Amplitude Of Capillary Waves Research Articles

A model of thermodynamic stabilization of nanocrystalline grain boundaries in alloy systems

Nanocrystalline (NC) materials are intrinsically unstable against grain growth. Significant research efforts have been dedicated to suppressing the grain growth by solute segregation, including the pursuit of a special NC structure that minimizes the total free energy and completely eliminates the driving force for grain growth. This fully stabilized state has been predicted theoretically and by simulations but is yet to be confirmed experimentally. To better understand the nature of the full stabilization, we propose a simple two-dimensional model capturing the coupled processes of grain boundary (GB) migration and solute diffusion. Kinetic Monte Carlo simulations based on this model reproduce the fully stabilized polycrystalline state and link it to the condition of zero GB free energy. The simulations demonstrate the emergence of a fully stabilized state by the divergence of capillary wave amplitudes on planar GBs and by fragmentation of a large grain into a stable ensemble of smaller grains. The role of solute diffusion in the full stabilization is examined. Possible extensions of the model are discussed.

Instability and breakup of rayleigh-plateau jets with capillary wave induced by electrowetting-on-dielectric

This paper discusses the lateral disturbances of vertical liquid flow enhancement using electrowetting-on-dielectric (EWOD) technique, which effectively reducing the breakup length of the liquid flow and minimizing the formation of satellite droplets. The EWOD technology is characterized by its minimal space occupation and low energy consumption. The successful implementation of the EWOD phenomenon relies on the formation of a three-phase contact line (TPCL) between the electrodes and the liquid, and the novel EWOD tube structure design provides an extended TPCL, enhancing the amplitude of capillary waves. Through experimental and theoretical analysis, this paper identifies key parameters affecting the liquid breakup process, such as the gap depth, angle of the EWOD tube, EWOD voltage amplitude, and frequency of the AC electrical signal. The research results indicate that the proposed EWOD tube responds rapidly and can consistently and stably manage liquid breakup and reduce the number of satellite droplets.

Effect of Surface Tension Relaxation on the Stability of the Charged Jet

In the asymptotic calculations of the first order of smallness by the dimensionless amplitude of capillary waves on the surface of charged jets of polar liquid, the effect of the relaxation effect of surface tension on the regularities of their implementation is investigated. Calculations are carried out on the model of an ideal non-compressible electrically conductive fluid. It has been shown that taking into account the effect of dynamic surface tension leads to an increase in the order of the dispersion equation, which has another damping root, which is obliged to destroy the near-surface double electric layer (destruction of the ordering of polar molecules in the near-surface layer), which undergoes electrostatic instability at sufficiently large charges (pre-breakdown in the sense of ignition of corona discharge in air). In the ideal fluid mathematical model used, the relaxation motion of the jet surface disturbances that occurs when the surface tension relaxation effect is turned on and the attenuation decrements of capillary wave motions are purely of a relaxation nature.

Measurement of capillary waves with a laser wave recorder

Objectives. Capillary waves on the sea surface play an important role in remote sensing, both in the optical and microwave wavelength ranges. However, processes of electromagnetic radiation scattering on a rough sea surface cannot be studied in the absence of reliable monitoring of the parameters of these capillary waves under natural conditions. Therefore, the aim of the present work was to develop methods for such monitoring purposes and test them under laboratory and field conditions.Methods. Novel laser-based methods for recording capillary waves at frequencies up to 100 Hz were developed in the laboratory. The proposed remote methods, which do not interfere with the sea surface, are based on the recording of scattered laser radiation using a video camera.Results. Under laboratory conditions, spatial profiles, time dependences of heights for all points of a laser sweep trajectory, and frequency power spectra were obtained. It is shown that slopes in capillary waves can reach 30° and that the amplitude of capillary waves at frequencies above 25 Hz does not exceed 0.5 mm. A new version of a scanning laser wave recorder was tested under natural conditions on an offshore platform. The measurements confirmed the possibility of measuring the parameters of sea waves on spatial scales covering 3 orders of magnitude: from units of millimeters to units of meters.Conclusions. The developed wave recorder can be used to carry out direct measurements of “instantaneous” sea surface profiles with a time synchronization precision of 10-4 s and a spatial accuracy of better than 0.5 mm. The method makes it possible to obtain large series (21000) of «instantaneous» wave profiles with a refresh rate of 60 Hz, which opens up opportunities for studying the physics of wave evolution and the influence of wave parameters on the scattering of electromagnetic waves. The advantage of the method is the direct nature of the measurement of applicates and other wave characteristics not only in time but also in space. The entirely remote method does not distort the properties of the surface and is not affected by wind, waves, or sea currents. The possibility of using the proposed method under natural conditions at any time of the day and in a wide range of weather conditions has been experimentally ascertained.

Morpho-dynamic evolution due to inertia-mediated impact of a compound drop on a deep liquid pool

A compound drop impacting on a liquid pool exhibits intriguing coalescence patterns that are primarily attributable to the complicated interplay of inertia with other physical parameters such as radius ratio of core to shell drop and density and viscosity contrasts of the two fluids. By executing comprehensive numerical investigations, here, we identify three different regimes based on the radius ratio of compound drop, viz., secondary drop pinch-off without bubble bursting, secondary drop pinch-off after bubble bursting, and compound breakage. Our findings also depict a transition in the shape of a secondary droplet from prolate to oblate or vice versa, a phenomenon non-trivially culminated by secondary drop pinch-off timing, neck radius, and amplitude and wavelength of capillary wave propagation. Our results bring out the fact that higher wavelength and amplitude of capillary waves are responsible for secondary drop pinch-off without bubble bursting. Furthermore, in the case of highly viscous core drop and surrounding fluid, we observe both complete and partial coalescence phenomena, which are critically dictated by the confluence of inertia and radius ratio of a compound drop leading to three different regimes, viz., complete coalescence without bubble bursting, complete coalescence with bubble bursting, and partial coalescence with bubble bursting, distinctively different from the observations for single droplet based investigations reported in earlier studies. These implications are likely to be beneficial in illustrating the physical functionalities accompanying the targeted release of encapsulated biological or pathological entities when they are transmitted under the action of an inertial force into another fluidic medium, a paradigm that has hitherto remained unexplored.

Toward Unveiling the Anomalies Associated with the Spontaneous Spreading of Droplets.

The liquid droplet spreads over a solid surface to minimize the surface energy when brought in direct contact with the surface. The spreading process is rapid in the early stages, tends to slow down during its progress, and has resulted in peculiarity due to the experimental difficulties in the accurate determination of the contact line radius. In the present numerical study, we found that drop spreading begins with a viscosity-dominated Stokes regime, where contact radius scales as r ∼ t for a wide range of drop liquid viscosities. Subsequent to the Stokes regime, the inertial regime is observed where contact radius scales as r ∼ t0.5 for low- to medium-viscous droplets, whereas for very high viscous drops, the spreading dynamics is completely dominated by the viscous regime. It is also found that the equilibrium wetting condition does not affect the power-law scaling for the contact radius of the drop. The amplitude of capillary waves induced across the interface of the drop is observed to be sufficiently high to cause necking and ejection of satellite drops from the main drop during its spreading for low-viscous liquids from complete wetting to partial wetting conditions. A regime plot between the Ohnesorge number and advancing contact angle of the substrate is presented to demarcate the regions of damped waves without pinch-off and drop spreading with satellite drops.

Asymmetric coalescence of two droplets with different surface tensions is caused by capillary waves

When two droplets with different surface tensions collide, the shape evolution of the merging droplets is asymmetric. Using experimental and numerical techniques, we reveal that this asymmetry is caused by asymmetric capillary waves, which are the result of the different surface tensions of the droplets. We show that the asymmetry is enhanced by increasing the surface tension difference, and suppressed by increasing the inertia of the colliding droplets. Furthermore, we study capillary waves in the limit of no inertia. We reveal that the asymmetry is not directly caused by Marangoni forces. In fact, somehow counterintuitive, asymmetry is strongly reduced by the Marangoni effect. Rather, the different intrinsic capillary wave amplitudes and velocities associated with the different surface tensions of the droplets lie at the origin of the asymmetry during droplet coalescence.

Dynamics of droplets under electrowetting effect with voltages exceeding the contact angle saturation threshold

Electrowetting on dielectric (EWOD) is a powerful tool in many droplet-manipulation applications with a notorious weakness caused by contact-angle saturation (CAS), a phenomenon limiting the equilibrium contact angle of an EWOD-actuated droplet at high applied voltage. In this paper, we study the spreading behaviours of droplets on EWOD substrates with the range of applied voltage exceeding the saturation limit. We experimentally find that at the initial stage of spreading, the driving force at the contact line still follows the Young–Lippmann law even if the applied voltage is higher than the CAS voltage. We then theoretically establish the relation between the initial contact-line velocity and the applied voltage using the force balance at the contact line. We also find that the amplitude of capillary waves on the droplet surface generated by the contact line's initial motion increases with the applied voltage. We provide a working framework utilising EWOD with voltages beyond CAS by characterising the capillary waves formed on the droplet surface and their self-similar behaviours. We finally propose a theoretical model of the wave profiles taking into account the viscous effects and verify this model experimentally. Our results provide avenues to utilise the EWOD effect with voltages beyond the CAS threshold, and have strong bearing on emerging applications such as digital microfluidic and ink-jet printing.

Capillary fluctuations of surface steps: An atomistic simulation study for the model Cu(111) system.

Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number (k) dependence of the mean squared capillary-wave amplitudes and associated relaxation times, is calculated for 〈110〉 and 〈112〉 steps on the {111} surface of elemental copper near the melting temperature of the classical potential model considered. Step stiffnesses are derived from the MD results, yielding values from the largest system sizes of (37±1)meV/A[over ˚] for the different line orientations, implying that the stiffness is isotropic within the statistical precision of the calculations. The fluctuation lifetimes are found to vary by approximately four orders of magnitude over the range of wave numbers investigated, displaying a k dependence consistent with kinetics governed by step-edge mediated diffusion. The values for step stiffness derived from these simulations are compared to step free energies for the same system and temperature obtained in a recent MD-based thermodynamic-integration (TI) study [Freitas, Frolov, and Asta, Phys. Rev. B 95, 155444 (2017)2469-995010.1103/PhysRevB.95.155444]. Results from the capillary-fluctuation analysis and TI calculations yield statistically significant differences that are discussed within the framework of statistical-mechanical theories for configurational contributions to step free energies.

Parallel Stability Analysis of Membrane Lamellar Structures and Foam Films

Fluctuating Hydrodynamics of TLF Abstract: Within the framework of the DLVO theory the root-mean-square amplitude of capillary waves in a thin liquid film is calculated and its dependence on some important physical parameters is unveiled. Two important models are considered: films with classical interfaces and films between lipid bilayers. The performed numerical analysis demonstrates essential difference in their behavior due to the dissimilar elastic properties of the film surfaces. It is shown that the film lifetime is significantly longer at some ‘magic’ film radii.

Capillary analogue of the “dead water” effect in a stratified liquid with a charged interface

In terms of a linear mathematical model of a capillary-gravitational flow in a two-layer liquid with a finite-thickness upper layer, it is shown analytically that an analogue of the dead water phenomenon exists in the domain of capillary waves, which was previously observed only in gravitational waves. This phenomenon shows up as an exponential increase in the capillary wave amplitude at the interface with the surface tension coefficient at the interface tending to zero. It is found that an external electric field displaces this phenomenon toward the range of finite surface tension coefficients.

Stability of a volumetrically charged dielectric fluid jet accelerated in an electric field collinear to the jet

In the approximation linear in the amplitude of capillary waves (generally nonaxisymmetric) on the surface of a volumetrically charged dielectric fluid jet accelerated in an external electrostatic field collinear to the jet axis, a dispersion equation is derived and analyzed. It is shown that for certain values of physical parameters the effect of the external electric field stabilizing the capillary waves and the destabilizing effect of the capillary forces and the electrostatic forces exerted by the jet charge may compensate one another for both axisymmetric and nonaxisymmetric, with a high degree of asymmetry, waves. The instability of flexural waves cannot be suppressed completely and can be realized for sufficiently small wave numbers.

Reasonable reduction in hydrophoby of mineral surface on flotation by carboxylic acids

Numerical estimation of the effect of surfactants on floatability of particles with different wettability is reported. It is proved that the particles with higher hydrophilic surface are recovered into a froth product at the “gas-pulp” interface at the presence of a film of normal alcohols and fat acids. Theoretical value of the suppression coefficient for the capillary wave amplitude coincides satisfactorily with the test values and may be used in calculations.

Capillary waves at the liquid-vapor interface and the surface tension of water

Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at the liquid-vapor interface, is compared for a number of standard three- and four-point water models. We study four three-point models (SPC/E, TIP3P, TIP3P-CHARMM, and TIP3P-Ew) and two four-point models (TIP4P and TIP4P-Ew). All of the models examined underestimate the surface tension; the TIP4P-Ew model comes closest to reproducing the experimental data. The surface tension can also be determined from the amplitude of capillary waves at the liquid-vapor interface by varying the surface area of the interface. The surface tensions determined from the amplitude of the logarithmic divergence of the capillary interfacial width and from the traditional thermodynamic method agree only if the density profile is fitted to an error function instead of a hyperbolic tangent function.

Nematic-isotropic interfaces under shear: A molecular-dynamics simulation

We present a large-scale molecular-dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with moving periodic boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First, we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry-breaking) flow in the vorticity direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.

Parametric buildup of the instability of a charged flat liquid surface imposed on Kelvin-Helmholtz instability

The instability of capillary gravitational waves that is developed at the charged flat interface between media is studied for the case when the upper medium moves parallel to the interface with a velocity that has constant and time-dependent components. It is shown that the Mathieu-Hill equation, describing the temporal evolution of the capillary wave amplitudes in such a system, has unstable solutions at those values of physical parameters (electric field strength and wind velocity) meeting the conditions for Saint Elmo fire initiation in the atmosphere.

On the cascade mechanism of short surface wave modulation

Abstract. Modulation of short surface ripples by long surface or internal waves by a cascade mechanism is considered. At the first stage, the orbital velocity of the long wave (LW) adiabatically modulates an intermediate length nonlinear gravity wave (GW), which generates a bound (parasitic) capillary wave (CW) near its crest in a wide spatial frequency band. Due to strong dependence of the CW amplitude on that of the GW, the resulting ripple modulation by LW can be strong. Adiabatic modulation at the first stage is calculated for an arbitrarily strong LW current. The CWs are calculated based on the Lonquet-Higgins theory, in the framework of a steady periodic solution, which proves to be sufficient for the cases considered. Theoretical results are compared with data from laboratory experiments. A discussion of related sea clutter data is given in the conclusion.

Direct measurement of the attenuation of capillary waves by laser interferometry: Noncontact determination of viscosity

The determination of viscosity from the damping of capillary waves has been of great interest, as it affords the possibility of measuring viscosity without contact with the fluid. Here we describe a noncontact method for precision measurement of the amplitude of capillary waves on fluids. The technique utilizes a miniature laser interferometer to map the wave profile with a resolution of about 10 nm. We use this technique to obtain the dispersion and attenuation of capillary waves on water as a test case. Furthermore, the attenuation data is used to obtain the viscosity of water as a function of temperature.

Effect of the cut-off radius of the intermolecular potential on phase equilibrium and surface tension in Lennard–Jones systems

We present the molecular dynamic simulation results for the liquid–vapour interface of the pure Lennard–Jones fluid. The thermodynamical properties, the surface tension, the effective thickness of interfacial layer and the mean-square amplitude of capillary waves are determined. Calculations have been performed at cut-off radii of the intermolecular potential r c 1 =2.6 σ and r c 2 =6.78 σ. It is shown that the cut-off radius of the interaction potential in the two-phase systems should be chosen to be larger than that in the one-phase systems for an adequate representation of properties.

Nonlinear excitation of capillary waves by the Marangoni motion induced with a modulated laser beam.

We have studied the amplitude and phase relationships of capillary waves produced by modulated laser light on the surface of strongly absorbing liquids. For increasing laser fluences a strong nonlinear behavior is observed. This is connected with the convective motion of the liquid created by surface tension gradients known as the Marangoni motion. The abrupt changes in both the capillary wave amplitude and the phase are found to be due to an autoblocking effect of the heat flux from the region of the laser absorption as the result of the development of a closed circulating flow of the liquid.