Interfacial Waves Research Articles

Two-layer-liquid and lattice considerations through a (3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system

Current studies on the liquids and lattices attract people’s attention. In this Letter, for certain interfacial waves in a two-layer liquid or elastic waves in a lattice, we investigate a (3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system via building a set of the similarity reductions. In respect of the amplitude or elevation of the relevant wave, our similarity reductions are from that system to a known ordinary differential equation, while dependent on the coefficients in that system.

Numerical simulation of interfacial resonant Faraday waves between two immiscible liquids

An in-house numerical model is extended to study the resonant Faraday waves at the interface between two immiscible liquids with the consideration of surface tension. The surface tension module was first added in this model and validated by two standard tests, i.e., the development of a non-equilibrium liquid droplet with square shape and the development of Rayleigh–Taylor instability on the interface of two fluids with different densities. Two experiments were conducted to investigate the resonant Faraday waves at the interface of two liquids in a tank under vertical excitation. The numerical results are compared with the experimental data in terms of wave profiles, and favorable agreements are obtained. It has been found that only when the surface tension is properly taken into account, the numerical model can describe the resonant Faraday waves satisfactorily, especially for the secondary interfacial instability and the wave breaking between two immiscible liquids. In addition, the comparisons between numerical results for different surface tensions indicate that the surface tension plays an important stabilizing role during the development of interfacial Faraday waves and the subsequent secondary instability, and the existence of surface tension can help prevent the flow structures transforming from two-dimensional to three-dimensional.

Four-Channel Ultrasonic Sensor for Bulk Liquid and Biochemical Surface Interrogation.

Custom electronics tailored for ultrasonic applications with four ultrasonic transmit-receive channels and a nominal 25 MHz single channel frequency were developed for ultrasound BAW and SAW biosensor uses. The designed integrated microcontroller, supported by Python with a SciPy library, and the developed system measured the time of flight (TOF) and other wave properties to characterize the acoustic properties of a bulk of the liquid in a microchannel or acoustic properties of biological species attached to an analytic surface in real time. The system can utilize both piezoelectric and capacitive micromachined ultrasound transducers. The device demonstrated a linear response to changes in water salinity. This response was primarily attributed to the time-of-flight (TOF) changes related to the varying solution density. Furthermore, real-time DNA oligonucleotide-based interactions between oligonucleotides immobilized on the device's analytical area and oligonucleotides attached to gold nanoparticles (Au NPs) in the solution were demonstrated. The biological interaction led to an exponential decrease in the acoustic interfacial wave propagating across the interface between the solution and the solid surface of the sensor, the TOF signal. This decrease was attributed to the increase in the effective density of the solution in the vicinity of the sensor's analytical area, as Au NPs modified by oligonucleotides were binding to the analytical area. The utilization of Au NPs in oligonucleotide surface binding yields a considerably stronger sensor signal than previously observed in earlier CMUT-based TOF biosensor prototypes.

Experimental and modeling study on liquid film thickness of horizontal gas-liquid annular flow using ultrasonic method

In horizontal annular flow, the high gas velocity leads to the strong randomness, rapidity and complexity of the structure and dynamic characteristics of gas-liquid interfacial wave. As one of the important parameters to describe the interfacial wave, the liquid film thickness is significant to study the hydrodynamic characteristics of the gas-liquid two-phase flow. In this paper, the ultrasonic echo resonance main frequency (UERMF) method and the ultrasonic reference signal elimination (URSE) method are compared by numerical simulation method. The minimum liquid film thickness measured by these two methods are 0.3 mm and 0.01 mm, respectively. Experiments are conducted on a stainless steel test section with an inner diameter of 50.0 mm to study annular air-water flow under five different pressure conditions (from 0.1 MPa to 0.7 MPa). The experimental data is processed using the URSE method to analyze the characteristics of the liquid film under different operating conditions. In addition, based on the aforementioned experimental dataset, a comparison is made regarding the performance of existing predictive correlations. It is found that the existing correlations have certain limitations in capturing the variations of liquid film thickness in annular flow, particularly at high pressures and for different pipe diameters. Therefore, a new liquid film thickness correlation suitable for different system pressures and pipe diameters is proposed. By expanding the range of fitted data points (220 data points), the 95 % relative error of improved model is within ±25 % error band for all available data (authors' and literature). The mean absolute percentage error (MAPE) is 11.08 %. The improved correlation has the applicability and extrapolation for different system pressure and pipe diameter conditions.

Study on copper-stainless steel explosive welding for nuclear fusion by generalized interpolated material point method and experiments

The thick copper stainless steel composite plate is an important component of the cooling coil terminal box of international nuclear fusion reactors. The composite rate, tensile strength, shear strength, and interface waveform of the metal plate are also far higher than the requirements of conventional explosive welding technology. It is difficult to obtain the best technical process parameters in a short time solely relying on conventional explosive welding tests. In order to solve the above-mentioned technical difficulties in explosive welding, this article applies the generalized interpolation material point method (GIMP) based on the explosive welding window, metal elastic-plastic mechanics, and explosive detonation theory to conduct macroscopic three-dimensional and microscopic two-dimensional numerical simulations of the copper stainless steel explosive welding process and the composite interface wave formation process, respectively. The experimental results demonstrate that the GIMP has significant advantages in numerical calculation and analysis for the explosive welding problem of high-speed impact collision of metal plates driven by explosive detonation, and it can effectively solve the technical problems of high technical specifications, low explosive processing composite rate, and low interface strength of large thickness copper stainless steel composite plates used in nuclear fusion.

Weakly nonlinear modulation of interfacial gravity-capillary waves

Weakly nonlinear modulation of interfacial gravity-capillary waves

On the steady-state interfacial waves with two-dimensional type-A double exact resonance

Steady-state interfacial waves under two-dimensional (2D) type-A exact triad resonance and other related resonances are researched in a two-layer liquid model with a free surface in contact with air. Five groups (groups 1–5) of convergent series solutions are achieved via the homotopy analysis method. It is found that the phenomenon of double exact resonance could exist in periodic interfacial waves if physical parameters correspond to the intersection of two exact resonance curves. The double exact resonance considered here contains a 2D type-A triad resonance and an other resonance. Under the 2D type-A exact triad resonance, the other resonant triad could obviously enlarge or reduce the wave amplitudes and energy proportions of primary and resonant components. Nevertheless, other resonant quartet, quintet, sextet, and septet all produce no influence on interfacial waves when the 2D type-A exact triad resonance occurs. The above-mentioned results indicate that in the neighborhood of the double exact triad resonance, small perturbations of wave vector of a primary component can cause huge changes on wave profiles of free surface and interface, wave amplitude spectrum, and energy distribution of internal waves in real ocean. In addition, the closer the interfacial waves are to the double exact triad resonance, the more possible energy combinations exist in the wave system, and the greater the number of steady-state interfacial wave solutions. All of this should deepen our understanding of nonlinear resonance interactions in short-crested internal waves.

Elliptic tangent imaging method for layered plate interfacial defects based on non-dispersive guided waves

Layered structures play an increasingly pivotal role in diverse fields such as aerospace, pipeline transportation, and petrochemical engineering. However, defects situated at the interfaces between layers pose a challenge for conventional Non-Destructive testing (NDT) methods, impeding accurate imaging. This research introduces the elliptic tangent imaging method based on interface wave modes to visualize interfacial defects within layered structures. The interface wave mode, characterized by high-frequency non-dispersive traits, facilitates precise localization of defects. Its energy concentration in the interface enhances sensitivity to interfacial defects. The elliptic tangent imaging method proposed in this paper capitalizes on the transmission coefficients of the oblique incidence technique for surface waves, enabling the concurrent determination of defect location and orientation using one pair of transducers. The application of the orthogonal matched pursuit algorithm for sparse representation of the raw signal further enhances positioning accuracy. This paper establishes an automatic detection system for interface waves, demonstrating swift transducer switching. Experimental validation of wave velocity aligns closely with theoretical calculations. In experiments focusing on interfacial defect imaging in bilayer aluminum-steel plates, the system exhibits the capability to accurately depict interfacial defects with varying orientations.

EFFECTS OF PIPE DIAMETER ON INTERFACIAL AND WALL FRICTION FACTORS OF SWIRLING ANNULAR FLOWS IN A VERTICAL PIPE

Interfacial and wall friction factors, <i>f<sub>i</sub></i> and <i>f<sub>w</sub></i>, of swirling annular flows in a vertical pipe of 20 mm in diameter D were measured for comparison with those in a vertical pipe of <i>D </i>= 30 mm. A three-fluid model was applied to evaluate the friction factors. Measurements were carried out in two sections, one near the swirler and the other far downstream the swirler. The swirl intensity of the flow was evaluated by the interfacial swirl number si defined by the ratio of the azimuthal to the axial components of interfacial wave velocity. The interfacial swirl numbers were smaller in the smaller pipe. The ratio of <i>f<sub>i</sub></i> in swirling annular flows to that in non-swirling annular flows decreased to unity with decreasing <i>s<sub>i</sub></i>* which is the arithmetic mean value of <i>s<sub>i</sub></i> for 0 ≤ <i>z</i>* (= <i>z/D</i>) ≤ 3.8, where <i>z</i> is the axial coordinate in the test section, and is higher in <i>D </i>= 20 mm than in <i>D </i>= 30 mm. The ratio of <i>f<sub>w</sub></i> in swirling annular flows to that in non-swirling annular flows decreased to less than unity with decreasing <i>s<sub>i</sub></i>* and is higher in <i>D </i>= mm than in <i>D </i>=30 mm.

Steady Flow Over a Finite Patch of Submerged Flexible Vegetation

AbstractAn immersed boundary‐finite element with soft‐body dynamics has been implemented to study steady flow over a finite patch of submerged flexible aquatic vegetation. The flow structure interaction model can resolve the flow interactions with flexible vegetation, and hence the reconfiguration of vegetation blades to ambient flow. Flow dynamics strongly depend on two dimensionless parameters, namely vegetation density and Cauchy number (defined as the ratio of the fluid drag force to the elastic force). Five different flow patterns have been identified based on vegetation density and Cauchy number, including the limited reach, swaying, “monami” A, “monami” B with slow moving interfacial wave, and prone. The “monami” B pattern occurred at high vegetation density and is different from “monami” A, in which the passage of Kelvin‐Helmholtz billows strongly affects the vegetation interface. With soft‐body dynamics, blade‐to‐blade interactions can also be resolved. At high vegetation density, the hydrodynamic interactions play an important role in blade‐to‐blade interactions, where adjacent vegetation blades interact via the interstitial fluid pressure. At low vegetation density, direct contacts among vegetation blades play important roles in preventing unphysical penetration of vegetation blades.

Stabilization responses of an infinite porous flow channel containing ferrofluids

This paper investigates the effect of a magnetic field on the stability of two interfacial waves propagating between three infinite layers of viscous fluids. The flow propagates saturated in porous media so that liquids have distinct physical properties and are immiscible. The principal purpose of this study is to examine the impact of the porosity outcome and fluid viscosity on the growth rate in the existence of a magnetic field. In the horizontal axis direction. Fluid stability results from the amplitude of the waves and the extent to which they are affected by the interference between magnetic features and the effect of the media's porosity. The stability conditions are realized theoretically in which stability diagrams are achieved. The influence of the various quantities of the problem on the interface stability is thoroughly evaluated.

Studies of interfacial wave properties during displacement with pure viscoelastic fluids in microchannels

In this study, new experimental data for the displacement of a Newtonian liquid by three pure viscoelastic (Boger) fluids with different relaxation times were obtained with imaging in a 500 μm microchannel. Results were compared against those from displacement using a Newtonian liquid. Small irregular waves were observed at the interface for the Newtonian displacement, while periodic instabilities were seen for all Boger fluid cases. The elastic Mach number (Ma), describing the ratio of the flow velocity with the elastic wave propagation velocity, was found to be the key parameter for correlating the wave properties in the case of Boger fluids. The amplitude of the wavy interface initially increased up to Ma = 0.5, before decreasing again. The frequency and the wave velocity increased monotonically with increasing Ma. For all configurations, a phase shift of π was found between the top and the bottom interfaces. Correlations from experimental data were developed for all wave properties. Based on these correlations, an empirical wave model was developed to describe the observed planar images and to reconstruct the three-dimensional waves, which resemble a helical structure.

Tidal Dissipation in Stably Stratified and Semiconvective Regions of Rotating Giant Planets: Incorporating Coriolis Forces

We study how stably stratified or semiconvective layers alter tidal dissipation rates associated with the generation of inertial, gravito-inertial, interfacial, and surface gravity waves in rotating giant planets. We explore scenarios in which stable (nonconvective) layers contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. Our model is an idealized spherical Boussinesq system incorporating Coriolis forces to study effects of stable stratification and semiconvective layers on tidal dissipation. Our detailed numerical calculations consider realistic tidal forcing and compute the resulting viscous and thermal dissipation rates. The presence of an extended stably stratified fluid core significantly enhances tidal wave excitation of both inertial waves (due to rotation) in the convective envelope and gravito-inertial waves in the dilute core. We show that a sufficiently strongly stratified fluid core enhances inertial wave dissipation in a convective envelope much like a solid core does. We demonstrate that efficient tidal dissipation rates (and associated tidal quality factors )—sufficient to explain the observed migration rates of Saturn's moons—are predicted at the frequencies of the orbiting moons due to the excitation of inertial or gravito-inertial waves in our models with stable layers (without requiring resonance locking). Stable layers could also be important for tidal evolution of hot and warm Jupiters and hot Neptunes, providing efficient tidal circularization rates. Future work should study more sophisticated planetary models that also account for magnetism and differential rotation, as well as the interaction of inertial waves with turbulent convection.

Stratified inclined duct: two-layer hydraulics and instabilities

The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of interfacial waves and their transition to turbulence as the tilt angle is increased appears to be linked to a threshold in the exchange flow rate given by inviscid two-layer hydraulics. We uncover these hydraulic mechanisms by (i) using recent direct numerical simulations (DNS) providing full flow data in the key flow regimes (Zhu et al., J. Fluid Mech., vol. 969, 2023, A20), (ii) averaging these DNS into two layers, and (iii) using an inviscid two-layer shallow-water and instability theory to diagnose interfacial wave behaviour and provide physical insight. The laminar flow is subcritical and stable throughout the duct and hydraulically controlled at the ends of the duct. As the tilt is increased, the flow becomes supercritical everywhere and unstable to long waves. An internal jump featuring stationary waves first appears near the centre of the duct, then leads to larger-amplitude travelling waves, and to stronger jumps, wave breaking and intermittent turbulence at the largest tilt angle. Long waves described by the (nonlinear) shallow-water equation are interpreted locally as linear waves on a two-layer parallel base flow described by the Taylor–Goldstein equation. This link helps us to interpret long-wave instability and contrast it with short-wave (e.g. Kelvin–Helmholtz) instability. Our results suggest a transition to turbulence in SID through long-wave instability relying on vertical confinement by the top and bottom walls.

An experimental investigation on R245fa and R1233zd(E) flow boiling at high saturation temperatures in a horizontal small diameter channel

The current study presents an investigation on flow patterns, pressure-drop and heat transfer coefficient for the refrigerants R1233zd(E) and R245fa flowing at saturation temperatures (Tsat) between 75 °C and 95 °C inside a horizontal 2 mm diameter tube. Experimental results are reported for mass velocities of 176–570 kg/m²s and heat fluxes of 18.1–54.5 kW/m². As expected, the pressure gradient increases as the mass velocity increases and the saturation temperature decreases. Flow image analysis indicated that the pressure gradient peak is associated with disturbance interfacial waves damping. Heat transfer coefficient data indicated strong contribution of nucleate boiling effects for most of the experimental conditions. The higher the saturation temperature and the heat flux, the higher the heat transfer coefficient, regardless of the vapor quality range. In general, the effect of mass velocity on the heat transfer coefficient was only marginal, with exception of low Tsat and heat flux conditions. Two of 20 pressure-drop prediction methods predicted more than 90% of the database within error bands of ±30%. Overestimation of heat transfer coefficient data was verified for most of the 16 evaluated prediction methods, especially at high Tsat. Only two methods predicted more than 80% of data within an error band of ±30%.

Inverse Determination Of Interfacial Properties of a Bonded Structure Using Lamb Waves Generated By Laser Lateral Excitation

Nondestructive testing of the adhesive bond properties of a bonded structure is essential in aviation, automotive, and other industries. In this study, a Lamb wave–based quantitative characterization method is proposed to determine the interfacial stiffness of bonded structures. A theoretical model is established, with which the dispersion relationship of Lamb waves in a bonded structure is investigated. Different interfacial states ranging from a perfect bond to a weak bond are simulated, and the numerical results show the sensitivity of Lamb waves to interfacial stiffness. A lateral excitation method is proposed to enhance the excitation of the interfacial sensitive Lamb wave modes, and laser ultrasonic experiments show the enhancement of the Lamb wave signals on aluminum-epoxy-aluminum samples generated by the lateral excitation method. Then, a rapid construction method of inversion objective function is presented to reconstruct the interfacial stiffness coefficient of a bonded structure, and its functionality is validated via finite element simulations. Finally, the interfacial properties of the samples are reconstructed using the inversion scheme.

Flow-driven interfacial waves: an inviscid asymptotic study

Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow, and construct a uniformly valid approximation for the perturbed streamfunction, or eigenfunction. We then expand the real part of the eigenvalue, the phase speed, in a power series of the inverse wavenumber and show that the imaginary part is exponentially small. We give expressions for the growth rates of the Miles (J. Fluid Mech., vol. 3, 1957, pp. 185–204) and rippling (e.g. Young & Wolfe, J. Fluid Mech., vol. 739, 2014, pp. 276–307) instabilities that are valid for an arbitrary shear flow. The accuracy of the results is demonstrated by a comparison with the exact solution of the eigenvalue problem in the case when both the wind and the current have an exponential profile.

Frequency response of certain temporal and complex transfer functions for the Interfacial 1D temperature wave

Frequency response of certain temporal and complex transfer functions for the Interfacial 1D temperature wave

Modeling of transition boundary from stratified to non-stratified liquid-liquid flows in small diameter pipe

Modeling the instability of the interfacial wave in stratified liquid-liquid flows is a popular topic and attracts the interest of scholars. In this study, an experimental study is implemented in horizontal and +5° inclined pipes with an inner diameter of 20 mm. A planar laser-induced fluorescence-60 (PLIF-60) system is utilized to visualize the flow structures at the pipe radial section, such as the curved interface and the droplet entrainment. Image processing is used to correct the PLIF-60 flow images and reconstruct quasi-3D flow structures. Flow pattern maps for horizontal and inclined flows are drawn to indicate the transition boundary between stratified and non-stratified flows. Young-Laplace equation with dynamic contact angle is developed to predict the interface configuration. The predicted interface configuration shows a good agreement with that detected by the PLIF-60 system. In view of the fact that the interface configuration is partly associated with the stratified/non-stratified flow transition, a modified model for the transition boundary is established based on Kelvin-Helmholtz (KH) stability. Comparisons of the proposed transitional criteria with experimental data and available data in liquid-liquid systems show reasonable agreement in small diameter pipes. Additionally, the proposed model with the consideration of interface configuration is basically not dependent on the wave parameters, such as wave amplitude and wavelength, providing a new way for predicting the transition boundary from stratified to non-stratified liquid-liquid flows in small diameter pipe.

Observations of transient wave-induced mean drift profiles caused by virtual wave stresses in a two-layer system

An experimental study of long interfacial gravity waves was conducted in a closed wave tank containing two layers of viscous immiscible fluids. The study focuses on the development in time of the mean particle drift that occurs close to the interface where the two fluids meet. From a theoretical analysis by Weber & Christensen (Eur. J. Mech.-B/Fluids, vol. 77, 2019, pp. 162–170) it is predicted that the growing drift in this region is associated with the action of the virtual wave stress. This effect has not been explored experimentally before. Interfacial waves of different amplitudes and frequencies were produced by a D-shaped paddle. Particle tracking velocimetry was used to track the time development of the Lagrangian mean drift. The finite geometry of the wave tank causes a mean return flow that is resolved by mass transport considerations. The measurements clearly demonstrate the importance of the virtual wave stress mechanism in generating wave drift currents near the interface.