Faraday Wave Turbulence on a Spherical Liquid Shell

The impact of an ultrasonic standing wave on the sorption behavior of proteins: Investigation of the role of acoustically induced non-spherical bubble oscillations

HYPOTHESIS

Protein molecules adsorb on the air/liquid interface due to possessing a hydrophobic side. A full surface coverage is important in many processes such as in protein harvesting by foam fractionation. The adsorption of proteins in low concentration solutions is preceded by a relatively long time lag known as the induction period. This has been attributed to the formation of an adsorbed monolayer, which relies on the reorientation of the protein molecules. The reduction of the induction period can significantly facilitate the sorption process to reach full protein coverage. For this purpose acoustically induced non-spherical bubble oscillations can aid in the formation of the monolayer and enhance the sorption process.

EXPERIMENT

In this study, low frequency ultrasound was used to induce non-spherical oscillations on an air bubble attached to a capillary. Profile analysis tensiometry was deployed to examine the effect of these non-spherical oscillations on the sorption dynamics of different proteins.

FINDINGS

We observed that during the initial stages of adsorption, when the bubble surface is almost empty, non-spherical oscillations occur, which were found to significantly expedite the adsorption process. However, during later stages of the adsorption process, despite the continued presence of several sonication phenomena such as the primary radiation force and acoustic streaming, no change in adsorption behavior of the proteins could be noted. The occurrence, duration, and intensity of the non-spherical bubble oscillations appeared to be the sole contributing factors for the change of the sorption dynamics of proteins.

Toward Enhanced Aerosol Particle Adsorption in Never-Bursting Bubble via Acoustic Levitation and Controlled Liquid Compensation

Bubbles in air are ephemeral because of gravity-induced drainage and liquid evaporation, which severely limits their applications, especially as intriguing bio/chemical reactors. In this work, a new approach using acoustic levitation combined with controlled liquid compensation to stabilize bubbles is proposed. Due to the suppression of drainage by sound field and prevention of capillary waves by liquid compensation, the bubbles can remain stable and intact permanently. It has been found that the acoustically levitated bubble shows a significantly enhanced particle adsorption ability because of the oscillation of the bubble and the presence of internal acoustic streaming. The results shed light on the development of novel air-purification techniques without consuming any solid filters.

Extraordinary Solidification Mechanism of Liquid Alloys Under Acoustic Levitation State

The acoustic levitation of various materials can be realized by highly intensive ultrasound, which provides a free surface and containerless state for materials processing under space simulation conditions. The nonlinear effects such as acoustic radiation pressure, acoustic streaming, and ultrasonic cavitation open up special access to modulate the fluid dynamics and solidification mechanisms of liquid materials. Here, the physical characteristics of liquid flow, undercooling capability, phase separation, and crystal nucleation and growth within acoustically levitated droplets are explored comprehensively to reveal the extraordinary solidification kinetics of liquid alloys. The sectorial shape oscillations of the 2nd to 10th order modes accompanying internal potential flow are observed for water droplets with modulated ultrasound amplitudes, while the enhanced ultrasound intensity promotes ice nucleation and thus reduces water undercooling. The migration of Sn-rich globules during phase separation of immiscible Al-Cu-Sn alloy is dominated by the droplet deformation and rotation related to acoustic levitation. The high undercooling states of liquid Ag-Cu-Ge and Ni-Sn alloys during acoustic levitation result in the refinement of (Ag) dendrites and the formation of anomalous (Ni+Ni₃ Sn) eutectics. The ultrasound-liquid interaction also induces surface waves during the containerless solidification of Ag-Cu and Ni-Sn eutectic alloys.

Experimental Dispersion Relation of Surface Waves along a Torus of Fluid

We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatiotemporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous, and sloshing modes. Standing azimuthal waves are also studied leading to polygonlike patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.

Hysteretic Faraday waves

We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate subcritically toward highly nonlinear ones with twice their amplitude. We relate this hysteresis with the change of shear stress using a simple stress balance, in agreement with numerical results.

Direct numerical simulations of capillary wave turbulence

This work presents direct numerical simulations of capillary wave turbulence solving the full three-dimensional Navier-Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency, in good agreement with weak turbulence theory. By estimation of the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction, and dissipative times is also observed. These numerical results confirm the validity of the weak turbulence approach to quantify out-of equilibrium wave statistics.

Energy flux measurement from the dissipated energy in capillary wave turbulence

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a liquid by changing its viscosity. We observe that the frequency power-law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the liquid. Here we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be nonconstant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.

Using laser Doppler vibrometry to measure capillary surface waves on fluid-fluid interfaces

Capillary wave phenomena are challenging to study, especially for microfluidics where the wavelengths are short, the frequencies are high, and the frequency distribution is rarely confined to a narrow range, let alone a single frequency. Those that have been studying Faraday capillary waves generated by vertical oscillation have chosen to work at larger scales and at low frequencies as a solution to this problem, trading simplicity in measurement for issues with gravity, boundary conditions, and the fidelity of the subharmonic capillary wave motion. Laser Doppler vibrometry using a Mach-Zehnder interferometer is an attractive alternative: The interface's motion can be characterized at frequencies up to 40 MHz and displacements of as little as a few tens of picometers.

Symmetry induced four-wave capillary wave turbulence

We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two immiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair (eta, Psi). Adding the symmetry z --> -z, the set of capillary waves display a Kolmogorov-Zakharov spectrum k(-4) in wave vector space and f(-8/3) in the frequency domain. The wave system is studied experimentally with two immiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low-frequency random forcing. The probability density function of the local wave amplitude shows a quasi-Gaussian behavior and the power spectral density is shows a power-law behavior in frequency with a slope of -2.75. Theoretical and experimental results are in fairly good agreement with each other.

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.

The mechanism of the attracting acoustic radiation force on a polymer-coated gold sphere in plane progressive waves

Acoustic plane progressive waves incident on a sphere immersed in a nonviscous fluid exert a steady force acting along the direction of wave motion. It is shown here that when an elastic gold sphere is coated with a polymer-type (polyethylene) viscoelastic layer, this force becomes a force of attraction in the long wavelength limit. Kinetic, potential and Reynolds stress energy densities are defined and evaluated with and in the absence of absorption in the layer. Without absorption, the mechanical energy density counteracts the Reynolds stress energy density, which causes a repulsive force. However, in the case of absorption, the attractive force is predicted to be a physical consequence of a mutual contribution of both the mechanical and the Reynolds stress energy densities. This condition provides an impetus for further designing acoustic tweezers operating with plane progressive waves as well as fabricating polymer-coated gold particles for specific biophysical and biomedical applications.

Observation of wave turbulence in vibrating plates

The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small length scales. Here, wave turbulence is observed in experiments on a vibrating plate. The frequency power spectra of the normal velocity of the plate may be rescaled on a single curve, with power-law behaviors that are incompatible with the weak turbulence theory of Düring et al. [Phys. Rev. Lett. 97, 025503 (2006)10.1103/PhysRevLett.97.025503]. Alternative scenarios are suggested to account for this discrepancy -- in particular the occurrence of wave breaking at high frequencies. Finally, the statistics of velocity increments do not display an intermittent behavior.

Observation of gravity-capillary wave turbulence

We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.

Polyhedra formation and transient cone ejection of a resonant microdrop forced by an ac electric field

New deformation or fission phenomena are reported for microdrops driven by an ac electric field at their resonant frequencies. The Maxwell forces that pull out the vertices from a drop can be enhanced when the ac frequency is comparable to both the drop resonant frequency and the inverse charge relaxation time of the diffuse layer. The selected polyhedra possess symmetries that ensure a global force balance of the Maxwell forces and a linear dimension consistent with a sphere whose nth harmonic (n is up to six in the observation) coincides with the applied ac frequency. At high voltages, the resonant focusing of charges by the vibration modes produces evenly distributed and transient Taylor cones that can eject charged nanodrops.

Dynamics of acoustically levitated disk samples

The acoustic levitation force on disk samples and the dynamics of large water drops in a planar standing wave are studied by solving the acoustic scattering problem through incorporating the boundary element method. The dependence of levitation force amplitude on the equivalent radius R of disks deviates seriously from the R3 law predicted by King's theory, and a larger force can be obtained for thin disks. When the disk aspect ratio gamma is larger than a critical value gamma(*) ( approximately 1.9 ) and the disk radius a is smaller than the critical value a(*) (gamma) , the levitation force per unit volume of the sample will increase with the enlargement of the disk. The acoustic levitation force on thin-disk samples ( gamma</= gamma(*) ) can be formulated by the shape factor f(gamma,a) when a</= a(*) (gamma) . It is found experimentally that a necessary condition of the acoustic field for stable levitation of a large water drop is to adjust the reflector-emitter interval H slightly above the resonant interval H(n) . The simulation shows that the drop is flattened and the central parts of its top and bottom surface become concave with the increase of sound pressure level, which agrees with the experimental observation. The main frequencies of the shape oscillation under different sound pressures are slightly larger than the Rayleigh frequency because of the large shape deformation. The simulated translational frequencies of the vertical vibration under normal gravity condition agree with the theoretical analysis.

Eutectic growth under acoustic levitation conditions

Samples of Pb-Sn eutectic alloy with a high density of 8.5 x 10(3) kg/m(3) are levitated with a single-axis acoustic levitator, and containerlessly melted and then solidified in argon atmosphere. High undercoolings up to 38 K are obtained, which results in a microstructural transition of "lamellas-broken lamellas-dendrites." This transition is further investigated in the light of the coupled zone for eutectic growth and the effects of ultrasound. The breaking of regular eutectic lamellas and suppression of gravity-induced macrosegregation of (Pb) and (Sn) dendrites are explained by the complicated internal flow inside the levitated drop, which is jointly induced by the shape oscillation, bulk vibration and rotation of the levitated drop. The ultrasonic field is also found to drive forced surface vibration, which subsequently excites capillary ripples and catalyzes nucleation on the sample surface.

Dynamics and fragmentation of thick-shelled microbubbles

Localized delivery could decrease the systemic side effects of toxic chemotherapy drugs. The unique delivery agents we examine consist of microbubbles with an outer lipid coating, an oil layer, and a perfluorobutane gas core. These structures are 0.5-12 microm in radius at rest. Oil layers of these acoustically active lipospheres (AALs) range from 0.3-1.5 microm in thickness and thus the agents can carry a large payload compared to nano-scale drug delivery systems. We show that triacetin-based drug-delivery vehicles can be fragmented using ultrasound. Compared with a lipid-shelled contrast agent, the expansion of the drug-delivery vehicle within the first cycle is similar, and a subharmonic component is demonstrated at an equivalent radius, frequency, and driving pressure. For the experimental conditions explored here, the pulse length required for destruction of the drug-delivery vehicle is significantly greater, with at least five cycles required, compared with one cycle for the contrast agent. For the drug-delivery vehicle, the observed destruction mechanism varies with the initial radius, with microbubbles smaller than resonance size undergoing a symmetric collapse and producing a set of small, equal-sized fragments. Between resonance size and twice resonance size, surface waves become visible, and the oscillations become asymmetrical. For agents larger than twice the resonance radius, the destruction mechanism changes to a pinch-off, with one fragment containing a large fraction of the original volume.

Dependence of acoustic levitation capabilities on geometric parameters

A two-cylinder model incorporating boundary element method simulations is developed, which builds up the relationship between the levitation capabilities and the geometric parameters of a single-axis acoustic levitator with reference to wavelength. This model proves to be successful in predicting resonant modes of the acoustic field and explaining axial symmetry deviation of the levitated samples near the reflector and emitter. Concave reflecting surfaces of a spherical cap, a paraboloid, and a hyperboloid of revolution are investigated systematically with regard to the dependence of the levitation force on the section radius R(b) and curvature radius R (or depth D) of the reflector. It is found that the levitation force can be remarkably enhanced by choosing an optimum value of R or D, and the possible degree of this enhancement for spherically curved reflectors is the largest. The degree of levitation force enhancement by this means can also be facilitated by enlarging R(b) and employing a lower resonant mode. The deviation of the sample near the reflector is found likely to occur in case of smaller R(b), larger D, and a higher resonant mode. The calculated dependence of levitation force on R, R(b), and the resonant mode is also verified by experiment and finally demonstrated to be in good agreement with experimental results, in which considerably a strong levitation force is achieved to levitate an iridium sphere which has the largest density of 22.6 g/cm(3).