Vibrations of a diamagnetically levitated water droplet

Droplet motion on sonically excited hydrophobic meshes

The sonic excitation of the liquid droplet on a hydrophobic mesh surface gives rise to a different oscillation behavior than that of the flat hydrophobic surface having the same contact angle. To assess the droplet oscillatory behavior over the hydrophobic mesh, the droplet motion is examined under the external sonic excitations for various mesh screen aperture ratios. An experiment is carried out and the droplet motion is recorded by a high-speed facility. The findings revealed that increasing sonic excitation frequencies enhance the droplet maximum displacement in vertical and horizontal planes; however, the vertical displacements remain larger than those of the horizontal displacements. The resonance frequency measured agrees well with the predictions and the excitation frequency at 105 Hz results in a droplet oscillation mode (n) of 4. The maximum displacement of the droplet surface remains larger for the flat hydrophobic surface than that of the mesh surface with the same contact angle. In addition, the damping factor is considerably influenced by the sonic excitation frequencies; hence, increasing sonic frequency enhances the damping factor, which becomes more apparent for the large mesh screen aperture ratios. The small-amplitude surface tension waves create ripples on the droplet surface.

Spontaneous Formation of Star-Shaped Surface Patterns in a Driven Bose-Einstein Condensate

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with l-fold symmetry, ranging from quadrupole (l=2) to heptagon modes (l=7), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the l=6 mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence.

A simple levitated-drop tensiometer

A reliable, simple, and affordable liquid tensiometer is presented in this paper. The instrument consists of 72 ultrasonic transmitters in a tractor beam configuration that levitates small liquid samples (droplets) in air. Under operation, the instrument imparts a pressure instability that causes the droplet to vibrate while still levitating. Droplet oscillations are then detected by a photodiode, and the signal is recorded by an oscilloscope. The frequency of these oscillations is obtained and then used to obtain the effective surface tension of the sample. The instrument operates at the millisecond scale time (t < 12.5 ms), with very small liquid volumes (∼0.5 μl), and the sample is recoverable after testing. The instrument has been experimentally validated with acetone, ethanol, Fluorinert FC-40, water, and whole milk.

Opto-mechanical oscillator in a nanoliter droplet

Droplets are very simple physical systems, whereby surface tension shapes liquids into ideal opto-mechanical devices. This has recently enabled low-viscosity liquid samples to serve as miniature acoustic resonators harnessing optical generation of bulk vibrations, capillaries, or surface waves. Uniquely, a simple room-temperature pendant droplet can be activated as a hypersound-laser emitter when illuminated by a free-space, low-power visible laser thanks to stimulated Brillouin scattering of optical and acoustic whispering-gallery modes. Here, we demonstrate continuous operation of a liquid polymer opto-mechanical resonator and characterize its quality factor and long-term frequency stability. Our results point to the feasibility of all-liquid micro-mechanical oscillators working in the 50-100 MHz range. The stimulated generation of high-quality surface waves on nanoliter droplets gives momentum to new optical schemes for characterization of material viscous-elastic properties, laboratory investigation of atmospheric phenomena, and mass sensing for direct analysis of biological fluids based on ultrasound-hypersound coherent generation and detection.

Shapes and Fissility of Highly Charged and Rapidly Rotating Levitated Liquid Drops

We use diamagnetic levitation to investigate the shapes and the stability of free electrically charged and spinning liquid drops of volume ∼1 ml. In addition to binary fission and Taylor cone-jet fission modes observed at low and high charge density, respectively, we also observe an unusual mode which appears to be a hybrid of the two. Measurements of the angular momentum required to fission a charged drop show that nonrotating drops become unstable to fission at the amount of charge predicted by Lord Rayleigh. This result is in contrast to the observations of most previous experiments on fissioning charged drops, which typically exhibit fission well below Rayleigh's limit.

Oscillating Ferrofluid Droplet Microrheology of Liquid-Immersed Sessile Droplets

The damped oscillations of liquid-immersed ferrofluid sessile droplets were studied with high-speed imaging experiments and analytical modeling to develop a novel microrheology technique. Droplet oscillations were induced with an external magnetic field, thereby avoiding transients in the resulting vibrational response of the droplet. By following the droplet relaxation with a high-speed camera, the frequency and relaxation time of the damped harmonic oscillations were measured. We extend upon existing analytical theories to describe our liquid-immersed sessile droplet system, and directly quantify the droplet relaxation with the viscosity of the internal and external fluid as well as the interfacial tension between these. The easily controllable magnetic droplets make our oscillating ferrofluid droplet technique a potential candidate for high-throughput microrheology and tensiometry in the future.

Optovibrometry: tracking changes in the surface tension and viscosity of multicomponent droplets in real-time

An instrument was developed for measuring real time changes in the surface tension and viscosity of multicomponent droplets of miscible liquids and other soft materials. Droplets containing glycerol and water were supported on superamphiphobic surfaces and vibrated by applying a short mechanical impulse. Laser light was refracted through the droplets and allowed to fall on the surface of a photodiode. Time dependent variations in the intensity measured by the photodiode during vibration were used to monitor the decay of the droplet oscillations. The frequencies and spectral widths of the droplet vibrational resonances were then obtained from Fourier transforms of these time dependent intensity signals. A recently developed model of viscoelastic droplet vibration was used along with these values and measurements of the drop dimensions to extract the surface tension and viscosity of the drops as they evaporated. Collection of data was automated and values of frequency, spectral width, drop size, surface tension and viscosity were obtained with a time resolution of three seconds over a period of thirty minutes. The values of surface tension and viscosity obtained were shown to be in good agreement with literature values obtained from bulk glycerol/water solutions; thus validating the technique for wider application to other multicomponent liquids and soft matter systems.

Rheological Properties of Viscoelastic Drops on Superamphiphobic Substrates

The rheological properties of microliter sized drops of polymer solutions were investigated using measurements of their mechanical vibrational response. Drops were suspended on superamphiphobic substrates and vibrated by the application of a short mechanical impulse. Surface vibrations were monitored by refracting laser light through the drops and focusing the refracted light onto the surface of a photodiode. Time dependent variations in the photodiode output were Fourier transformed to obtain the frequency and spectral width of the mechanical resonances of the drops. These quantities were related to the frequency dependent shear storage and loss moduli (G' and G″, respectively) using a simple theoretical model. The resulting rheological properties were found to be in agreement with microrheology measurements of the same solutions. Drop vibration therefore provides a fast and accurate method of quantifying the rheological properties of single drops.

Mechanical vibrations of pendant liquid droplets

A simple optical deflection technique was used to monitor the vibrations of microlitre pendant droplets of deuterium oxide, formamide, and 1,1,2,2-tetrabromoethane. Droplets of different volumes of each liquid were suspended from the end of a microlitre pipette and vibrated using a small puff of nitrogen gas. A laser was passed through the droplets and the scattered light was collected using a photodiode. Vibration of the droplets resulted in the motion of the scattered beam and time-dependent intensity variations were recorded using the photodiode. These time-dependent variations were Fourier transformed and the frequencies and widths of the mechanical droplet resonances were extracted. A simple model of vibrations in pendant/sessile drops was used to relate these parameters to the surface tension, density and viscosity of the liquid droplets. The surface tension values obtained from this method were found to be in good agreement with results obtained using the standard pendant drop technique. Damping of capillary waves on pendant drops was shown to be similar to that observed for deep liquid baths and the kinematic viscosities obtained were in agreement with literature values for all three liquids studied.

Artificial tektites: an experimental technique for capturing the shapes of spinning drops

Determining the shapes of a rotating liquid droplet bound by surface tension is an archetypal problem in the study of the equilibrium shapes of a spinning and charged droplet, a problem that unites models of the stability of the atomic nucleus with the shapes of astronomical-scale, gravitationally-bound masses. The shapes of highly deformed droplets and their stability must be calculated numerically. Although the accuracy of such models has increased with the use of progressively more sophisticated computational techniques and increases in computing power, direct experimental verification is still lacking. Here we present an experimental technique for making wax models of these shapes using diamagnetic levitation. The wax models resemble splash-form tektites, glassy stones formed from molten rock ejected from asteroid impacts. Many tektites have elongated or ‘dumb-bell' shapes due to their rotation mid-flight before solidification, just as we observe here. Measurements of the dimensions of our wax ‘artificial tektites' show good agreement with equilibrium shapes calculated by our numerical model, and with previous models. These wax models provide the first direct experimental validation for numerical models of the equilibrium shapes of spinning droplets, of importance to fundamental physics and also to studies of tektite formation.

Tuneable paramagnetic susceptibility and exciton g-factor in Mn-doped PbS colloidal nanocrystals

We report on PbS colloidal nanocrystals that combine within one structure solubility in physiological solvents with near-infrared photoluminescence, and magnetic and optical properties tuneable by the controlled incorporation of magnetic impurities (Mn). We use high magnetic fields (B up to 30 T) to measure the magnetization of the nanocrystals in liquid and the strength of the sp-d exchange interaction between the exciton and the Mn-ions. With increasing Mn-content from 0.1% to 7%, the mass magnetic susceptibility increases at a rate of ∼ 10(-7) m(3) kg(-1) per Mn percentage; correspondingly, the exciton g-factor decreases from 0.47 to 0.10. The controlled modification of the paramagnetism, fluorescence and exciton g-factor of the nanocrystals is relevant to the implementation of these paramagnetic semiconductor nanocrystals in quantum technologies ranging from quantum information to magnetic resonance imaging.

Mechanical vibrations of magnetically levitated viscoelastic droplets

The mechanical vibrations of magnetically levitated droplets were investigated using a simple optical deflection technique. Droplets of water and a water-based solution of poly(acrylamide-co-acrylic acid) were levitated in the bore of a superconducting magnet and perturbed with a short puff of air. Centre of mass and surface vibrations were monitored using laser light refracted through the droplet, focussed on to the end of an optical fiber and detected using a photodiode. Time dependent variations in the voltage generated by the photodiode were Fourier transformed to obtain the frequency and spectral width of the drops' mechanical resonances. A simple theory of drop vibration was developed to extract the rheological properties of the droplets from these quantities. The resulting values of G' and G'' that were extracted were found to be in good agreement with values obtained using conventional rheology techniques.

Rayleigh wave scattering from sessile droplets

Radiation of energy by large-amplitude leaky Rayleigh waves is regarded as one of the key physical mechanisms regulating the actuation and manipulation of droplets in surface acoustic wave (SAW) microfluidic devices. The interaction between a SAW and a droplet is highly complex and is presently the subject of extensive research. This paper investigates the existence of an additional interaction mechanism based on the propagation of quasi-Stoneley waves inside sessile droplets deposited on a solid substrate. In contrast with the leaky Rayleigh wave, the energy of the Stoneley wave is confined within a thin fluid layer in contact with the substrate. The hypothesis is confirmed by three-dimensional finite element simulations and ultrasonic scattering experiments measuring the reflection of Rayleigh waves from droplets of different diameters. Moreover, real-time monitoring of the droplet evaporation process reveals a clear correlation between the droplet contact angle and the spectral information of the reflected Rayleigh signal, thus paving the way for ultrasonic measurements of surface tension.

Meristematic cell proliferation and ribosome biogenesis are decoupled in diamagnetically levitated Arabidopsis seedlings

BACKGROUND

Cell growth and cell proliferation are intimately linked in the presence of Earth's gravity, but are decoupled under the microgravity conditions present in orbiting spacecraft. New technologies to simulate microgravity conditions for long-duration experiments, with stable environmental conditions, in Earth-based laboratories are required to further our understanding of the effect of extraterrestrial conditions on the growth, development and health of living matter.

RESULTS

We studied the response of transgenic seedlings of Arabidopsis thaliana, containing either the CycB1-GUS proliferation marker or the DR5-GUS auxin-mediated growth marker, to diamagnetic levitation in the bore of a superconducting solenoid magnet. As a control, a second set of seedlings were exposed to a strong magnetic field, but not to levitation forces. A third set was exposed to a strong field and simulated hypergravity (2 g). Cell proliferation and cell growth cytological parameters were measured for each set of seedlings. Nucleolin immunodetection was used as a marker of cell growth. Collectively, the data indicate that these two fundamental cellular processes are decoupled in root meristems, as in microgravity: cell proliferation was enhanced whereas cell growth markers were depleted. These results also demonstrated delocalisation of auxin signalling in the root tip despite the fact that levitation of the seedling as a whole does not prevent the sedimentation of statoliths in the root cells.

CONCLUSIONS

In our model system, we found that diamagnetic levitation led to changes that are very similar to those caused by real- [e.g. on board the International Space Station (ISS)] or mechanically-simulated microgravity [e.g. using a Random Positioning Machine (RPM)]. These changes decoupled meristematic cell proliferation from ribosome biogenesis, and altered auxin polar transport.

Substrate constraint modifies the Rayleigh spectrum of vibrating sessile drops

In this work, we study the resonance behavior of mechanically oscillated, sessile water drops. By mechanically oscillating sessile drops vertically and within prescribed ranges of frequencies and amplitudes, a rich collection of resonance modes are observed and their dynamics subsequently investigated. We first present our method of identifying each mode uniquely, through association with spherical harmonics and according to their geometric patterns. Next, we compare our measured resonance frequencies of drops to theoretical predictions using both the classical theory of Lord Rayleigh and Lamb for free, oscillating drops, and a prediction by Bostwick and Steen that explicitly considers the effect of the solid substrate on drop dynamics. Finally, we report observations and analysis of drop mode mixing, or the simultaneous coexistence of multiple mode shapes within the resonating sessile drop driven by one sinusoidal signal of a single frequency. The dynamic response of a deformable liquid drop constrained by the substrate it is in contact with is of interest in a number of applications, such as drop atomization and ink jet printing, switchable electronically controlled capillary adhesion, optical microlens devices, as well as digital microfluidic applications where control of droplet motion is induced by means of a harmonically driven substrate.

Vibrational modes of elongated sessile liquid droplets

Vibrations of small (microliter) sessile liquid droplets were studied using a simple optical deflection technique. The droplets were made to elongate in one direction by taking advantage of the anisotropic wetting of the liquids on structured diffraction grating surfaces. They were vibrated by applying a puff of nitrogen gas. Motion of the droplets was monitored by scattering laser light from their surfaces. The scattered light was collected using a photodiode, and the resulting time-dependent intensity signals were Fourier-transformed to obtain the vibrational response of the drops. The vibrational spectra of elongated sessile drops were observed to contain two closely spaced peaks. A simple model that considers the frequency of capillary wave fluctuations on the surfaces of the drops was used to show that the vibrational frequencies of these peaks correspond to standing wave states that exist along the major and minor profile lengths of the droplets.

Spontaneous orbiting of two spheres levitated in a vibrated liquid

In the absence of gravity, particles can form a suspension in a liquid irrespective of the difference in density between the solid and the liquid. If such a suspension is subjected to vibration, there is relative motion between the particles and the fluid which can lead to self-organization and pattern formation. Here, we describe experiments carried out to investigate the behavior of two identical spheres suspended magnetically in a fluid, mimicking weightless conditions. Under vibration, the spheres mutually attract and, for sufficiently large vibration amplitudes, the spheres are observed to spontaneously orbit each other. The collapse of the experimental data onto a single curve indicates that the instability occurs at a critical value of the streaming Reynolds number. Simulations reproduce the observed behavior qualitatively and quantitatively, and are used to identify the features of the flow that are responsible for this instability.

Ponderomotive manipulation of cold subwavelength plasmas

Ponderomotive forces (PFs) induced in cold subwavelength plasmas by an externally applied electromagnetic wave are studied analytically. To this end, the plasma is modeled as a sphere with a radially varying permittivity, and the internal electric fields are calculated by solving the macroscopic Maxwell equations using an expansion in Debye potentials. It is found that the PF is directed opposite to the plasma density gradient, similarly to large-scale plasmas. In the case of a uniform density profile, a residual spherically symmetric compressive PF is found, suggesting possibilities for contactless ponderomotive manipulation of homogeneous subwavelength objects. The presence of a surface PF on discontinuous plasma boundaries is derived. This force is essential for a microscopic description of the radiation-plasma interaction consistent with momentum conservation. It is shown that the PF integrated over the plasma volume is equivalent to the radiation pressure exerted on the plasma by the incident wave. The concept of radiative acceleration of subwavelength plasmas, proposed earlier, is applied to ultracold plasmas. It is estimated that these plasmas may be accelerated to keV ion energies, resulting in a neutralized beam with a brightness comparable to that of current high-performance ion sources.

Ground-based facilities for simulation of microgravity: organism-specific recommendations for their use, and recommended terminology

Research in microgravity is indispensable to disclose the impact of gravity on biological processes and organisms. However, research in the near-Earth orbit is severely constrained by the limited number of flight opportunities. Ground-based simulators of microgravity are valuable tools for preparing spaceflight experiments, but they also facilitate stand-alone studies and thus provide additional and cost-efficient platforms for gravitational research. The various microgravity simulators that are frequently used by gravitational biologists are based on different physical principles. This comparative study gives an overview of the most frequently used microgravity simulators and demonstrates their individual capacities and limitations. The range of applicability of the various ground-based microgravity simulators for biological specimens was carefully evaluated by using organisms that have been studied extensively under the conditions of real microgravity in space. In addition, current heterogeneous terminology is discussed critically, and recommendations are given for appropriate selection of adequate simulators and consistent use of nomenclature.

Vibration spectroscopy of a sessile drop and its contact line

Resonance frequencies of small sessile liquid drops (1-20 μL) were estimated from the power spectra of their height fluctuations after subjecting them to white noise vibration. Various resonance modes could be identified with this method as a function of the mass of the drop. Studies with water drops on such supports as polystyrene (θ ≈ 80°) and a superhydrophobic surface of microfibrillar silicone rubber (θ ≈ 162°) demonstrated that the resonant frequency decreases with the contact angle, θ. This trend is in remarkable agreement with the current models of the resonant vibration of sessile drops. A novel aspect of this study is the analysis of the modes of a slipping contact line that indicated that its higher frequency modes are more severely damped than its lower ones. Another case is with the glycerol-water solutions, where the resonance frequency decreases with the concentration of glycerol purely due to the capillary effects. The interface fluctuation, on the other hand, is strongly correlated with the kinematic viscosity of the liquid. Thus, these experiments provide a means to measure the surface tension and the viscosity of very small droplets.

Microgravity simulation by diamagnetic levitation: effects of a strong gradient magnetic field on the transcriptional profile of Drosophila melanogaster

BACKGROUND

Many biological systems respond to the presence or absence of gravity. Since experiments performed in space are expensive and can only be undertaken infrequently, Earth-based simulation techniques are used to investigate the biological response to weightlessness. A high gradient magnetic field can be used to levitate a biological organism so that its net weight is zero.

RESULTS

We have used a superconducting magnet to assess the effect of diamagnetic levitation on the fruit fly D. melanogaster in levitation experiments that proceeded for up to 22 consecutive days. We have compared the results with those of similar experiments performed in another paradigm for microgravity simulation, the Random Positioning Machine (RPM). We observed a delay in the development of the fruit flies from embryo to adult. Microarray analysis indicated changes in overall gene expression of imagoes that developed from larvae under diamagnetic levitation, and also under simulated hypergravity conditions. Significant changes were observed in the expression of immune-, stress-, and temperature-response genes. For example, several heat shock proteins were affected. We also found that a strong magnetic field, of 16.5 Tesla, had a significant effect on the expression of these genes, independent of the effects associated with magnetically-induced levitation and hypergravity.

CONCLUSIONS

Diamagnetic levitation can be used to simulate an altered effective gravity environment in which gene expression is tuned differentially in diverse Drosophila melanogaster populations including those of different age and gender. Exposure to the magnetic field per se induced similar, but weaker, changes in gene expression.

Effect of magnetically simulated zero-gravity and enhanced gravity on the walk of the common fruitfly

Understanding the effects of gravity on biological organisms is vital to the success of future space missions. Previous studies in Earth orbit have shown that the common fruitfly (Drosophila melanogaster) walks more quickly and more frequently in microgravity, compared with its motion on Earth. However, flight preparation procedures and forces endured on launch made it difficult to implement on the Earth's surface a control that exposed flies to the same sequence of major physical and environmental changes. To address the uncertainties concerning these behavioural anomalies, we have studied the walking paths of D. melanogaster in a pseudo-weightless environment (0g*) in our Earth-based laboratory. We used a strong magnetic field, produced by a superconducting solenoid, to induce a diamagnetic force on the flies that balanced the force of gravity. Simultaneously, two other groups of flies were exposed to a pseudo-hypergravity environment (2g*) and a normal gravity environment (1g*) within the spatially varying field. The flies had a larger mean speed in 0g* than in 1g*, and smaller in 2g*. The mean square distance travelled by the flies grew more rapidly with time in 0g* than in 1g*, and slower in 2g*. We observed no other clear effects of the magnetic field, up to 16.5 T, on the walks of the flies. We compare the effect of diamagnetically simulated weightlessness with that of weightlessness in an orbiting spacecraft, and identify the cause of the anomalous behaviour as the altered effective gravity.

Addendum to "Vibrations of a diamagnetically levitated water droplet"

We derive an analytical expression for the frequency of the shape oscillations of a diamagnetically levitated water droplet, in which the equilibrium shape is not spherical. We give the eigenfrequencies of all modes to first order in the oscillation amplitude and potential energy of the magnetogravitational trap confining the droplet. We compare the result with experimental measurements of the eigenfrequencies.

Contact angle dependence of the resonant frequency of sessile water droplets

The resonant vibrations of small (microliter) sessile water droplets supported on solid substrates were monitored using a simple optical detection technique. A small puff of air was used to apply an impulse to the droplets and their time dependent oscillations were monitored by passing a laser beam through the droplet and measuring the variations of the intensity of the scattered light using a simple photodiode arrangement. The resulting time dependent intensity changes were then Fourier transformed to obtain information about the vibrational frequencies of the droplets. The resonant frequencies of droplets with masses in the range 0.005-0.03 g were obtained on surfaces with water contact angles ranging from 12 ± 4° to 160 ± 5°. The contact angle dependence of the resonant frequency of the droplets was found to be in good agreement with a simple theory which considers standing wave states along the meridian profile length of the droplets.

Diamagnetic levitation enhances growth of liquid bacterial cultures by increasing oxygen availability

Diamagnetic levitation is a technique that uses a strong, spatially varying magnetic field to reproduce aspects of weightlessness, on the Earth. We used a superconducting magnet to levitate growing bacterial cultures for up to 18 h, to determine the effect of diamagnetic levitation on all phases of the bacterial growth cycle. We find that diamagnetic levitation increases the rate of population growth in a liquid culture and reduces the sedimentation rate of the cells. Further experiments and microarray gene analysis show that the increase in growth rate is owing to enhanced oxygen availability. We also demonstrate that the magnetic field that levitates the cells also induces convective stirring in the liquid. We present a simple theoretical model, showing how the paramagnetic force on dissolved oxygen can cause convection during the aerobic phases of bacterial growth. We propose that this convection enhances oxygen availability by transporting oxygen around the liquid culture. Since this process results from the strong magnetic field, it is not present in other weightless environments, e.g. in Earth orbit. Hence, these results are of significance and timely to researchers considering the use of diamagnetic levitation to explore effects of weightlessness on living organisms and on physical phenomena.