Droplet Oscillation Research Articles

Droplet oscillation mechanism and its free surface behavior on impacting a heated hydrophobic surface at low Weber numbers

Oscillation mechanism and free surface behavior of micro-droplets (300, 400, and 500 µm in diameter), impinging on a dry, hydrophobic heated surface was investigated using the volume of fluid (VOF) method. It was observed that the droplets exhibit unique oscillation characteristics at low Weber numbers for different contact angles and surface temperatures. At higher contact angles, droplet deformation was retarded, and it tends to retain its shape. This increased its chances of bouncing away from the surface. With increasing surface temperature, the tendency of the droplet to bounce away from the surface also increased. The oscillation behavior was significantly influenced by droplet size, contact angle with the surface and by surface temperature. Larger sized droplets had lower oscillation frequency. An increase in contact angle or surface temperature led to the lowering of the oscillation frequency of droplets. However, droplet Weber number was found to have no significant effect on oscillation frequency. At these low value of Weber numbers, all droplet sizes investigated showed slightly under-damped harmonic motion with amplitude exponentially decaying toward zero.

Experimental study on fusion and break-up motion after droplet collision

Abstract The interactions between droplets have an important influence on the atomization of liquid fuel, the combustion efficiency, and the reduction of particulate matter emissions for an engine. For this reason, this paper presents results from an experimental study on the coalescence and break-up of droplets after collision. According to the shape and parameters of the droplets at different times after the collision of the droplets was captured by a high speed camera, analysis was done for the following effects of droplet collisions: the collision-coalescence motion for the collision between the droplets, the change history of the dimensionless length-to-width ratio of the oscillation motion, the critical size ratio of the breakup motion, and the liquid physical properties of the particles. The results show that the droplets collide and exhibit two forms of coalescence oscillation and break-up: for oscillating motion, at higher droplet collision velocities and dimensionless size ratios, there will be a larger dimensionless length-to-width ratio for the droplet oscillation; for the break-up motion, at higher collision velocities, there will be lower dimensionless size ratios, and lower liquid surface tension, shorter times over which the droplet breaks, and facilitated droplet break-up. The research results presented here can be used for atomization in engine cylinder, increasing the gas/liquid contact area and enhancing the combustion efficiency of gas/liquid heat transfer to improve the combustion efficiency of the engine.

Computational and experimental analysis of droplet transportation/jetting behaviours driven by thin film surface acoustic waves

A Coupled Level Set Volume of Fluid (CLSVOF) approach has been applied to investigate severe deformation/transportation/jetting behaviours of sessile droplet driven by thin-film surface acoustic waves (SAW) devices. For validation of this computational method, a series of experimental studies of droplet transportation/jetting were performed using ZnO/Si thin film based SAW devices with resonant frequencies ranging from 64.49 MHz to 271.36 MHz. Good agreements between the computational and experimental results showed the capability of the developed CLSVOF method in modelling complex acoustofluidics phenomena such as significant internal streaming, pumping and jetting of the droplet driven by the propagating SAW.Results obtained from the computational model are used to clarify the fluidic mechanisms of droplet oscillation and wobbling behaviours during transportation. Numerical results reveal the liquid streaming patterns and airflow velocity field around the droplet at different stages of transportation/jetting process. Effects of droplet volume, the resonant frequency of SAW devices and applied SAW power on droplet transportation/jetting were investigated both theoretically and experimentally. In particular, comparisons between experimental and computational results showed that the model predicted well the minimum RF power to start droplet pumping and jetting at various resonant frequencies.

Experiments and modeling of nonlinear frequency response of oscillations of a sessile droplet subjected to horizontal vibrations.

In this paper, we experimentally studied the response frequency of oscillations of a sessile water droplet, subjected to horizontal vibrations at varying excitation frequency (5-250 Hz and 40 kHz) and amplitude (0.015 mm to 0.5 mm for low frequencies and 600nm for ultrasonic frequency), as well as static contact angle of the glass substrate ([Formula: see text], [Formula: see text] , [Formula: see text], [Formula: see text]). The droplets were pinned during the experiments and non-axisymmetric oscillation modes were excited due to the horizontal vibrations. For the first time, we observed that at a sufficiently high vibration amplitude, when the excitation frequency is lower than the smallest natural frequency of the sessile droplet, the droplet oscillates at a response frequency multiple of the excitation frequency. At higher excitation frequencies up to several hundreds of Hz, the droplet oscillates nearly at the excitation frequency. At ultrasonic excitation frequency, however, the droplet cannot follow the excitations, since there is a physical limitation for forming infinite modes (infinite wavenumber) on the surface of a small droplet. We have modeled these behaviors with a nonlinear mass-spring-damper system by combining two established models: the Duffing and Van der Pol equations, in order to simulate both nonlinear damping and stiffness.

A simple levitated-drop tensiometer.

A reliable, simple, and affordable liquid tensiometer is presented in this paper. The instrument consists of 72 ultrasonic transmitters in a tractor beam configuration that levitates small liquid samples (droplets) in air. Under operation, the instrument imparts a pressure instability that causes the droplet to vibrate while still levitating. Droplet oscillations are then detected by a photodiode, and the signal is recorded by an oscilloscope. The frequency of these oscillations is obtained and then used to obtain the effective surface tension of the sample. The instrument operates at the millisecond scale time (t < 12.5 ms), with very small liquid volumes (∼0.5 μl), and the sample is recoverable after testing. The instrument has been experimentally validated with acetone, ethanol, Fluorinert FC-40, water, and whole milk.

Strong rotating flow in stationary droplets in low power budget using wire electrode configuration.

We explore a simple strategy of generating strong rotating flow in a stationary surface-droplet, using an intricate interplay of local electrical and thermal fields. Wire electrodes are employed to generate on-spot heating without necessitating any elaborate micro-fabrication, which causes strong local gradients in electrical properties to induce mobile charges into the droplet. Applying a low voltage (∼10V), strong rotational velocity of the order of mm/s can be achieved in the system, within the standard operating ranges of operating and geometrical parameters. Further, altering the diameter of the electrode, vortices can be tuned locally or globally in low power budget, without incurring any droplet oscillations. These results may turn out to be of immense consequence in enhancing micromixing in a plethora of droplet based applications ranging from thermal management to medical diagnostics to be potentially employed in resource-limited settings.

Microdrop impact on soft substrates at low Weber numbers

In this work, we experimentally investigate the impact of microdrops on diverse soft substrates at low Weber numbers. We show that the dynamic behaviors of the impinging microdrops are very different from that of macroscopic droplets reported in the literature. Whereas various impact phenomena have been identified for millimeter-sized water droplets in previous studies, we only observed regular deposition for droplets of a few tens of micrometers in the experiment. In contrast to the significant slowdown of the receding millimeter-sized droplets, no effects of substrate stiffness on the impact process have been identified at microscale. These different dynamics are explained by the different dynamic response of soft viscoelastic materials during droplet impact over different timescales. Finally, the analysis of the post-impact droplet oscillation with the theory for damped harmonic oscillators reveals that the damping coefficient is also size-dependent while the spring constant is not. A simple scaling argument was proposed to understand this finding.

Density and viscosity of liquid ZrO2 measured by aerodynamic levitation technique

Liquid ZrO2 is one of the most important materials involved in severe accident analysis of a light-water reactor. Despite its importance, the physical properties of liquid ZrO2 are scarcely reported. In particular, there are no experimental reports on the viscosity of liquid ZrO2. This is mainly due to the technical difficulties involved in the measurement of thermo-physical properties of liquid ZrO2, which has an extremely high melting point. To address this problem, an aerodynamic levitation technique was used in this study. The density of liquid ZrO2 was calculated from its mass and volume, estimated based on the recorded image of the sample. The viscosity was measured by a droplet oscillation technique. The density and viscosity of liquid ZrO2 at temperatures ranging from 2753 K to 3273 K, and 3170 K–3471 K, respectively, were successfully evaluated. The density of liquid ZrO2 was found to be 4.7 g/cm 3 at its melting point of 2988 K and decreased linearly with increasing temperature, and the viscosity of liquid ZrO2 was 13 mPa at its melting point.

Numerical investigation of vibration-induced droplet shedding on microstructured superhydrophobic surfaces

The vibration-induced droplet shedding mechanism on microstructured superhydrophobic surfaces was simulated using the lattice Boltzmann method. The numerical simulations of natural droplet oscillations for various surface structures show that the natural frequency of the droplet is strongly dependent on surface morphology. The results show good agreement with basic theoretical values. Furthermore, simulations of the motion of the droplet subjected to vertical surface vibration demonstrate that droplets in the Cassie wetting state are easily removed from the surface, whereas for Wenzel state droplets, pinch-off occurs and only partial removal is possible. Microstructure spacing was found to be a key factor in the shedding process. On a surface with small microstructure spacing, the increased surface adhesion leads to a decrease of droplet departure velocity. In contrast, for large roughness spacing, the droplet is impaled on the microstructures, which causes the departure velocity to decrease. Reperforming the simulations under different vibration intensities reveals that as the vibration amplitude is increased, the optimum frequency for droplet removal decreases. The findings of this study shed light on the underlying mechanisms involved in forced vibrations of droplets and can be helpful in engineering applications in which droplet shedding processes are critical.

Numerical study of droplet deformation in shear flow using a conservative level-set method

This paper is concerned with a numerical study on the behavior of a single Newtonian droplet suspended in another Newtonian fluid, all subjected to a simple shear flow. Conservative finite-volume approximation on a collocated three-dimensional grid along with a conservative Level-set method are used to solve the governing equations. Four parameters of capillary number (Ca), Viscosity ratio (λ), Reynolds number (Re) and walls confinement ratio are used to physically define the problem. The main focus of the current study is to investigate the effect of viscosity on walls critical confinement ratio. In this paper, the phrase critical is used to specify a state of governing parameters in which divides the parameter space into the subcritical and supercritical regions where droplets attain a steady shape or breakup, respectively. To do so, first, we validate the ability of proposed method on capturing the physics of droplet deformation including: steady-state subcritical deformation of non-confined droplet, breakup of supercritical conditioned droplet, steady-state deformation of moderate confined droplet, subcritical oscillation of highly-confined droplet, and the effect of viscosity ratio on deformation of the droplet. The extracted results are compared with available experimental, analytical and numerical data from the literature. Afterward, for a constant capillary number of 0.3 and a low Reynolds number of 1.0, subcritical (steady-state) and supercritical (breakup) deformations of the droplet for a wide range of walls confinement in different viscosity ratios are studied. The results indicate the existence of two steady-state regions in a viscosity ratio-walls confinement ratio graph which are separated by a breakup region.

Droplet impact on a layer of solid particles placed above a substrate: A 3D lattice Boltzmann study

A 3D isothermal solid–liquid–air lattice Boltzmann method (LBM) is used to study numerically a droplet impacting on a layer of particles placed on the top of a horizontal substrate. Effects of wettabilities of the particle and the substrate on particles transfer from the substrate to droplet's surface after droplet's impact are simulated. It is shown that hydrophilic particles are more easily to adhere on droplet's surface than hydrophobic particles after droplet impact because of stronger adhesive force. For droplet's subsequent spreading motion, adhering particles which are hydrophilic move in the same direction as liquid flow of the droplet. On the other hand, adhering particles which are hydrophobic move in the direction opposite to liquid flow of the droplet, which hinders droplet's spreading motion. It is found that droplet's maximum spread factors after impacting on hydrophilic particles are larger than those after impacting on hydrophobic particles on the same substrate at low Weber numbers (i.e., We < 10), and differences of maximum spread factors between hydrophilic and hydrophobic particles become negligible at high Weber numbers (i.e., We > 10). It is also found that hydrophilic particles attached on droplet's surface can weaken droplet's oscillation motion, while hydrophobic particles attached to the droplet can enlarge droplet's oscillation motion on a hydrophilic substrate or induce droplet's bouncing motion on a hydrophobic substrate. Maximum spread factors obtained from simulation are shown to match reasonably well with existing experimental data and correlation equations, validating the accuracy of the present numerical model.

A comprehensive SPH model for three-dimensional multiphase interface simulation

Smoothed particle hydrodynamics is a typical Lagrangian meshless method, which has unique advantages in modelling multiphase phenomena with interface deformation and fragmentation. Current study proposes a comprehensive multiphase SPH model, which takes the advantages of some numerical techniques such as numerical interfacial force and damping technique. An improved boundary model is also introduced to deal with the solid walls. Additionally, the multiphase phenomena are investigated by solving an enhanced continuous surface force (CSF) model. In order to verify the proposed model, the droplet in shear flow is firstly considered and the results are consistent with the analytical solutions. Furthermore, the oscillations of square droplets are simulated under different particle resolutions, density and viscosity ratios. Finally, two and three dimensional bubble rising at high density ratios (up to 1000) are tested.

Surface treatment technique of MPS method for free surface flows

A surface treatment technique is developed for moving particle semi-implicit (MPS) method in the simulation of incompressible free surface flows. The free surface particles are accurately detected by a developed geometrical method. Material interface is reconstructed at the interface of the fluid. According to the definition of level set function, the level set value of each particle is set to be the signed distance to the interface. The normal vector and curvature of interface are calculated at the position of interface via level set function, which help to obtain the accurate calculation of surface tension. The smoothness of level set function improves the computational accuracy of the interface curvature. The computational curvature has high convergence in current method. For example, the computational curvature of a circle has 1.75-order convergence. Benchmark tests including square droplet oscillation, head-on and off-center binary collision illustrate the advantages of current method. The developed method has higher accuracy and stability in the simulation of low speed incompressible free surface flows.

Shape oscillations of a nonspherical water droplet.

The dynamics of a nonspherical droplet falling in air is investigated via three-dimensional numerical simulations of the Navier-Stokes and continuity equations. The main focus of this work is to study the effects of the relative influence of surface tension force over the inertial force and the orientation of the droplet. The values of the dimensionless parameters considered in this study are similar to those of a typical falling raindrop. Our results obtained from the numerical simulations for low values of Galilei number agree well with the theoretical predictions in the microgravity condition and in the limit of creeping flow. However, in the inertia-dominated region and for high initial aspect ratio, the droplet undergoes predominant nonlinear oscillations and subsequently breaks up. To the best of our knowledge, none of the previous studies have investigated dynamics of a tilted drop and observed the behavior reported in the present study.

An Alternative High-Density Ratio Pseudo-potential Lattice Boltzmann Model with Surface Tension Adjustment Capability

In this paper, an alternative model is presented to simultaneously achieve thermodynamic consistency, leading to high-density ratios, and surface tension adjustment capability based on the pseudo-potential lattice Boltzmann model (LBM). These features are achieved by adding two relatively simple terms, each with an adjustable coefficient, selected from the Taylor expansion of the original interaction force, one for achieving and maintaining thermodynamic consistency, and the other for adjusting the surface tension independent of the density ratio. The model also takes advantage of being independent of using SRT, MRT, 2D or 3D lattice models. The capability of the model is evaluated and verified by performing several static and dynamic benchmark test cases. First, the coexistence densities extracted for a flat interface from the model are compared with those of the Maxwell equal area rule in a wide temperature range. Results show that the thermodynamic consistency is well achieved and the coexistence densities are independent of the surface tension strength as well. Next, the well-known Laplace law for a droplet is evaluated and satisfied with the model. In addition, a wide range of surface tension values is achievable at a fixed temperature by adjusting the surface tension adjustment coefficient. After that, the ellipsoidal droplet oscillation is simulated with a good agreement between the analytical and numerical results for the oscillation period. The spurious velocities around the droplet are then evaluated and shown to be reasonable, and comparatively low even at a relatively high-density ratio around of 2400. It was found that the magnitude of these velocities can be further reduced, especially at high-density ratios, by reducing the liquid to gas dynamic viscosity ratio or equivalently increasing the gas to liquid kinematic viscosity ratio. Next, the stability, and the fascinating phenomenon of symmetric bifurcation of a rotating planar droplet are simulated and formation of two- and four-lobed shapes along with rigid rotation is presented depending on the value of the surface tension. Finally, the droplet impact on a liquid film is simulated at a relatively high-density ratio around of 720, and Reynolds number of 1440. However, the upper limit of physical parameters for simulating this phenomenon is found to be a density ratio of 720 and Re and We numbers of 6600 and 275, respectively. Effects of the surface tension strength are shown as well. The crown spread radius from the model agrees well with the analytical solution reported in the literature.

A new model for the bouncing regime boundary in binary droplet collisions

This work experimentally investigates binary collisions of identical droplets over a range of liquid viscosities, using 2%, 4%, and 8% of hydroxypropyl methylcellulose solutions in water. The collisions were captured by using a high-speed camera, and regime maps of collision outcomes were derived. The performance of existing models of the boundary of the bouncing regime was assessed and found to give poor predictions. This was attributed to assumptions and errors in the treatment of kinetic energy and the droplet shape factors used in these models. A new model was derived which addresses these issues: the definition of the kinetic energy that contributes to deformation was corrected; a new shape factor that accurately reflects the geometry of the droplet at maximum deformation was proposed, and, importantly, an empirical approach was implemented to account for the effect of the impact parameter on this shape factor. Moreover, the model includes an estimate of the viscous dissipation, which is calculated directly from the experimentally observed difference between the impact and the rebound kinetic energies and measurements of the post-collision droplet oscillations. The proposed model shows a striking improvement versus the existing models, reducing the mean absolute error by an order of magnitude.

Coupling light and sound: giant nonlinearities from oscillating bubbles and droplets

Abstract Nonlinear optical processes are vital for fields including telecommunications, signal processing, data storage, spectroscopy, sensing and imaging. As an independent research area, nonlinear optics began with the invention of the laser, because practical sources of intense light needed to generate optical nonlinearities were not previously available. However, the high power requirements of many nonlinear optical systems limit their use, especially in portable or medical applications, and so there is a push to develop new materials and resonant structures capable of producing nonlinear optical phenomena with low-power light emitted by inexpensive and compact sources. Acoustic nonlinearities, especially giant acoustic nonlinear phenomena in gas bubbles and liquid droplets, are much stronger than their optical counterparts. Here, we suggest employing acoustic nonlinearities to generate new optical frequencies, thereby effectively reproducing nonlinear optical processes without the need for laser light. We critically survey the current literature dedicated to the interaction of light with nonlinear acoustic waves and highly nonlinear oscillations of gas bubbles and liquid droplets. We show that the conversion of acoustic nonlinearities into optical signals is possible with low-cost incoherent light sources such as light-emitting diodes, which would usher new classes of low-power photonic devices that are more affordable for remote communities and developing nations, or where there are demanding requirements on size, weight and power.

Al-assisted high frequency self-powered oscillations of liquid metal droplets.

It is of great scientific and practical significance to explore and imitate the rhythmic oscillating behaviors. Achieving oscillating behaviours via liquid metal is regarded as an excellent strategy and the "mercury beating heart" is a well-known representative. However, the oscillating behaviours achieved over the past few decades either require external power supply or exhibit low frequency. Here, intriguing Al-assisted high frequency self-powered oscillations of liquid metal droplets were discovered and the general mechanisms were interpreted. For this dynamic process, Al is added into the liquid metal for generating gas and activating liquid metal by forming countless tiny galvanic cells and an iron plate is used to passivate the liquid metal via electrochemical oxidation. Therefore, the high frequency self-fueled oscillations can be achieved due to the synergistic effect of these two factors. Furthermore, we predict and confirm that the oscillating behaviors can also be achieved on other eligible substrates (e.g., Ni plate) based on the proposed universal mechanism. The ability to achieve high frequency oscillations of liquid metal droplets promises rich opportunities in developing self-powered soft oscillators.

Квадрупольное излучение незаряженной капли, осциллирующей в однородном электростатическом поле

AbstractCapillary oscillations of an uncharged spheroid droplet of nonviscous conducting uncompressible liquid in the presence of uniform electric field are analyzed in the first order of smallness with respect to the ratio of the oscillation amplitude to a linear size of the droplet and in the second order of smallness with respect to the squared ratio of the linear size to the radiation wavelength. It is shown that the electric quadrupole moment of the droplet is time-dependent due to surface oscillations, which lead to the emission of quadrupole electromagnetic waves. A mathematical model of the quadrupole electromagnetic radiation of an uncharged droplet that oscillates in the presence of electrostatic field is constructed, and the radiation intensity and frequency are estimated.

Динамика зажатой капли в неоднородном электрическом поле

The forced oscillations of an incompressible liquid drop under the influence of an alternating electric field are considered. The drop is sandwiched between two homogeneous plates and surrounded by an incompressible fluid of a different density. In equilibrium, the drop has the shape of a circular cylinder which is bounded axially by parallel solid plates. These plates have different surface properties. An external electric field acts as an external force which is a reason of the motion of the contact line. A modified Hocking boundary condition is used to describe the motion of the contact line: the velocity of the contact line is proportional to the deviation of the contact angle and the rate of fast relaxation processes, the frequency of which is proportional to the doubled frequency of the electric field. Using this equation allows one to qualitatively describe the experimental dependence of the contact angle as a function of stress, in contrast to the Young – Lippmann equation. The solution to the problem is presented as a Fourier series expansion in eigen functions of the Laplace operator. Graphs of the amplitude-frequency characteristics and evolution of the drop shape are constructed for various values of the problem parameters. In the case of identical surfaces, only odd modes of droplet oscillations are excited, while for different surfaces, even harmonics additionally appear. It was found that in a wide range of parameters the shape of the side surface of the drop is close to the description by an odd function. The oscillation amplitude of even modes is significant only near resonances at the frequencies of these modes. In the case of an inhomogeneous field, azimuthal oscillations are excited, which leads to the appearance of additional resonance peaks. Travel waves propagate along the lateral surface of the drop, which are caused by vibrations of the contact line and the contact angle. The dependences of the values of the contact angle on the upper and lower surfaces on the square root of the amplitude for different values of the frequency of the electric field, which qualitatively coincide with similar graphs of experimental data, are constructed. It is possible to determine the parameters of the Hocking.