Parametrically excited sectorial oscillation of liquid drops floating in ultrasound

Coalescence and mixing dynamics of droplets in acoustic levitation by selective colour imaging and measurement

Acoustic levitation is well-suited to 'lab-on-a-drop' contactless chemical analysis of droplets. Rapid mixing is of fundamental importance in lab-on-a-drop platforms and many other applications involving droplet manipulation. Small droplets, however, have low Reynolds numbers; thus, mixing via turbulence is not possible. Inducing surface oscillation is effective in this regard, however, the relationship between internal flow and mixing dynamics of droplets remains unclear. In this study, we conducted a set of simultaneous optical measurements to assess both the flow field and the distribution of fluid components within acoustically levitated droplets. To achieve this, we developed a technique to selectively separate fluorescent particles within each fluid, permitting the measurement of the concentration field based on the data from the discrete particle distribution. This approach revealed a relationship between the mixing process and the internal flow caused by surface oscillation. Thus, the internal flow induced by surface oscillation could enhance droplet mixing. Our findings will be conducive to the application and further development of lab-on-a-drop devices.

Sloshing Resonance of an Acoustically Levitated Air-in-Liquid Compound Drop

An acoustically levitated air-in-liquid compound drop is set into an out-of-phase azimuthal sloshing resonance by a modulated frequency with modes n = 4-9. Waveforms of the inner and outer liquid-air interfaces conform to the classical Saffren model. Resonance peaks and their harmonics in the frequency spectrum are found to be a function of drop dimension and resonance modes. Drops with multiple small air bubbles do not resonate in sync because of asymmetry. This work has significant implications in the dynamics of core-shell compound drops.

Natural oscillation frequencies of a Rayleigh sphere levitated in standing acoustic waves

Acoustic levitation is an important method of container-free processing, which counteracts gravity through exerting the acoustic radiation force on levitated objects. The Gorkov potential function is used to simplify the calculation of the acoustic radiation force acting on a Rayleigh sphere whose radius is much smaller than the wave length. For the case of a plane standing wave levitation system, a systematic analysis of the sphere dynamics is provided in the axial direction, assuming a small perturbation around the stable equilibrium locations. A generalized extension to an arbitrary standing wave field is provided, which gives formal expressions of the axial and transverse natural oscillation frequencies for the sphere. Particular emphasis is put on the natural oscillation frequencies with and without taking gravity into consideration. The computational results for Gauss and Bessel standing waves are provided as two special cases, which show that the transverse natural oscillation frequency will be overestimated when neglecting gravity, especially for a sphere with a relatively large density. Corresponding experiments are conducted to verify the dependence of the transverse natural oscillation frequency on the sphere density. The results obtained in this work are expected to provide a theoretical guide for enhancing the levitation stability and inversing the physical parameters from the sphere dynamics.

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.

Periodicity in ultrasonic atomization involving beads-fountain oscillations and mist generation: Effects of driving frequency

Ultrasonic atomization induced by high driving frequency, generally on the order of 1 MHz or higher, could involve a liquid fountain in the form of a corrugated jet, or a chain of "beads" of submillimeter diameter in contact. This study concerns dynamics/instability of such beads fountain, observed under lower input power density (≤ 6 W/cm²) of the "flat" ultrasound transducer with a "regulating" nozzle equipped, exhibiting time-varying characteristics with certain periodicity. High-speed, high-resolution images are processed for quantitative elucidation: frequency analysis (fast Fourier transform) and time-frequency analysis (discrete wavelet transform) are employed, respectively, to evaluate dominant frequencies of beads-surface oscillations and to reveal factor(s) triggering mist emergence. The resulting time variation in the measured (or apparent) fountain structure, associated with the recurring-beads size scalable to the ultrasound wavelength, subsumes periodic nature predictable from simple physical modeling as well as principle. It is further found that such dynamics in (time-series data for) the fountain structure at given height(s) along a series of beads would signal "bursting" of liquid droplets emanating out of a highly deformed bead often followed by a cloud of tiny droplets, or mist. In particular, the bursting appears to be not a completely random phenomenon but should concur with the fountain periodicity with a limited extent of probability.

Kilohertz-Frequency Rotation of Acoustically Levitated Particles

The achievable rotational frequency of acoustically levitated particles is limited by the suspension stability and the achievable driving torque. In this work, a spherical ring arrangement of piezoelectric transducers and an improved excitation concept are presented to increase the rotational speed of an acoustically levitated particle by more than a factor of 10 compared to previously published results. A maximum rotational frequency of 3.6 kHz using asymmetric expanded polystyrene (EPS) particles is demonstrated. At such rotational speeds, high-frequency resonances of the transducers cause disturbances of the acoustic field which present a previously unexplored limit to the achievable manipulation rate of the particle. This limit is investigated in this work by means of calculations based on an analytical model and high precision measurements of the transducer characteristics beyond the conventional frequency range.

Oscillation-Induced Mixing Advances the Functionality of Liquid Marble Microreactors

Droplet-based microreactors often uncover fascinating phenomena and exhibit diverse functionality, which make them applicable in various fields. Liquid marbles (LMs) are non-wetting droplets coated with particles, and these features highlight their potential as microreactors. However, sophisticated experimental designs are typically hindered because it is difficult to obtain sufficient substance mixing in these miniature, damage-prone, self-supporting liquid containers. Here, we demonstrate that subjecting LMs to vertical oscillations by audio signals represents a controllable approach that allows sufficient mixing with variable dynamic modes. The characteristics and key issues in LM oscillation are systematically explored. The effects of oscillation on application potential are examined. Under oscillation conditions, homogeneous mixing can be achieved within a few seconds in LMs consisting of either water or viscous liquids. Importantly, the structures of materials synthesized in LMs can be regulated by modulating the oscillation modes. The variable modes, flexible adjustability, high efficiency, and wide applicability of this oscillation method make it a verified manipulation strategy for advancing the functionality of LM microreactors.

An alternate approach to simulate the dynamics of perturbed liquid drops

Liquid drops when subjected to external periodic perturbations can execute polygonal oscillations. In this work, a simple model is presented that demonstrates these oscillations and their characteristic properties. The model consists of a spring-mass network such that masses are analogous to liquid molecules and the springs correspond to intermolecular links. Neo-Hookean springs are considered to represent these intermolecular links. The restoring force of a neo-Hookean spring depends nonlinearly on its length such that the force of a compressed spring is much higher than the force of the spring elongated by the same amount. This is analogous to the incompressibility of liquids, making these springs suitable to simulate the polygonal oscillations. It is shown that this spring-mass network can imitate most of the characteristic features of experimentally reported polygonal oscillations. Additionally, it is shown that the network can execute certain dynamics, which so far have not been observed in a perturbed liquid drop. The characteristics of dynamics that are observed in the perturbed network are polygonal oscillations, rotation of network, numerical relations (rational and irrational) between the frequencies of polygonal oscillations and the forcing signal, and that the shape of the polygons depends on the parameters of perturbation.

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.

Contactless Picking of Objects Using an Acoustic Gripper

Acoustic levitation forces can be used to manipulate small objects and liquids without mechanical contact or contamination. This work presents analytical models based on which concepts for the controlled insertion of objects into the acoustic field are developed. This is essential for the use of acoustic levitators as contactless robotic grippers. Three prototypes of such grippers are implemented and used to experimentally verify the lifting of objects into an acoustic pressure field. Lifting of high-density objects (ρ > 7 g/cm3) from acoustically transparent surfaces is demonstrated using a double-sided acoustic gripper that generates standing acoustic waves with dynamically adjustable acoustic power. A combination of multiple acoustic traps is used to lift lower density objects (ρ≤0.25g/cm3) from acoustically reflective surfaces using a single-sided arrangement. Furthermore, a method that uses standing acoustic waves and thin reflectors to lift medium-density objects (ρ≤1g/cm3) from acoustically reflective surfaces is presented. The provided results open up new possibilities for using acoustic levitation in robotic grippers, which has the potential to be applied in a variety of industrial use cases.

Acoustofluidic centrifuge for nanoparticle enrichment and separation

Liquid droplets have been studied for decades and have recently experienced renewed attention as a simplified model for numerous fascinating physical phenomena occurring on size scales from the cell nucleus to stellar black holes. Here, we present an acoustofluidic centrifugation technique that leverages an entanglement of acoustic wave actuation and the spin of a fluidic droplet to enable nanoparticle enrichment and separation. By combining acoustic streaming and droplet spinning, rapid (<1 min) nanoparticle concentration and size-based separation are achieved with a resolution sufficient to identify and isolate exosome subpopulations. The underlying physical mechanisms have been characterized both numerically and experimentally, and the ability to process biological samples (including DNA segments and exosome subpopulations) has been successfully demonstrated. Together, this acoustofluidic centrifuge overcomes existing limitations in the manipulation of nanoscale (<100 nm) bioparticles and can be valuable for various applications in the fields of biology, chemistry, engineering, material science, and medicine.

Controlled Chemistry via Contactless Manipulation and Merging of Droplets in an Acoustic Levitator

A unique, versatile, and material-independent approach to manipulate contactlessly and merge two chemically distinct droplets suspended in an acoustic levitator is reported. Large-amplitude axial oscillations are induced in the top droplet by low-frequency amplitude modulation of the ultrasonic carrier wave, which causes the top sample to merge with the sample in the pressure minimum below. The levitator is enclosed within a pressure-compatible process chamber to enable control of the environmental conditions. The merging technique permits precise control of the substances affecting the chemical reactions, the sample temperature, the volumes of the liquid reactants down to the picoliter range, and the mixing locations in space and time. The performance of this approach is demonstrated by merging droplets of water (H₂O) and ethanol (C₂H₅OH), conducting an acid-base reaction between aqueous droplets of sodium hydroxycarbonate (NaHCO₃) and acetic acid (CH₃COOH), the hypergolic explosion produced via merging a droplet of an ionic liquid with nitric acid (HNO₃), and the coalescence of a solid particle (CuSO₄·5H₂O) and a water droplet followed by dehydration using a carbon dioxide laser. The physical and chemical changes produced by the merging are traced in real time via complementary Raman, Fourier-transform infrared, and ultraviolet-visible spectroscopies. The concept of the contactless manipulation of liquid droplets and solid particles may fundamentally change how scientists control and study chemical reactions relevant to, for example, combustion systems, material sciences, medicinal chemistry, planetary sciences, and biochemistry.

Experiments and modeling of nonlinear frequency response of oscillations of a sessile droplet subjected to horizontal vibrations

In this paper, we experimentally studied the response frequency of oscillations of a sessile water droplet, subjected to horizontal vibrations at varying excitation frequency (5-250 Hz and 40 kHz) and amplitude (0.015 mm to 0.5 mm for low frequencies and 600nm for ultrasonic frequency), as well as static contact angle of the glass substrate ([Formula: see text], [Formula: see text] , [Formula: see text], [Formula: see text]). The droplets were pinned during the experiments and non-axisymmetric oscillation modes were excited due to the horizontal vibrations. For the first time, we observed that at a sufficiently high vibration amplitude, when the excitation frequency is lower than the smallest natural frequency of the sessile droplet, the droplet oscillates at a response frequency multiple of the excitation frequency. At higher excitation frequencies up to several hundreds of Hz, the droplet oscillates nearly at the excitation frequency. At ultrasonic excitation frequency, however, the droplet cannot follow the excitations, since there is a physical limitation for forming infinite modes (infinite wavenumber) on the surface of a small droplet. We have modeled these behaviors with a nonlinear mass-spring-damper system by combining two established models: the Duffing and Van der Pol equations, in order to simulate both nonlinear damping and stiffness.

Contactless Fluid Manipulation in Air: Droplet Coalescence and Active Mixing by Acoustic Levitation

Acoustic manipulation by an ultrasonic phased array provides an entirely new approach to processes such as coalescence, mixing, separation, and evaporation occurring in the generation of new materials, physical property measurement, the biomedical industry, etc. However, to date, ultrasonic phased arrays have not been fully investigated for applications in fluid manipulation. This paper provides contactless coalescence and mixing techniques for droplets in air by controlling the acoustic potential by using an ultrasonic phased array. We focused on mode oscillation to propose an efficient mixing technique for liquid without contact. A comparison of mixing performance between cases with mode oscillation and without mode oscillation showed that the flow induced by mode oscillation promotes droplet mixing. Our paper demonstrates the feasibility of contactless coalescence and mixing as a first step in fluid manipulation with a phased array.

Instabilities triggered in different conducting fluid geometries due to slowly time-dependent magnetic fields

The main objective of this work is the study and analysis of non-linearities forced through oscillating magnetic fields in a conducting fluid where the instabilities are triggered due to magnetohydrodynamic forces. Different geometries have been studied and different surface patterns that break the symmetries have been observed. First, an InGaSn drop of fluid where the system breaks the azimuthal and radial symmetries depending on the volume is observed. Second, we extend the study to an InGaSn annular configuration where the presence of patterns opens the door to discuss the possibility to extend these results to other configurations as biological systems, where the conducting fluid is an electrolyte. This configuration has an added interest, as it has been proposed that the vertigoes triggered on patients in an MRI test could be generated by the interaction of the magnetic field with the electrolyte present in the inner ear.

Instabilities of conducting fluid layers in weak time-dependent magnetic fields

We present the experimental analysis of the instabilities generated on a large drop of liquid metal by a time-dependent magnetic field. The study is done exploring the range of tiny values of the control parameter (the ratio between the Lorentz forces and inertia) avoiding nonlinear effects. Two different instabilities break the symmetries generating spatial patterns that appear without a threshold for some specific frequencies (up to the experimental precision) and have been observed for parameter values two orders of magnitude lower than in previously published experiments [J. Fluid Mech. 239, 383 (1992)JFLSA70022-112010.1017/S0022112092004452]. One of the instabilities corresponds to a boundary condition oscillation that generates surface waves and breaks the azimuthal symmetry. The other corresponds to a parametric forcing through a modulation of the Lorentz force. The competition between these two mechanisms produces time-dependent patterns near codimension-2 points.

Dynamics of levitated objects in acoustic vortex fields

Acoustic levitation in gaseous media provides a tool to process solid and liquid materials without the presence of surfaces such as container walls and hence has been used widely in chemical analysis, high-temperature processing, drop dynamics and bioreactors. To date high-density objects can only be acoustically levitated in simple standing-wave fields. Here we demonstrate the ability of a small number of peripherally placed sources to generate acoustic vortex fields and stably levitate a wide range of liquid and solid objects. The forces exerted by these acoustic vortex fields on a levitated water droplet are observed to cause a controllable deformation of the droplet and/or oscillation along the vortex axis. Orbital angular momentum transfer is also shown to rotate a levitated object rapidly and the rate of rotation can be controlled by the source amplitude. We expect this research can increase the diversity of acoustic levitation and expand the application of acoustic vortices.

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.

Acoustic levitation of liquid drops: Dynamics, manipulation and phase transitions

The technique of acoustic levitation normally produces a standing wave and the potential well of the sound field can be used to trap small objects. Since no solid surface is involved it has been widely applied for the study of fluid physics, nucleation, bio/chemical processes, and various forms of soft matter. In this article, we survey the works on drop dynamics in acoustic levitation, focus on how the dynamic behavior is related to the rheological properties and discuss the possibility to develop a novel rheometer based on this technique. We review the methods and applications of acoustic levitation for the manipulation of both liquid and solid samples and emphasize the important progress made in the study of phase transitions and bio-chemical analysis. We also highlight the possible open areas for future research.

Footprint geometry and sessile drop resonance

In this work, we examine experimentally the resonance of a sessile drop with a square footprint (square drop) on a flat plate. Two families of modal behaviors are reported. One family is identified with the modes of sessile drops with circular footprints (circular drop), denoted as "spherical modes." The other family is associated with Faraday waves on a square liquid bath (square Faraday waves), denoted as "grid modes." The two families are distinguished based on their dispersion behaviors. By comparing the occurrence of the modes, we recognize spherical modes as the characteristic of sessile drops, and grid modes as the constrained response. Within a broader context, we further discuss the resonance modes of circular sessile drops and free spherical drops, and we recognize various modal behaviors as surface waves under different extents of constraint. From these, we conclude that sessile drops resonate according to how wave-number selection by footprint geometry and capillarity compete. For square drops, a dominant effect of footprint constraint leads to grid modes; otherwise, the drops exhibit spherical modes, the characteristic of sessile drops on flat plates.

Experimental evidence of nonlinear mode coupling between spherical and nonspherical oscillations of microbubbles

We report observations of strong nonlinear interactions between the spherical, translational, and shape oscillations of micrometer-size bubbles. This is achieved through high-speed recordings of single bubble dynamics driven by amplitude-modulated ultrasound. The features of mode coupling are highlighted through (i) the exponential growth of the parametrically excited mode (n=3) triggered by the spherical oscillations followed by a saturation due to energy transfer towards the translation and even modes, (ii) the excitation of modes well below their parametric pressure threshold, and (iii) clear modification of the breathing mode R(t). These results are compared to recent theories accounting for nonlinear mode coupling, providing predictions in agreement with the observed bubble dynamics.

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.

Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding

We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.

Model of heap formation in vibrated gravitational suspensions

In vertically vibrated dense suspensions, several localized structures have been discovered, such as heaps, stable holes, expanding holes, and replicating holes. Because an inclined free fluid surface is difficult to maintain because of gravitational pressure, the mechanism of those structures is not understood intuitively. In this paper, as a candidate for the driving mechanism, we focus on the boundary condition on a solid wall: the slip-nonslip switching boundary condition in synchronization with vertical vibration. By applying the lubrication approximation, we derived the time evolution equation of the fluid thickness from the Oldroyd-B fluid model. In our model we show that the initially flat fluid layer becomes unstable in a subcritical manner, and heaps and convectional flow appear. The obtained results are consistent with those observed experimentally. We also find that heaps climb a slope when the bottom is slightly inclined. We show that viscoelasticity enhances heap formation and climbing of a heap on the slope.

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.

Can vibrations control drop motion?

We discuss a mechanism for controlled motion of drops with applications for microfluidics and microgravity. The mechanism is the following: a solid plate supporting a liquid droplet is simultaneously subject to lateral and vertical harmonic oscillations. In this way the symmetry of the back-and-forth droplet movement along the substrate under inertial effects is broken and thus will induce a net driven motion of the drop. We study the dependency of the traveled distance on the oscillation parameters (forcing amplitude, frequency, and phase shift between the two perpendicular oscillations) via phase field simulations. The internal flow structure inside the droplet is also investigated. We make predictions on resonance frequencies for drops on a substrate with a varying wettability.

Droplet manipulation in a microfluidic chamber with acoustic radiation pressure and acoustic streaming

The present paper reports a novel manipulation method for droplets using acoustic radiation pressure and acoustic streaming. In an acoustic field, droplets deform, oscillate and move in a wide range of applied frequencies. The behavior of a droplet depends on the droplet size, acoustic field and interfacial tension between the two phases. The acoustic field is controlled by the voltage and frequency of the piezoelectric actuator. The results demonstrate a method for low-frequency acoustic actuation of droplets in a microfluidic environment.

Electrowetting-driven oscillating drops sandwiched between two substrates

Drops sandwiched between two substrates are often found in lab-on-chip devices based on digital microfluidics. We excite azimuthal oscillations of such drops by periodically modulating the contact line via ac electrowetting. By tuning the frequency of the applied voltage, several shape modes can be selected one by one. The frequency of the oscillations is half the frequency of the contact angle modulation by electrowetting, indicating a parametric excitation. The drop response to sinusoidal driving deviates substantially from sinusoidal behavior in a "stop and go" fashion. Although our simple theoretical model describes the observed behavior qualitatively, the resonances appear at lower frequencies than expected. Moreover, the oscillations produce a nonperiodic fluid transport within the drop with a typical velocity of 1 mm/s. In digital microfluidic devices, where the typical drop size is less than 1 mm, this flow can result in very fast mixing on the spot.

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.

Oscillating and star-shaped drops levitated by an airflow

We investigate the spontaneous oscillations of drops levitated above an air cushion, eventually inducing a breaking of axisymmetry and the appearance of "star drops". This is strongly reminiscent of the Leidenfrost stars that are observed for drops floating above a hot substrate. The key advantage of this work is that we inject the airflow at a constant rate below the drop, thus eliminating thermal effects and allowing for a better control of the flow rate. We perform experiments with drops of different viscosities and observe stable states, oscillations, and chimney instabilities. We find that for a given drop size the instability appears above a critical flow rate, where the latter is largest for small drops. All these observations are reproduced by numerical simulations, where we treat the drop using potential flow and the gas as a viscous lubrication layer. Qualitatively, the onset of instability agrees with the experimental results, although the typical flow rates are too large by a factor 10. Our results demonstrate that thermal effects are not important for the formation of star drops and strongly suggest a purely hydrodynamic mechanism for the formation of Leidenfrost stars.

Stationary shapes of confined rotating magnetic liquid droplets

We study the family of steady shapes which arise when a magnetic liquid droplet is confined in a rotating Hele-Shaw cell and subjected to an azimuthal magnetic field. Two different scenarios are considered: first, the magnetic fluid is assumed to be a Newtonian ferrofluid, and then it is taken as a viscoelastic magnetorheological fluid. The influence of the distinct material properties of the fluids on the ultimate morphology of the emerging stationary patterns is investigated by using a vortex-sheet formalism. Some of these exact steady structures are similar to the advanced time patterns obtained by existing time-evolving numerical simulations of the problem. A weakly nonlinear approach is employed to examine this fact and to gain analytical insight about relevant aspects related to the stability of such exact stationary solutions.