Session S06: Drops: Levitation (5:45pm - 6:30pm CST)

Mechanical characterization of an acoustically levitated liquid droplet by bending plate oscillation

Resonance oscillation of an acoustically levitated liquid droplet has been widely used to characterize viscosity and surface tension for non-/ Newtonian liquids and gels. The classical theoretical models by Rayleigh and Lamb are proved to be useful in describing the behavior of inviscid liquids. However, significant modification is necessary to adapt to highly viscous liquids such as glycerin and engine oil with high molecular weight. In fact, it is difficult to observe the classical peripheral oscillations in such liquids. We lately observed a new oscillation mode. These liquids possess long relaxation time thus can be flattened by acoustic pressure to behave like an elastic plate. Three characteristic resonance modes were experimentally observed, namely, see-saw, saddleback, and monkey saddle at an increasing resonance frequency. The waveform conforms to an elastic plate with an out-of-plane oscillation along the azimuthal direction. A well-defined flexural rigidity can be empirically measured and correlated to the surface tension, viscosity, droplet dimension, and ``plate'' thickness. A dimensionless number analysis related to the Ohnesorge and Capillary numbers is found to fit the measurement. The experimental technique and analysis methods can be used to characterize a wide spectrum of Newtonian liquids.   

Higher order resonance in electrostatically levitated liquid droplets for the measurement of surface tension

The Faraday forcing method in levitated liquid droplets has recently been introduced as a method for measuring surface tension using resonance. By subjecting an electrostatically-levitated liquid metal droplet to a continuous, oscillatory, electric field, at a frequency nearing that of the droplet’s first principal mode of oscillation (known as mode 2), the method was previously shown to determine surface tension of materials that would be particularly difficult to process by other means, e.g. liquid metals and alloys. It also offered distinct advantages over the conventional levitation-based method of pulse-decay, particularly for high viscosity samples, avoiding undesirable control system perturbations to the sample upon pulse-release. This work presents 1) a benchmarking experimental method to measure surface tension by excitation of the second principal mode of oscillation (known as mode 3) in a levitated liquid droplet and 2) a more rigorous quantification of droplet excitation using a projection method. Surface tension measurements compare favorably to literature values for Zirconium, Inconel 625, and Rhodium, using both modes 2 and 3. Thus, this new method serves as a credible, self-consistent benchmarking technique for the measurement of surface tension.   

Phase Change Through Levitating Sound Waves

Sound waves exhibit fascinating properties. Particularly, they can generate heat as they are absorbed, potentially enough to create phase change. Through second law constraints, we are currently creating a levitating device that not only suspends objects with one source of sound but also generates heat through another source. A material’s molecules and atoms have some amount of resistance before yielding to the strength from the sound waves disrupting the ordered pattern. The acoustic pressure from sound waves will maintain stability while a secondary source will produce heat without destructively interfering with the sound waves. These sound waves are positioned facing each other from two directions with the same frequency and wavelength to produce a standing wave, which is responsible for maintaining mid-air suspension. While the levitation system maintains a standing wave to suspend objects, the second set of waves enters from opposing directions perpendicular to the standing wave to keep the object from moving outside the levitation boundaries while maintaining sound wave pressure stability. We hope to eventually demonstrate the efficacy of this process through a table-top experimental device.   

On the stability of Leidenfrost drop inner flows

Recent experimental observation by Bouillant et al. (Nat. Phys., vol. 14, 2018) revealed that below a certain radius, a Leidenfrost water drop starts to roll. To better describe this internal mode transition, we study experimentally and numerically the global stability of a water drop in a Leidenfrost regime. In experiment, the surface temperature and the internal flow fields of a drop with initial radius $R\approx 3.7$ mm are measured by infrared camera and particle induced velocimetry, respectively, and show the existence of critical radii on successive azimuthal mode (of wavenumber $m$) transitions. Numerically, the steady base flow is computed assuming non-deformable interface and the heat exchange on the boundary is modeled by an empirical correlation law. In absence of precise knowledge of the surface contamination properties, the surface tension gradient appears as the only tunable parameter to match experimental observations. The stability analysis of nominally axisymmetric base flow shows the dominant unstable azimuthal mode transitions at radii close to the experimental observations. The unstable eigenvectors for the azimuthal wavenumber $m=3$ and $m=2$ are reminiscent to the experimental observation while the rolling mode is best described by the $m=1$ eigenvector.   

Computational modeling of quasistatic Leidenfrost drops

In the Leidenfrost effect, drops levitate on a thin film of vapor generated by the evaporation of the liquid above a solid surface heated beyond the Leidenfrost temperature. A previous model [1] predicted the quasistatic shape of a Leidenfrost drop by using the lubrication approximation for the vapor but neglecting flow in the drop. We find that the original numerical solution of the model in [1] contains inaccuracies; the corrected solution exhibits new experimentally-observed features including (i) a regime with a dimple-less bottom surface of the drop and (ii) a minimum in the vapor layer thickness as a function of the drop size [2]. Next, we extend the model by coupling the lubrication equation for the vapor to the axisymmetric Navier-Stokes equations for the flow within the drop and solve the resulting model computationally. For high liquid viscosities, our results agree with the corrected solution of the model in [1], as expected. However, for water viscosity there are discrepancies for large drops and paradoxically, the model in [1] agrees better with experiments [3]. We discuss possible reasons for this result. [1] Sobac et al., Phys. Rev. E. 90, 053011 (2014). [2] Celestini et al., Phys. Rev. Lett. 109, 034501 (2012). [3] Burton et al., Phys. Rev. Lett. 109, 074301 (20   

A physical picture of the inverse Leidenfrost effect holding in the limit of vanishing crispation number $Cr$

Assuming axisymmetry and zero gravity, computation and asymptotic analysis are used to find the maximum value of the force $F$ with which a heated non--evaporating sphere (radius $b$) can be pushed against the surface of a volatile liquid. Mass evaporated beneath the sphere flows to the atmosphere as a thin film of vapour, and the pool surface is deformed by the pressure field driving that flow. For $f=F/(2\pi\gamma b)\ll 1$ (surface tension $\gamma$), film thickness $h$ increases monotonically with angle $\theta$ (measured from the sphere bottom). Once $f$ exceeds a critical value, $h(\theta)$ changes form; a maximum $h_0$ occurs at $\theta=0$, and a minimum $h_1$ at $\theta=\theta_1$. With increasing $f$, the ratio $h_0/h_1$ increases, causing an apparent contact line to form at $\theta_1$. For $\theta<\theta_1$, $p(\theta)$ is asymptotically uniform and the pool surface is a spherical cap; for $\theta>\theta_1$, $p$ is atmospheric and the pool surface is the minimal surface tangent to the sphere at $\theta_1$. $p(\theta)$ falls from $p_0$ to atmospheric across a narrow barrier rim within which $h=O(h_1)$. From this picture, it follows that $F=2\pi\gamma b \sin^2\theta_1$, and that the maximum force is $2\pi\gamma b$. A formula for the evaporation rate is also provided.   

Acoustic vortex beam scattering measurements and a review of modulated radiation pressure for levitation experiments

An acoustic vortex beam has a null on the axis of propagation and an angular phase ramp proportional to the order of the beam. The beam carries orbital angular momentum [1]. The phase ramp facilitates high-resolution imaging and acoustical alignment.~First order vortex beams were generated in water and spheres were raster scanned in the beams. Forward scattering [2] and backscattering [3] were investigated with array-based signal detection and processing. Three types of helicity-projection processing reveal phase evolution and regularities in such measurements. This is supported by theoretical Fermat phase spirals. In other work some noteworthy experimental and theoretical aspects and early modulated acoustic radiation pressure experiments for studying modes of acoustically levitation of drops [4] (and subsequently bubbles) have been reviewed [5]. The review was needed to correct analytical errors in recent work by others. [1] B. T. Hefner {\&} P. L. Marston, J. Acoust. Soc. Am. 106, 3313 (1999). [2] V. Bollen, et al., Proc. Meet. on Acoustics, 19, 070075 (2013). [3] V. Bollen {\&} P. Marston, J. Acoust. Soc. Am. 148(2), EL135 (2020). [4] P. Marston {\&} R. E. Apfel, Bull. Am. Phys. Soc. 22, DFD-1283 (1977). [5] P. Marston, J. Quant. Spectrosc. {\&} Radiat. Transf. 254, 107226 (2020).   

Leidenfrost Hysteresis with Hydrodynamic Collapse

The Leidenfrost effect occurs when a heated solid contacts a liquid, and a thin, insulating vapor film forms due to evaporation. The Leidenfrost transition temperature, TL, has a variety of reported values. The effect of hydrophobicity, surface roughness, geometry, and salt concentration are a few variables linked to changes in TL. Here we show how failure occurs when a stable film is cooled well below the temperature at which it was formed. We use an electrical technique with sub-microsecond resolution to measure the thickness of the vapor film under various conditions. Our measurement treats the film as a complex circuit component with measurable impedance. Upon heating, a stable film is formed at an upper critical temperature consistent with recent predictions. Upon cooling, we observe hysteresis. The film can exist near or below the boiling temperature of the liquid, the lower critical temperature, Tc. Failure is characterized by an average thickness and temperature at collapse that does not depend on salt concentration or thermal conductivity for smooth metallic surfaces. Our accompanying numerical simulations suggest that the hydrodynamics of the lubricating vapor film play a dominant role in determining Tc, and depends strongly on the geometry of contact.   

Levitation of evaporating microscale droplets over solid surfaces

We develop an analytical model to describe recent experimental observations of levitation of evaporating microscale droplets over heated solid surfaces for temperatures far below the Leidenfrost point. Flow patterns around the droplet are determined. Formulas for levitation force are obtained and used to determine the levitation height as a function of drop radius. The results are compared to the predictions of models representing the droplets as point sources in the hydrodynamic equations and with the experimental data. Our model predictions are in good agreement with the experiments except for very small droplets which tend to levitate at higher than expected height.