Instability Of Capillary Waves Research Articles

Acoustic resonance effects and cavitation in SAW aerosol generation

The interaction of surface acoustic waves (SAWs) with liquids enables the production of aerosols with adjustable droplet sizes in the micrometer range expelled from a very compact source. Understanding the nonlinear acousto-hydrodynamics of SAWs with a regulated micro-scale liquid film is essential for acousto-microfluidics platforms, particularly aerosol generators. In this study, we demonstrate the presence of micro-cavitation in a MHz-frequency SAW aerosol generation platform, which is touted as a leap in aerosol technology with versatile application fields including biomolecule inhalation therapy, micro-chromatography and spectroscopy, olfactory displays, and material deposition. Using analysis methods with high temporal and spatial resolution, we demonstrate that SAWs stabilize spatially arranged liquid micro-domes atop the generator's surface. Our experiments show that these liquid domes become acoustic resonators with highly fluctuating pressure amplitudes that can even nucleate cavitation bubbles, as supported by analytical modeling. The observed fragmentation of liquid domes indicates the participation of three droplet generation mechanisms, including cavitation and capillary-wave instabilities. During aerosol generation, the cavitation bubbles contribute to the ejection of droplets from the liquid domes and also explain observed microstructural damage patterns on the chip surface eventually caused by cavitation-based erosion.

On Increments of Instability of Capillary Waves on the Surface of a Charged Electrically Conductive Jet Moving Relative to the Medium

For the first azimuthal modes of a charged jet of an electrically conductive incompressible liquid, the increments of the instability of capillary waves, their magnitude and dependence on the physical parameters of the task, the position of the instability zones on the set of wave numbers were investigated. In the conducted studies, it was found that the widths of the ranges of wave numbers of un-stable waves and the values of instability increments depend on the square of the intensity of an electrostatic field and the square of the speed of relative motion, increasing at a higher field strength and speed. In the absence of a charge on the jet, bending instability has a threshold character, and it is realized not at any low speed value but starting from some final value of it.

An approximated volume of fluid method with the modified height function method in the simulation of surface tension driven flows

Surface tension in two-phase flow problems plays a dominant role in many micro-flow phenomena and has an important influence on the development of flow instability phenomena that contain free surfaces. In this study, the multi-moment finite volume method is extended for direct numerical simulation of two-phase flow problems. A constraint interpolation profile–CSL (semi-Lagrangian) scheme is used for discretization of the advection part in the momentum equation. A compact volume of fluid method–approximated piecewise linear calculation method without flux limiter is proposed for capturing the moving interface. For modeling the surface tension accurately, the logic in curvature estimation is redesigned based on the height function (HF) method. The isolated volumetric fractions that may reduce accuracy in HF integration are excluded, and the numerical solution shows that the accuracy in the curvature estimation is improved for a coarse mesh. The present method is implemented with a parallel block-structured adaptive mesh refinement (BAMR) strategy; thus, the computational cost can be reduced significantly. Numerical tests show that the present BAMR solver is capable of reproducing the theoretical predictions of capillary wave instability problems with high accuracy. The simulation of droplet collisions further demonstrates the accuracy of the surface tension model. Finally, we extend it to the liquid jet atomization. The wavy disturbance, film breakup, liquid filament pinch-off, and droplet generation are well reproduced. The droplet size distribution satisfies the experimental measurement and theoretical predictions power-law. BAMR shows a huge advantage in computational efficiency than the traditional Cartesian grid. The findings of this study can help for a better understanding of the micro-mechanism of surface tension driven flows.

Simulation of binary droplet collision with different angles based on a pseudopotential multiple-relaxation-time lattice Boltzmann model

Understanding the physics of droplet collisions is of crucial importance in many industrial processes such as inkjet printing, spray cooling, and spray combustion. In this paper, a modified multiple-relaxation-time pseudopotential multiphase lattice Boltzmann model is proposed to investigate binary droplet collision with different collision angles. The surface tension can be adjusted independently under the condition of high Reynolds number and large density ratio using this model. Then the model validation is performed by simulating three benchmark cases including stationary droplet, oscillating droplet, and capillary wave instability, respectively. Finally, different regimes of binary droplet collision are presented, and collision features such as liquid filament and satellite droplet are investigated at collision angles of 30°, 60°, 90°, 120°, and 150°. The results show that there is no liquid filament or satellite droplet at the collision angle of 30°, yet both of them appear as the angle increases. When the collision angle is 60°, the percentage of satellite droplet to liquid phase reaches 30%, while the proportions are less than 10% at collision angles of 90°, 120°, and 150°. Besides, two break-up mechanisms of “end-pinching” and capillary wave instability are inspected. It is found out that the back-flow phenomena at the joints of droplets and the liquid filament are caused by the “end-pinching” mechanism, which further leads to the capillary wave instability of the liquid filament.

A study of two unequal-sized droplets undergoing oblique collision

The oblique collision of two unequal-sized liquid droplets in a gaseous environment is investigated numerically. It is found that the asymmetry in the flow field arising due to unequal-sized droplets and oblique collision greatly alters the collision outcomes observed in the case of the head-on collision of identical droplets. Our results reveal that permanent coalescence occurs at intermediate collision angles, but head-on and large-angle collisions result in reflexive separation and stretching separation, respectively. Moreover, we found that the end-pinching mechanism is operational in the case of head-on collision, and the capillary wave instability is responsible for the ligament breakup for large collision angles. It is also observed that the droplets coalesce permanently for low velocity ratios and high radius ratios, but for high velocity ratios and low radius ratios, the droplets coalesce temporarily and then split again. By conducting a large number of numerical simulations, the collision outcomes and the boundary separating them are plotted on Rr−We and θ−We planes, where We, Rr, and θ represent the Weber number, radius ratio of droplets, and collision angle, respectively.

Numerical simulation of the collision behaviors of binary unequal-sized droplets at high Weber number

In the spray combustion process, the distribution of droplet size and velocity will affect the atomization performance of the fuel and the combustion effect. Compared with binary equal-sized droplet collisions, binary unequal-sized droplet collisions are more in line with the actual situation. In this paper, a numerical investigation of binary unequal-sized droplet collision has been performed under different high Weber numbers (from 210 to 810) and impact parameters (B ≈ 0.3–0.9) by a coupled level-set and volume of fluid method with adaptive mesh refinement technology. Unlike the coalescence and separation phenomena at low and medium Weber numbers, at high Weber numbers, due to the difference in velocity between large and small droplets, the rim expands radially outward in different ways and further breaks up. The splashing behavior of the droplets can also be observed. As the Weber number increases, the breakup moment of the droplets advances and the maximum radial deformation diameter increases first (We = 210–360) and then decreases (We = 360–810). By changing the impact parameters, it can be found that binary off-center collisions are associated with rotational motion. At larger impact parameters, the features of the capillary wave instability can be observed on the surface of the ligament.

Об инкрементах неустойчивости волн различной симметрии на движущейся относительно материальной среды объемно заряженной струе

The increments of instability of capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers ) on the surface of a volume charged cylindrical jet of an ideal incompressible dielectric fluid moving relative to an ideal incompressible material dielectric medium are investigated. It is shown that at not too high velocities of the jet motion, with an increase in the volume charge density, the axisymmetric mode ( m=0) becomes unstable first, then the bending mode ( m=1), and then the bending-deformation mode (m=2 ).This sequence of realization of the instability of azimuthal modes and determines the patterns of fragmentation of charged jets in the experiments. At jet speeds comparable to the critical for the realization of aerodynamic instability, the first loses stability mode whis . For all azimuthal modes, the dependences of the maximum increments on the wave numbers are determined.

A nonlinear Schrödinger equation for gravity–capillary water waves on arbitrary depth with constant vorticity. Part 1

A nonlinear Schrödinger equation for the envelope of two-dimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of vorticity. The vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive vorticity and amplified in the presence of negative vorticity; (ii) in finite depth, it is reduced when the vorticity is positive and amplified and finally reduced when the vorticity is negative. The combined effect of vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative vorticity and attenuated by positive vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the vorticity.

Simulation of binary droplet collisions with the entropic lattice Boltzmann method

The recently introduced entropic lattice Boltzmann method (ELBM) for multiphase flows is extended here to simulation of droplet collisions. Thermodynamically consistent, non-linearly stable ELBM together with a novel polynomial equation of state is proposed for simulation large Weber and Reynolds number collisions of two droplets. Extensive numerical investigations show that ELBM is capable of accurately capturing the dynamics and complexity of droplet collision. Different types of the collision outcomes such as coalescence, reflexive separation, and stretching separation are identified. Partition of the parameter plane is compared to the experiments and excellent agreement is observed. Moreover, the evolution of the shape of a stable lamella film is quantitatively compared with experimental results. The end pinching and the capillary-wave instability are shown to be the main mechanisms behind formation of satellite droplets for near head-on and off-center collisions with high impact parameter, respectively. It is shown that the number of satellite drops increases with increasing Weber number, as predicted by experiments. Also, it is demonstrated that the rotational motion due to angular momentum and elongation of the merged droplet play essential roles in formation of satellite droplets in off-center collisions with an intermediate impact parameter.

Interaction dynamics of a spherical particle with a suspended liquid film

Hydrodynamics of collision interactions between a particle and gas‐liquid interface such as droplet/film is of keen interest in many engineering applications. The collision interaction between a suspended liquid (water) film of thickness 3.41 ± 0.04 mm and an impacting hydrophilic particle (glass ballotini) of different diameters (1.1–3.0 mm) in low particle impact Weber number ( ) range (1.4–33) is reported. Two distinct outcomes were observed—particle retention in the film at lower Weber number and complete penetration of the film toward higher Weber number cases. A collision parameter was defined based on energy balance approach to demarcate these two interaction regimes which agreed reasonably well with the experimental outcomes. It was shown that the liquid ligament forming in the complete penetration cases breaks up purely by “dripping/end pinch‐off” mechanism and not due to capillary wave instability. An analytical model based on energy balance approach was proposed to determine the liquid mass entrainment associated with the ligament which compared well with the experimental measurements. A good correlation between the %film mass entrained and the particle Bond number ( ) was obtained which indicated a dependency of Bo1.72. Computationally, a three‐dimensional CFD model was developed to simulate these interactions using different contact angle boundary conditions which in general showed reasonable agreement with experiment but also indicated deficiency of a constant contact angle value to depict the interaction physics in entirety. The computed force profiles from computational fluid dynamics (CFD) model suggest dominance of the pressure force over the viscous force almost by an order of magnitude in all the Weber number cases studied. © 2015 American Institute of Chemical Engineers AIChE J, 62: 295–314, 2016

The role of bubbles in the atomization of liquids and tissues

Ultrasonic atomization, or the emission of droplets from a liquid exposed to air, has been studied for many decades. The most accepted theory of atomization, the cavitation-wave hypothesis, states that droplets are emitted by a combination of capillary wave instabilities and cavitation bubble collapses. Recently, it was shown that tissues could also be atomized and that the result of atomization was surface erosion. Using a high static pressure chamber, we investigated the role of bubbles in the atomization of tissues and liquids. A 2-MHz, aluminum-lensed transducer was focused at the surface of either water or ex vivo bovine liver. In water at 1200 W/cm2 (p + = 6.8 MPa, p- = 5.3 MPa), we found that atomization ceased at an overpressure of 6.9 MPa, yet droplets were again released when the static pressure was increased to 13.8 MPa. In tissue at a linear in situ intensity of 22 000 W/cm2 (p + = 67 MPa, p- = 16 MPa), we found that a small increase in the static pressure (1.4 MPa) produced a qualitative change in atomization and caused thermal denaturation of the fractionated tissue rather than ejection from the surface. [Work supported by NIH EB007643, NIH DK043881, and NSBRI through NASA NCC 9-58.]

Motion of a drop along the centreline of a capillary in a pressure-driven flow

The deformation of a drop as it flows along the axis of a circular capillary in low Reynolds number pressure-driven flow is investigated numerically by means of boundary integral computations. If gravity effects are negligible, the drop motion is determined by three independent parameters: the size a of the undeformed drop relative to the radius R of the capillary, the viscosity ratio λ between the drop phase and the wetting phase and the capillary number Ca, which measures the relative importance of viscous and capillary forces. We investigate the drop behaviour in the parameter space (a/R, λ, Ca), at capillary numbers higher than those considered previously. If the fluid flow rate is maintained, the presence of the drop causes a change in the pressure difference between the ends of the capillary, and this too is investigated. Estimates for the drop deformation at high capillary number are based on a simple model for annular flow and, in most cases, agree well with full numerical results if λ ≥ 1/2, in which case the drop elongation increases without limit as Ca increases. If λ < 1/2, the drop elongates towards a limiting non-zero cylindrical radius. Low-viscosity drops (λ < 1) break up owing to a re-entrant jet at the rear, whereas a travelling capillary wave instability eventually develops on more viscous drops (λ > 1). A companion paper (Lac & Sherwood, J. Fluid Mech., doi:10.1017/S002211200999156X) uses these results in order to predict the change in electrical streaming potential caused by the presence of the drop when the capillary wall is charged.

Phase Randomization of Three-Wave Interactions in Capillary Waves

We present new experimental results on the transition from coherent-phase to random-phase three-wave interactions in capillary waves under parametric excitation. Above the excitation threshold, coherent wave harmonics spectrally broaden. An increase in the pumping amplitude increases spectral widths of wave harmonics and eventually causes a strong decrease in the degree of the three-wave phase coupling. The results point to the modulation instability of capillary waves, which leads to breaking of continuous waves into ensembles of short-lived wavelets or envelope solitons, as the reason for the phase randomization of three-wave interactions.

A new predictive model for fragmenting and non-fragmenting binary droplet collisions

A new predictive model for collisional interactions between liquid droplets, which is valid for moderate to high Weber numbers (>40), has been developed and validated. Four possible collision outcomes, viz., bouncing, coalescence, reflexive separation and stretching separation, are considered. Fragmentations in stretching and reflexive separations are modeled by assuming that the interacting droplets form an elongating ligament that either breaks up by capillary wave instability, or retracts to form a single satellite droplet. The outcome of a collision, number of satellites formed from separation processes and the post-collision characteristics such as velocity and drop-size are compared with available experimental data. The comparisons include colliding mono- and poly-disperse streams of droplets of different fuels under atmospheric conditions, and the results agree reasonably well.

On the mechanism of ion evaporation from solutions with the help of strong electric field

Mechanism of ion evaporation from solutions with help of strong electric field has been studied in detail. The mechanism includes the following steps: (1) the crests of capillary waves at a surface of liquid are drawn in liquid needles (Tonks–Frenkel’s instability), (2) strong local electric fields are originated at the tips of these needles, which are centers of evaporation of ions from solutions, (3) the potential barrier at the tips of these needles is lowered essentially because of Shottky’s effect, which leads to the essential increase of the probability of ion evaporation from solutions. The dispersion equation connecting the increment of instability of capillary waves with the physical parameters of liquid and with the strength of electric field was used to describe the suggested mechanism. The satisfactory explanation of the available experimental data indicates a sufficient correctness of this mechanism.

Numerical simulation of binary liquid droplet collision

A numerical investigation of binary droplet collision has been conducted. The complete process of the collision of two liquid droplets is dynamically simulated by solving the incompressible Navier-Stokes equations coupled with the convective equation of the level set function that captures the interface between the liquid and the gas phases. The simulations cover four major regimes of binary collision: bouncing, coalescence, reflexive separation, and stretching separation. For water droplets in air, the numerical results are compared with the experiments by and Ashgriz and Poo [J. Fluid Mech. 221, 183 (1990)] on collision consequences. For hydrocarbon (C14H30) droplets in nitrogen gas, the simulated results are compared in detail with the time-resolved photographic images of the collision processes obtained by Qian and Law [J. Fluid Mech. 331, 59 (1997)] in every collision regime. The present numerical results suggest that the mechanism of a bouncing collision is governed by the macroscopic dynamics. However, the fact that the present macroscopic numerical model is unable to capture the collision regime of coalescence after minor deformation supports the speculation that its mechanism is related to the microscopic dynamics. Furthermore, the transition from bouncing to coalescence collisions has been predicted and agrees well with the analytical model. The mechanism of satellite droplet formation for head-on collision and stretching separation collision is also studied based on the detailed time-resolved dynamic simulation results. It is then confirmed that end pinching is the main cause of satellite formation in head-on collisions whereas the capillary-wave instability becomes dominant in large impact parameter cases. In the case of an intermediate impact parameter, the effects of twisting and stretching due to the angular momentum and the inertia of the colliding droplets are significant for the satellite formation.

Flow focusing in microchannels

A volume-of-fluid numerical method is used to predict the dynamics of drop formation in an axi-symmetric microfluidic flow-focusing geometry for a liquid-liquid system. The Reynolds numbers and Weber numbers approximate those of a three-dimensional flow in recently published experiments. We compare the predicted drop formation with the experimental results at various flow rates, and discuss the mechanisms of drop formation in this context. Despite the differences in geometry, we find qualitative correspondence between the numerical and experimental results. Both end-pinching and capillary-wave instability are important for droplet break-up at the higher flow rates.

Spinodal Dewetting of Thin Polymer Films

Dewetting of polystyrene films on a silicon substrate is investigated as a function of film thickness $h$. We observe the nucleation of holes in the early stage of dewetting for relatively thick films $(h>100\AA{})$, as observed previously, but the breakup of thinner films occurs through the growth of uniformly distributed surface undulations (``spinodal dewetting''). The average amplitude $\ensuremath{\delta}h$ of these undulations increases exponentially up to the film rupture point where $\ensuremath{\delta}h$ becomes comparable to $h$, as predicted by a capillary wave instability model.

Mechanisms of melt droplets and solid-particle ejection from a target surface by pulsed laser action

We suggest an explanation of the effect of melt droplets and solid particle ejection from a target surface under the impact of laser radiation with intensity 108–1010 W/cm2. We consider the capillary wave instabilities on the evaporating surface of melt, which lead to growth of large-scale surface structures and ejection of macroparticles. The instability increments and characteristic droplet sizes are determined. Conditions are found for droplet-free evaporation in terms of the dynamic pressure of evaporated matter.

Influence of Disjoining Pressure upon Stability in the Electric Field of a Charged Liquid Film on the Surface of a Hard Core

This work deals with finding the critical condition of capillary wave instability development in a thin charged liquid film on the surface of a hard core in an external electric field, taking into account the disjoining pressure. It is shown that the critical values of the Rayleigh and Taylor parameters for instability development increase sharply with decreasing thickness of a liquid film. This testifies to the stabilizing influence of the disjoining pressure. The influence of viscous dissipation of capillary wave energy on the critical condition for their instability development is evaluated. The analytical expression is obtained which connects the critical values of the system charge and of the external electric field intensity for instability development with those of the thickness of a liquid film and dimensions of a hard core, as well as with those of the coefficients of surface tension and the kinematic viscosity of liquid.