In addition, the effect of welding current on the short-circuiting frequency is studied. The results of the simulations conducted agree well with the experimental results obtained. An analysis method for optimal welding current during SCT is also proposed, and the droplet transport stability is discussed. Simulation results demonstrate that the relative displacement of the droplet mass center and the average equivalent diameter of the transfer droplets are at a minimum under the optimal welding current condition. This research provides a reference for further simulation of the SCT process and useful guidance for the selection of optimum technics parameters.

Sectorial oscillation of acoustically levitated nanoparticle-coated droplet

We have investigated the dynamics of a third mode sectorial oscillation of nanoparticle-coated droplets using acoustic levitation in combination with active modulation. The presence of nanoparticles at the droplet surface changes its oscillation amplitude and frequency. A model linking the interfacial rheology and oscillation dynamics has been proposed in which the compression modulus ε of the particle layer is introduced into the analysis. The ε obtained with the model is in good agreement with that obtained by the Wilhelmy plate approach, highlighting the important role of interfacial rheological properties in the sectorial oscillation of droplets.

Electric field makes Leidenfrost droplets take a leap.

Leidenfrost droplets, i.e. droplets whose mobility is ensured by a thin vapor film between the droplet and a hot plate, are exposed to an external electric field. We find that in a strong vertical electric field the droplet can start to bounce progressively higher, defying gravitational attraction. From the droplet's trajectory we infer the temporal evolution of the amount of charge on the droplet. This reveals that the charge starts high and then decreases in steps as the droplet slowly evaporates. After each discharge event the charge is in a fixed proportion to the droplet's surface area. We show that this behavior can be accurately modeled by treating the droplet as a conducting sphere that occasionally makes electrical contact with the hot plate, at intervals dictated by an electro-capillary instability in the vapor film. An analysis of the kinetic and potential energies of the bouncing droplet reveals that, while the overall motion is damped, the droplet occasionally experiences a sudden boost, keeping its energy close to the value for which the free fall trajectory and droplet oscillation are in sync. This helps the droplet to escape from the hot surface when finally the electrical surface forces overtake gravity.

Optovibrometry: tracking changes in the surface tension and viscosity of multicomponent droplets in real-time.

An instrument was developed for measuring real time changes in the surface tension and viscosity of multicomponent droplets of miscible liquids and other soft materials. Droplets containing glycerol and water were supported on superamphiphobic surfaces and vibrated by applying a short mechanical impulse. Laser light was refracted through the droplets and allowed to fall on the surface of a photodiode. Time dependent variations in the intensity measured by the photodiode during vibration were used to monitor the decay of the droplet oscillations. The frequencies and spectral widths of the droplet vibrational resonances were then obtained from Fourier transforms of these time dependent intensity signals. A recently developed model of viscoelastic droplet vibration was used along with these values and measurements of the drop dimensions to extract the surface tension and viscosity of the drops as they evaporated. Collection of data was automated and values of frequency, spectral width, drop size, surface tension and viscosity were obtained with a time resolution of three seconds over a period of thirty minutes. The values of surface tension and viscosity obtained were shown to be in good agreement with literature values obtained from bulk glycerol/water solutions; thus validating the technique for wider application to other multicomponent liquids and soft matter systems.

Numerical simulation of oscillation phenomenon for droplet spreading on solid surface by lattice Boltzmann method

The oscillation phenomenon during droplet spreading on solid surface is studied. Simulations based on the lattice Boltzmann method with the mass processed by the volume of fluid show that the oscillation continues during the whole spreading process and the maximum oscillation value occurs at the initial phase. By observing the amplitude of droplet contour volume and liquid membrane velocity, the amplitude change is obtained. The influence of droplet characteristics on amplitude is studied. Simulated results show that the effect of kinematic viscosity on droplet oscillation is greater than that of droplet surface tension. The velocity vectors inside the droplet are also tracked to understand the oscillation.

Numerical Study for Shape Oscillation of Free Viscoelastic Drop Using the Arbitrary Lagrangian-Eulerian Method

The free oscillation of liquid droplet is one of the classical questions in science research, liquid drops play important role in a lot of engineering applications. Theory study of droplet oscillation mainly based on the linear method, this method is only adapted to the small-amplitude oscillatory motion of drops. Except the linear method used in this study, numerical method have been successfully applied in simulation of the free oscillation of liquid droplet. In this paper, the finite element method is used to investigate numerically the influence of viscoelasticity on the small-amplitude oscillation of drop of polymer solutions. A spatial discretization is accomplished by the finite element method, the time descretization is carried by the Crank-Nicolson method, and the arbitrary Lagangian-Eulerian (ALE) method is used to track the change of the interface. Numerical results are compared with the ones of linear theory. The behaviors of oscillation are found to depend on the viscosity and the stress relaxation time of viscoelastic fluid, the results of numerical simulation and linear theory are identical.